@article{Tarkhanov2016, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantization and boundary value problems}, series = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology}, volume = {13}, journal = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-8878}, doi = {10.1142/S0219887816500079}, pages = {176 -- 195}, year = {2016}, abstract = {We describe a natural construction of deformation quantization 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formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.}, language = {en} } @unpublished{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {On the root functions of general elliptic boundary value problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29822}, year = {2005}, abstract = {We consider a boundary value problem for an elliptic differential operator of order 2m in a domain D ⊂ n. The boundary of D is smooth outside a finite number of conical points, and the Lopatinskii condition is fulfilled on the smooth part of δD. The corresponding spaces are weighted Sobolev spaces H(up s,Υ)(D), and this allows one to define ellipticity of weight Υ for the problem. The resolvent of the problem is assumed to possess rays of minimal growth. The main result says that if there are rays of minimal growth with angles between neighbouring rays not exceeding π(Υ + 2m)/n, then the root functions of the problem are complete in L²(D). In the case of second order elliptic equations the results remain true for all domains with Lipschitz boundary.}, language = {en} } @unpublished{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Unitary solutions of partial differential equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29852}, year = {2005}, abstract = {We give an explicit construction of a fundamental solution for an arbitrary non-degenerate partial differential equation with smooth coefficients.}, language = {en} } @unpublished{Tarkhanov2003, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A fixed point formula in one complex variable}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26495}, year = {2003}, abstract = {We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.}, language = {en} } @book{TarkhanovVasilevski2005, author = {Tarkhanov, Nikolai Nikolaevich and Vasilevski, Nikolai}, title = {Microlocal analysis of the Bochner-Martinelli Integral}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {9 S.}, year = {2005}, language = {en} } @unpublished{TarkhanovVasilevski2005, author = {Tarkhanov, Nikolai Nikolaevich and Vasilevski, Nikolai}, title = {Microlocal analysis of the Bochner-Martinelli integral}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30012}, year = {2005}, abstract = {In order to characterise the C*-algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in Cn, we compute its principal symbol. We show then that the Szeg{\"o} projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral.}, language = {en} } @unpublished{TarkhanovWallenta2012, author = {Tarkhanov, Nikolai Nikolaevich and Wallenta, Daniel}, title = {The Lefschetz number of sequences of trace class curvature}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56969}, year = {2012}, abstract = {For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.}, language = {en} } @unpublished{Tepoyan2000, author = {Tepoyan, Liparit}, title = {Degenerated operator equations of higher order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25888}, year = {2000}, abstract = {Content: 1 Introduction 2 The one-dimensional case 2.1 The space Wm sub (α) 2.2 Self-adjoint Equation 2.3 Non-selfadjoint Equation 3 Operator Equation}, language = {en} } @unpublished{Tepoyan2008, author = {Tepoyan, Liparit}, title = {The mixed problem for a degenerate operator equation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30334}, year = {2008}, abstract = {We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.}, language = {en} } @article{Thiem1996, author = {Thiem, Wolfgang}, title = {Didaktik der Erziehungswissenschaft (P{\"a}dagogik) - ein weites Feld?}, year = {1996}, language = {de} } @article{TillmannKroemkerHornetal.2018, author = {Tillmann, Alexander and Kr{\"o}mker, Detlef and Horn, Florian and Gattinger, Thorsten}, title = {Analysing \& Predicting Students Performance in an Introductory Computer Science Course}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416307}, pages = {29 -- 45}, year = {2018}, abstract = {Students of computer science studies enter university education with very different competencies, experience and knowledge. 145 datasets collected of freshmen computer science students by learning management systems in relation to exam outcomes and learning dispositions data (e. g. student dispositions, previous experiences and attitudes measured through self-reported surveys) has been exploited to identify indicators as predictors of academic success and hence make effective interventions to deal with an extremely heterogeneous group of students.}, language = {en} } @phdthesis{Tinpun2019, author = {Tinpun, Kittisak}, title = {Relative rank of infinite full transformation semigroups with restricted range}, school = {Universit{\"a}t Potsdam}, year = {2019}, language = {en} } @article{TinpunKoppitz2016, author = {Tinpun, Kittisak and Koppitz, J{\"o}rg}, title = {Generating sets of infinite full transformation semigroups with restricted range}, series = {Acta scientiarum mathematicarum}, volume = {82}, journal = {Acta scientiarum mathematicarum}, publisher = {Institutum Bolyaianum Universitatis Szegediensis}, address = {Szeged}, issn = {0001-6969}, doi = {10.14232/actasm-015-502-4}, pages = {55 -- 63}, year = {2016}, abstract = {In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks.}, language = {en} } @phdthesis{Trappmann2007, author = {Trappmann, Henryk}, title = {Arborescent numbers : higher arithmetic operations and division trees}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15247}, school = {Universit{\"a}t Potsdam}, year = {2007}, abstract = {The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the hassle-free definition of arbitrary high arithmetic operations (hyper ... hyperpowers). To construct the division trees the algebraic structure "coppice" is introduced which is a group with an addition over which the multiplication is right-distributive. Q+ is the initial associative coppice. The present work accomplishes one step in the program "arborescent numbers". That is the construction of the arborescent equivalent(s) of the positive fractional numbers. These equivalents are the "division binary trees" and the "fractional trees". A representation with decidable word problem for each of them is given. The set of functions f:R1->R1 generated from identity by taking powers is isomorphic to P and can be embedded into a coppice by taking inverses.}, language = {en} } @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} } @misc{Tschisgale2020, type = {Master Thesis}, author = {Tschisgale, Paul}, title = {Introduction to the Glauber dynamics for the Curie-Weiss Potts model}, doi = {10.25932/publishup-48676}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-486769}, school = {Universit{\"a}t Potsdam}, pages = {104}, year = {2020}, abstract = {This thesis aims at presenting in an organized fashion the required basics to understand the Glauber dynamics as a way of simulating configurations according to the Gibbs distribution of the Curie-Weiss Potts model. Therefore, essential aspects of discrete-time Markov chains on a finite state space are examined, especially their convergence behavior and related mixing times. Furthermore, special emphasis is placed on a consistent and comprehensive presentation of the Curie-Weiss Potts model and its analysis. Finally, the Glauber dynamics is studied in general and applied afterwards in an exemplary way to the Curie-Weiss model as well as the Curie-Weiss Potts model. The associated considerations are supplemented with two computer simulations aiming to show the cutoff phenomenon and the temperature dependence of the convergence behavior.}, language = {en} } @article{TyFangGonzalezetal.2019, author = {Ty, Alexander J. A. and Fang, Zheng and Gonzalez, Rivver A. and Rozdeba, Paul J. and Abarbanel, Henry D.}, title = {Machine learning of time series using time-delay embedding and precision annealing}, series = {Neural Computation}, volume = {31}, journal = {Neural Computation}, number = {10}, publisher = {MIT Press}, address = {Cambridge}, issn = {0899-7667}, doi = {10.1162/neco_a_01224}, pages = {2004 -- 2024}, year = {2019}, abstract = {Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (-log[P]). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series s(tn);tn=t0+n Delta t and, using methods of nonlinear time series analysis, show how to produce a DE>1-dimensional time-delay embedding space in which the time series has no false neighbors as does the observed s(tn) time series. In that DE-dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on DE-dimensional input and producing DE-dimensional outputs.}, language = {en} } @inproceedings{VallerianiRoellyKulik2017, author = {Valleriani, Angelo and Roelly, Sylvie and Kulik, Alexei Michajlovič}, title = {Stochastic processes with applications in the natural sciences}, series = {Lectures in pure and applied mathematics}, booktitle = {Lectures in pure and applied mathematics}, number = {4}, editor = {Roelly, Sylvie and H{\"o}gele, Michael and Rafler, Mathias}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-414-2}, issn = {2199-4951}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-401802}, pages = {ix, 124}, year = {2017}, abstract = {The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogot{\´a}, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics. The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume. Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam. Sylvie Rœlly, Docteur en Math{\´e}matiques, is the head of the chair of Probability at the University of Potsdam. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.}, 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} } @misc{vanLeeuwenKunschNergeretal.2019, author = {van Leeuwen, Peter Jan and Kunsch, Hans R. and Nerger, Lars and Potthast, Roland and Reich, Sebastian}, title = {Particle filters for high-dimensional geoscience applications: A review}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {145}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {723}, publisher = {Wiley}, address = {Hoboken}, issn = {0035-9009}, doi = {10.1002/qj.3551}, pages = {2335 -- 2365}, year = {2019}, abstract = {Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high-dimensional geoscience systems has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state-of-the-art discussion of present efforts of developing particle filters for high-dimensional nonlinear geoscience state-estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo-code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction, suggesting that they will become mainstream soon.}, language = {en} } @article{VasilievTarchanov2017, author = {Vasiliev, Sergey B. and Tarchanov, Nikolaj Nikolaevič}, title = {Construction of series of perfect lattices by layer superposition}, series = {Journal of Siberian Federal University : Mathematics \& physics}, volume = {10}, journal = {Journal of Siberian Federal University : Mathematics \& physics}, number = {3}, publisher = {Sibirskij Federalʹnyj Universitet}, address = {Krasnojarsk}, issn = {1997-1397}, doi = {10.17516/1997-1397-2017-10-3-353-361}, pages = {353 -- 361}, year = {2017}, abstract = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.}, language = {en} } @unpublished{VasilievTarkhanov2016, author = {Vasiliev, Serguei and Tarkhanov, Nikolai Nikolaevich}, title = {Construction of series of perfect lattices by layer superposition}, volume = {5}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100591}, pages = {11}, year = {2016}, abstract = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.}, language = {en} } @article{VidalGarciaBandaraKeogh2018, author = {Vidal-Garcia, Marta and Bandara, Lashi and Keogh, J. Scott}, title = {ShapeRotator}, series = {Ecology and evolution}, volume = {8}, journal = {Ecology and evolution}, number = {9}, publisher = {Wiley}, address = {Hoboken}, issn = {2045-7758}, doi = {10.1002/ece3.4018}, pages = {4669 -- 4675}, year = {2018}, abstract = {The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.}, language = {en} } @article{Vogel1997, author = {Vogel, Hans-J{\"u}rgen}, title = {Relations as morphisms of a certain monoidal category}, year = {1997}, language = {en} } @article{Vogel1998, author = {Vogel, Hans-J{\"u}rgen}, title = {On functors between certain monoidal categories}, year = {1998}, language = {en} } @article{Vogel1995, author = {Vogel, Hans-J{\"u}rgen}, title = {On quasivarieties generated by - algebras}, year = {1995}, language = {en} } @book{Vogel1998, author = {Vogel, Hans-J{\"u}rgen}, title = {On morphisms between partial algebras}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 13}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {27 Bl.}, year = {1998}, language = {en} } @article{Vogel1999, author = {Vogel, Hans-J{\"u}rgen}, title = {On morphisms between partial algebras}, year = {1999}, language = {en} } @article{Vogel1999, author = {Vogel, Hans-J{\"u}rgen}, title = {Halfdiagonal-halfterminal-symmetric monoidal categories with inversions}, year = {1999}, language = {en} } @article{Vogel1999, author = {Vogel, Hans-J{\"u}rgen}, title = {On properties of dht -symmetric categories}, year = {1999}, language = {en} } @article{VogelMarkiPoeschel1996, author = {Vogel, Hans-J{\"u}rgen and Marki, Laszlo and P{\"o}schel, Reinhard}, title = {Contributions to general algebra and categories}, year = {1996}, language = {en} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Schuette, Christof and Huisinga, Wilhelm}, title = {HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs}, series = {PLoS one}, volume = {6}, journal = {PLoS one}, number = {3}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0018204}, pages = {12}, year = {2011}, abstract = {The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at \& 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial.}, language = {en} } @unpublished{Voss2010, author = {Voss, Carola Regine}, title = {Harness-Prozesse}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49651}, year = {2010}, abstract = {Harness-Prozesse finden in der Forschung immer mehr Anwendung. Vor allem gewinnen Harness-Prozesse in stetiger Zeit an Bedeutung. Grundlegende Literatur zu diesem Thema ist allerdings wenig vorhanden. In der vorliegenden Arbeit wird die vorhandene Grundlagenliteratur zu Harness-Prozessen in diskreter und stetiger Zeit aufgearbeitet und Beweise ausgef{\"u}hrt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen {\"u}ber Z beziehungsweise R+ nachzuweisen.}, language = {de} } @phdthesis{Vu2014, author = {Vu, Dinh Phuong}, title = {Using video study to investigate eighth-grade mathematics classrooms in Vietnam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72464}, school = {Universit{\"a}t Potsdam}, pages = {273}, year = {2014}, abstract = {The International Project for the Evaluation of Educational Achievement (IEA) was formed in the 1950s (Postlethwaite, 1967). Since that time, the IEA has conducted many studies in the area of mathematics, such as the First International Mathematics Study (FIMS) in 1964, the Second International Mathematics Study (SIMS) in 1980-1982, and a series of studies beginning with the Third International Mathematics and Science Study (TIMSS) which has been conducted every 4 years since 1995. According to Stigler et al. (1999), in the FIMS and the SIMS, U.S. students achieved low scores in comparison with students in other countries (p. 1). The TIMSS 1995 "Videotape Classroom Study" was therefore a complement to the earlier studies conducted to learn "more about the instructional and cultural processes that are associated with achievement" (Stigler et al., 1999, p. 1). The TIMSS Videotape Classroom Study is known today as the TIMSS Video Study. From the findings of the TIMSS 1995 Video Study, Stigler and Hiebert (1999) likened teaching to "mountain ranges poking above the surface of the water," whereby they implied that we might see the mountaintops, but we do not see the hidden parts underneath these mountain ranges (pp. 73-78). By watching the videotaped lessons from Germany, Japan, and the United States again and again, they discovered that "the systems of teaching within each country look similar from lesson to lesson. At least, there are certain recurring features [or patterns] that typify many of the lessons within a country and distinguish the lessons among countries" (pp. 77-78). They also discovered that "teaching is a cultural activity," so the systems of teaching "must be understood in relation to the cultural beliefs and assumptions that surround them" (pp. 85, 88). From this viewpoint, one of the purposes of this dissertation was to study some cultural aspects of mathematics teaching and relate the results to mathematics teaching and learning in Vietnam. Another research purpose was to carry out a video study in Vietnam to find out the characteristics of Vietnamese mathematics teaching and compare these characteristics with those of other countries. In particular, this dissertation carried out the following research tasks: - Studying the characteristics of teaching and learning in different cultures and relating the results to mathematics teaching and learning in Vietnam - Introducing the TIMSS, the TIMSS Video Study and the advantages of using video study in investigating mathematics teaching and learning - Carrying out the video study in Vietnam to identify the image, scripts and patterns, and the lesson signature of eighth-grade mathematics teaching in Vietnam - Comparing some aspects of mathematics teaching in Vietnam and other countries and identifying the similarities and differences across countries - Studying the demands and challenges of innovating mathematics teaching methods in Vietnam - lessons from the video studies Hopefully, this dissertation will be a useful reference material for pre-service teachers at education universities to understand the nature of teaching and develop their teaching career.}, language = {en} } @article{Wallenta2012, author = {Wallenta, D.}, title = {Elliptic quasicomplexes on compact closed manifolds}, series = {Integral equations and operator theor}, volume = {73}, journal = {Integral equations and operator theor}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {0378-620X}, doi = {10.1007/s00020-012-1983-7}, pages = {517 -- 536}, year = {2012}, abstract = {We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalisation of the Atiyah-Singer index theorem.}, language = {en} } @article{Wallenta2014, author = {Wallenta, Daniel}, title = {A Lefschetz fixed point formula for elliptic quasicomplexes}, series = {Integral equations and operator theor}, volume = {78}, journal = {Integral equations and operator theor}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {0378-620X}, doi = {10.1007/s00020-014-2122-4}, pages = {577 -- 587}, year = {2014}, abstract = {In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.}, 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} } @unpublished{Wallenta2013, author = {Wallenta, Daniel}, title = {A Lefschetz fixed point formula for elliptic quasicomplexes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67016}, year = {2013}, abstract = {In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.}, language = {en} } @phdthesis{Waltz1994, author = {Waltz, Christine}, title = {Adjungierte Polynomideale und duale Typen auf Banachr{\"a}umen und ihre Anwendung}, pages = {109 Bl.}, year = {1994}, language = {de} } @book{Waltz1992, author = {Waltz, Christine}, title = {Interpolation von holomorphen Typen}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 01}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {23 Bl.}, year = {1992}, language = {de} } @article{WangLiZhangetal.2018, author = {Wang, Guang and Li, Pei-zhi and Zhang, Shi-yao and Zhong, Shan and Chu, Chang and Zeng, Shufei and Yan, Yu and Cheng, Xin and Chuai, Manli and Hocher, Berthold and Yang, Xuesong}, title = {Lipopolysaccharides (LPS) Induced Angiogenesis During Chicken Embryogenesis is Abolished by Combined ETA/ETB Receptor Blockade}, series = {Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology}, volume = {48}, journal = {Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology}, number = {5}, publisher = {Karger}, address = {Basel}, issn = {1015-8987}, doi = {10.1159/000492547}, pages = {2084 -- 2090}, year = {2018}, abstract = {Background/Aims: Angiogenesis plays a key role during embryonic development. The vascular endothelin (ET) system is involved in the regulation of angiogenesis. Lipopolysaccharides (LPS) could induce angiogenesis. The effects of ET blockers on baseline and LPS-stimulated angiogenesis during embryonic development remain unknown so far. Methods: The blood vessel density (BVD) of chorioallantoic membranes (CAMs), which were treated with saline (control), LPS, and/or BQ123 and the ETB blocker BQ788, were quantified and analyzed using an IPP 6.0 image analysis program. Moreover, the expressions of ET-1, ET-2, ET3, ET receptor A (ETRA), ET receptor B (ETRB) and VEGFR2 mRNA during embryogenesis were analyzed by semi-quantitative RT-PCR. Results: All components of the ET system are detectable during chicken embryogenesis. LPS increased angiogenesis substantially. This process was completely blocked by the treatment of a combination of the ETA receptor blockers-BQ123 and the ETB receptor blocker BQ788. This effect was accompanied by a decrease in ETRA, ETRB, and VEGFR2 gene expression. However, the baseline angiogenesis was not affected by combined ETA/ETB receptor blockade. Conclusion: During chicken embryogenesis, the LPS-stimulated angiogenesis, but not baseline angiogenesis, is sensitive to combined ETA/ETB receptor blockade.}, language = {en} } @article{WangHainzlZoelleretal.2012, author = {Wang, Lifeng and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Stress- and aftershock-constrained joint inversions for coseismic and postseismic slip applied to the 2004 M6.0 Parkfield earthquake}, series = {Journal of geophysical research : Solid earth}, volume = {117}, journal = {Journal of geophysical research : Solid earth}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2011JB009017}, pages = {18}, year = {2012}, abstract = {Both aftershocks and geodetically measured postseismic displacements are important markers of the stress relaxation process following large earthquakes. Postseismic displacements can be related to creep-like relaxation in the vicinity of the coseismic rupture by means of inversion methods. However, the results of slip inversions are typically non-unique and subject to large uncertainties. Therefore, we explore the possibility to improve inversions by mechanical constraints. In particular, we take into account the physical understanding that postseismic deformation is stress-driven, and occurs in the coseismically stressed zone. We do joint inversions for coseismic and postseismic slip in a Bayesian framework in the case of the 2004 M6.0 Parkfield earthquake. We perform a number of inversions with different constraints, and calculate their statistical significance. According to information criteria, the best result is preferably related to a physically reasonable model constrained by the stress-condition (namely postseismic creep is driven by coseismic stress) and the condition that coseismic slip and large aftershocks are disjunct. This model explains 97\% of the coseismic displacements and 91\% of the postseismic displacements during day 1-5 following the Parkfield event, respectively. It indicates that the major postseismic deformation can be generally explained by a stress relaxation process for the Parkfield case. This result also indicates that the data to constrain the coseismic slip model could be enriched postseismically. For the 2004 Parkfield event, we additionally observe asymmetric relaxation process at the two sides of the fault, which can be explained by material contrast ratio across the fault of similar to 1.15 in seismic velocity.}, language = {en} } @article{WangZoellerHainzl2015, author = {Wang, Lifeng and Z{\"o}ller, Gert and Hainzl, Sebastian}, title = {Joint Determination of Slip and Stress Drop in a Bayesian Inversion Approach: A Case Study for the 2010 M8.8 Maule Earthquake}, series = {Pure and applied geophysics}, volume = {172}, journal = {Pure and applied geophysics}, number = {2}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-014-0868-x}, pages = {375 -- 388}, year = {2015}, abstract = {Stress drop is a key factor in earthquake mechanics and engineering seismology. However, stress drop calculations based on fault slip can be significantly biased, particularly due to subjectively determined smoothing conditions in the traditional least-square slip inversion. In this study, we introduce a mechanically constrained Bayesian approach to simultaneously invert for fault slip and stress drop based on geodetic measurements. A Gaussian distribution for stress drop is implemented in the inversion as a prior. We have done several synthetic tests to evaluate the stability and reliability of the inversion approach, considering different fault discretization, fault geometries, utilized datasets, and variability of the slip direction, respectively. We finally apply the approach to the 2010 M8.8 Maule earthquake and invert for the coseismic slip and stress drop simultaneously. Two fault geometries from the literature are tested. Our results indicate that the derived slip models based on both fault geometries are similar, showing major slip north of the hypocenter and relatively weak slip in the south, as indicated in the slip models of other studies. The derived mean stress drop is 5-6 MPa, which is close to the stress drop of similar to 7 MPa that was independently determined according to force balance in this region Luttrell et al. (J Geophys Res, 2011). These findings indicate that stress drop values can be consistently extracted from geodetic data.}, language = {en} } @phdthesis{Wei2008, author = {Wei, Yawei}, title = {Operators on manifolds with edge and boundary with singular trace conditions}, address = {Potsdam}, pages = {128 S.: graph. Darst.}, year = {2008}, language = {en} } @phdthesis{Wei2008, author = {Wei, Yawei}, title = {Operators on Manifolds with Edge and Boundary with Singular Trace Conditions}, address = {Potsdam}, pages = {127 S., : graph. Darst.}, year = {2008}, language = {en} } @book{Weian2002, author = {Weian, Liu}, title = {Viscosity Solutions of Fully Nonlinea Parabolic Systems}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {31 S.}, year = {2002}, language = {en} } @article{Weicker2018, author = {Weicker, Karsten}, title = {Vorlesungs-Pflege}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416315}, pages = {47 -- 59}, year = {2018}, abstract = {{\"A}hnlich zu Alterungsprozessen bei Software degenerieren auch Vorlesungen, wenn sie nicht hinreichend gepflegt werden. Die Gr{\"u}nde hierf{\"u}r werden ebenso beleuchtet wie m{\"o}gliche Indikatoren und Maßnahmen - der Blick ist dabei immer der eines Informatikers. An drei Vorlesungen wird erl{\"a}utert, wie der Degeneration von Lehrveranstaltungen gegengewirkt werden kann. Mangels hinreichend großer empirischer Daten liefert das Paper keine unumst{\"o}ßlichen Wahrheiten. Ein Ziel ist es vielmehr Kollegen, die {\"a}hnliche Ph{\"a}nomene beobachten, einen ersten Anker f{\"u}r einen inneren Diskurs zu bieten. Ein langfristiges Ziel ist die Sammlung eines Katalogs an Maßnahmen zur Pflege von Informatikvorlesungen.}, language = {de} } @article{WeineltStegemannTheloeetal.2022, author = {Weinelt, Ferdinand Anton and Stegemann, Miriam Songa and Theloe, Anja and Pf{\"a}fflin, Frieder and Achterberg, Stephan and Weber, Franz and D{\"u}bel, Lucas and Mikolajewska, Agata and Uhrig, Alexander and Kiessling, Peggy and Huisinga, Wilhelm and Michelet, Robin and Hennig, Stefanie and Kloft, Charlotte}, title = {Evaluation of a meropenem and piperacillin monitoring program in intensive care unit patients calls for the regular assessment of empirical targets and easy-to-use dosing decision tools}, series = {Antibiotics : open access journal}, volume = {11}, journal = {Antibiotics : open access journal}, number = {6}, publisher = {MDPI}, address = {Basel}, issn = {2079-6382}, doi = {10.3390/antibiotics11060758}, pages = {17}, year = {2022}, abstract = {The drug concentrations targeted in meropenem and piperacillin/tazobactam therapy also depend on the susceptibility of the pathogen. Yet, the pathogen is often unknown, and antibiotic therapy is guided by empirical targets. To reliably achieve the targeted concentrations, dosing needs to be adjusted for renal function. We aimed to evaluate a meropenem and piperacillin/tazobactam monitoring program in intensive care unit (ICU) patients by assessing (i) the adequacy of locally selected empirical targets, (ii) if dosing is adequately adjusted for renal function and individual target, and (iii) if dosing is adjusted in target attainment (TA) failure. In a prospective, observational clinical trial of drug concentrations, relevant patient characteristics and microbiological data (pathogen, minimum inhibitory concentration (MIC)) for patients receiving meropenem or piperacillin/tazobactam treatment were collected. If the MIC value was available, a target range of 1-5 x MIC was selected for minimum drug concentrations of both drugs. If the MIC value was not available, 8-40 mg/L and 16-80 mg/L were selected as empirical target ranges for meropenem and piperacillin, respectively. A total of 356 meropenem and 216 piperacillin samples were collected from 108 and 96 ICU patients, respectively. The vast majority of observed MIC values was lower than the empirical target (meropenem: 90.0\%, piperacillin: 93.9\%), suggesting empirical target value reductions. TA was found to be low (meropenem: 35.7\%, piperacillin 50.5\%) with the lowest TA for severely impaired renal function (meropenem: 13.9\%, piperacillin: 29.2\%), and observed drug concentrations did not significantly differ between patients with different targets, indicating dosing was not adequately adjusted for renal function or target. Dosing adjustments were rare for both drugs (meropenem: 6.13\%, piperacillin: 4.78\%) and for meropenem irrespective of TA, revealing that concentration monitoring alone was insufficient to guide dosing adjustment. Empirical targets should regularly be assessed and adjusted based on local susceptibility data. To improve TA, scientific knowledge should be translated into easy-to-use dosing strategies guiding antibiotic dosing.}, language = {en} } @article{WeissHuisinga2011, author = {Weiss, Andrea Y. and Huisinga, Wilhelm}, title = {Error-controlled global sensitivity analysis of ordinary differential equations}, series = {Journal of computational physics}, volume = {230}, journal = {Journal of computational physics}, number = {17}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-9991}, doi = {10.1016/j.jcp.2011.05.011}, pages = {6824 -- 6842}, year = {2011}, abstract = {We propose a novel strategy for global sensitivity analysis of ordinary differential equations. It is based on an error-controlled solution of the partial differential equation (PDE) that describes the evolution of the probability density function associated with the input uncertainty/variability. The density yields a more accurate estimate of the output uncertainty/variability, where not only some observables (such as mean and variance) but also structural properties (e.g., skewness, heavy tails, bi-modality) can be resolved up to a selected accuracy. For the adaptive solution of the PDE Cauchy problem we use the Rothe method with multiplicative error correction, which was originally developed for the solution of parabolic PDEs. We show that, unlike in parabolic problems, conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time. We provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy. The performance of the method is studied by means of low-dimensional case studies. The favorable properties of the spatial discretization technique suggest that this may be the starting point for an error-controlled sensitivity analysis in higher dimensions.}, language = {en} } @misc{WeisserStueblerMatheisetal.2017, author = {Weisser, Karin and St{\"u}bler, Sabine and Matheis, Walter and Huisinga, Wilhelm}, title = {Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products}, series = {Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology}, volume = {88}, journal = {Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology}, publisher = {Elsevier}, address = {San Diego}, issn = {0273-2300}, doi = {10.1016/j.yrtph.2017.02.018}, pages = {310 -- 321}, year = {2017}, abstract = {As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved.}, language = {en} }