@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@unpublished{Tarkhanov2005,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@unpublished{Tarkhanov2005,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}
}