TY - CHAP A1 - Hafer, Jörg A1 - Kiy, Alexander ED - Buchem, Ilona ED - Graham, Attwell ED - Tur, Gemma T1 - The university-wide introduction of an ePortfolio system as transdisciplinary task BT - Results of an implementation process and perspectives on an optimized process model T2 - Proceedings of the PLE Conference 2013: Learning and Diversity in the Cities of the Future Y1 - 2013 SP - 363 EP - 373 PB - Logos CY - Berlin ER - TY - JOUR A1 - Koppitz, Jörg A1 - Supaporn, Worakrit T1 - Categary equivalences of clones of operations preserving unaryoperations JF - COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES N2 - Any clones on arbitrary set A can be written of the form Pol (A)Q for some set Q of relations on A. We consider clones of the form Pal (A)Q where Q is a set of unary relations on a finite set A. A clone Pol (A)Q is said to be a clone on a set of the smallest cardinality with respect to category equivalence if vertical bar A vertical bar <= vertical bar S vertical bar for all finite sets S and all clones C on S that category equivalent to Pol (A)Q. We characterize the clones on a set of the smallest cardinality with respect to category equivalent and show how we can find a clone on a set of the smallest cardinality that category equivalent to a given clone. KW - category equivalence of clones KW - clone of operations Y1 - 2013 SN - 1310-1331 VL - 66 IS - 2 SP - 177 EP - 184 PB - Publ. House of the Bulgarian Acad. of Sciences CY - Sofia ER - TY - JOUR A1 - Reich, Sebastian T1 - A nonparametric ensemble transform method for bayesian inference JF - SIAM journal on scientific computing N2 - Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. KW - Bayesian inference KW - Monte Carlo method KW - sequential data assimilation KW - linear programming KW - resampling Y1 - 2013 U6 - https://doi.org/10.1137/130907367 SN - 1064-8275 VL - 35 IS - 4 SP - A2013 EP - A2024 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Debussche, Arnaud A1 - Hoegele, Michael A1 - Imkeller, Peter T1 - The source of stochastic models in conceptual climate dynamics JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8 SN - 0075-8434 VL - 2085 IS - 3 SP - 151 EP - 157 PB - Springer CY - Berlin ER - TY - JOUR A1 - Debussche, Arnaud A1 - Högele, Michael A1 - Imkeller, Peter T1 - Localization and metastability JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics N2 - In this chapter, equipped with our previously obtained knowledge of exit and transition times in the limit of small noise amplitude ??0 , we shall investigate the global asymptotic behavior of our jump diffusion process in the time scale in which transitions occur, i.e. in the scale given by ?0(?)=?(1?Bc?(0)),?,?>0 . It turns out that in this time scale, the switching of the diffusion between neighborhoods of the stable solutions ? ± can be well described by a Markov chain jumping back and forth between two states with a characteristic Q-matrix determined by the quantities ?((D±0)c)?(Bc?(0)) as jumping rates. Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_7 SN - 0075-8434 VL - 2085 SP - 131 EP - 149 PB - Springer CY - Berlin ER - TY - JOUR A1 - Debussche, Arnaud A1 - Hoegele, Michael A1 - Imkeller, Peter T1 - Asymptotic transition times JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_6 SN - 0075-8434 VL - 2085 SP - 121 EP - 130 PB - Springer CY - Berlin ER - TY - JOUR A1 - Debussche, Arnaud A1 - Hoegele, Michael A1 - Imkeller, Peter T1 - Asymptotic exit times JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_5 SN - 0075-8434 VL - 2085 SP - 87 EP - 120 PB - Springer CY - Berlin ER - TY - JOUR A1 - Debussche, Arnaud A1 - Hoegele, Michael A1 - Imkeller, Peter T1 - The small deviation of the small noise solution JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_4 SN - 0075-8434 VL - 2085 SP - 69 EP - 85 PB - Springer CY - Berlin ER - TY - JOUR A1 - Debussche, Arnaud A1 - Högele, Michael A1 - Imkeller, Peter T1 - The stochastic chafee-infante equation JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics N2 - In this preparatory chapter, the tools of stochastic analysis needed for the investigation of the asymptotic behavior of the stochastic Chafee-Infante equation are provided. In the first place, this encompasses a recollection of basic facts about Lévy processes with values in Hilbert spaces. Playing the role of the additive noise processes perturbing the deterministic Chafee-Infante equation in the systems the stochastic dynamics of which will be our main interest, symmetric ?-stable Lévy processes are in the focus of our investigation (Sect. 3.1). Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_3 SN - 0075-8434 VL - 2085 SP - 45 EP - 68 PB - Springer CY - Berlin ER - TY - JOUR A1 - Debussche, Arnaud A1 - Högele, Michael A1 - Imkeller, Peter T1 - The Fine Dynamics of the Chafee-Infante Equation JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics N2 - In this chapter, we introduce the deterministic Chafee-Infante equation. This equation has been the subject of intense research and is very well understood now. We recall some properties of its longtime dynamics and in particular the structure of its attractor. We then define reduced domains of attraction that will be fundamental in our study and give a result describing precisely the time that a solution starting form a reduced domain of attraction needs to reach a stable equilibrium. This result is then proved using the detailed knowledge of the attractor and classical tools such as the stable and unstable manifolds in a neighborhood of an equilibrium. Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_2 SN - 0075-8434 VL - 2085 SP - 11 EP - 43 PB - Springer CY - Berlin ER - TY - INPR A1 - Debussche, Arnaud A1 - Hoegele, Michael A1 - Imkeller, Peter T1 - The dynamics of nonlinear reaction-diffusion equations with small levy noise preface T2 - Lecture notes in mathematics : a collection of informal reports and seminars T2 - Lecture Notes in Mathematics Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 SN - 0075-8434 VL - 2085 SP - V EP - + PB - Springer CY - Berlin ER - TY - INPR A1 - Debussche, Arnaud A1 - Högele, Michael A1 - Imkeller, Peter T1 - The dynamics of nonlinear reaction-diffusion equations with small levy noise T2 - Lecture notes in mathematics : a collection of informal reports and seminars T2 - Lecture Notes in Mathematics N2 - Our primary interest in this book lies in the study of dynamical properties of reaction-diffusion equations perturbed by Lévy noise of intensity ? in the small noise limit ??0 . Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_1 SN - 0075-8434 VL - 2085 SP - 1 EP - 10 PB - Springer CY - Berlin ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - The tetralogy of Birkhoff theorems JF - General relativity and gravitation N2 - We classify the existent Birkhoff-type theorems into four classes: first, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with can be expressed by the Schwarzschild metric; for , it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of 2-D pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to 2-D. KW - Birkhoff theorem KW - Einstein space KW - Isometry group Y1 - 2013 U6 - https://doi.org/10.1007/s10714-012-1478-5 SN - 0001-7701 VL - 45 IS - 2 SP - 395 EP - 410 PB - Springer CY - New York ER - TY - JOUR A1 - Osterloh, Lukas A1 - Böckmann, Christine A1 - Nicolae, Doina A1 - Nemuc, Anca T1 - Regularized inversion of microphysical atmospheric particle parameters - theory and application JF - Journal of computational physics N2 - Retrieving the distribution of aerosols in the atmosphere via remote sensing techniques is a highly complex task that requires dealing with a wide range of different problems stemming both from Physics and Mathematics. We focus on retrieving this distribution from multi-wavelength lidar data for aerosol ensembles consisting of spherical particles via an iterative regularization technique. The optical efficiencies for spherical scatterers are examined to account for the behavior of the underlying integral equation. The ill-posedness of the problem and the conditioning of the discretized problem are analyzed. Some critical points in the model, like the assumed wavelength-independence of the refractive index and the fixed grid of investigated refractive indices, are studied with regard to their expected impact on the regularized solution. A new Monte-Carlo type method is proposed for retrieval of the refractive index. To validate the results, the developed algorithm is applied to two measurement cases of burning biomass gained from multi-wavelength Raman lidar. KW - Inverse ill-posed problem KW - Regularization KW - Lidar remote sensing KW - Microphysical particle properties Y1 - 2013 U6 - https://doi.org/10.1016/j.jcp.2012.11.040 SN - 0021-9991 VL - 237 IS - 11 SP - 79 EP - 94 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Karpuz, Eylem Guzel A1 - Cevik, Ahmet Sinan A1 - Koppitz, Jörg A1 - Cangul, Ismail Naci T1 - Some fixed-point results on (generalized) Bruck-Reilly *-extensions of monoids JF - Fixed point theory and applications N2 - In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly *-extensions of arbitrary monoids to be regular, coregular and strongly pi-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal. KW - Bruck-Reilly extension KW - generalized Bruck-Reilly *-extension KW - pi-inverse monoid KW - regular monoid Y1 - 2013 U6 - https://doi.org/10.1186/1687-1812-2013-78 SN - 1687-1812 IS - 3 PB - Springer CY - Cham ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias A1 - Hainzl, Sebastian T1 - The Maximum Earthquake Magnitude in a Time Horizon: Theory and Case Studies JF - Bulletin of the Seismological Society of America N2 - We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference. Y1 - 2013 U6 - https://doi.org/10.1785/0120120013 SN - 0037-1106 VL - 103 IS - 2A SP - 860 EP - 875 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Exact radial solution in 2+1 gravity with a real scalar field JF - Physics letters : B N2 - In this Letter we give some general considerations about circularly symmetric, static space-times in 2 + 1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3 + 1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of (2 + 1)-dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to (2 + 1)-dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3 + 1 dimensions but with certain oddities connected with the (2 + 1)-dimensional character of the space-time. The solution is unique to 2 + 1 dimensions; it does not carry over to 3 + 1 dimensions. KW - (2+1)-dimensional gravity KW - Exact solution KW - BTZ black hole KW - Self-interacting scalar field Y1 - 2013 U6 - https://doi.org/10.1016/j.physletb.2013.03.007 SN - 0370-2693 VL - 721 IS - 4-5 SP - 294 EP - 298 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Cotronei, Mariantonia A1 - Holschneider, Matthias T1 - Partial parameterization of orthogonal wavelet matrix filters JF - Journal of computational and applied mathematics N2 - In this paper we propose a procedure which allows the construction of a large family of FIR d x d matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank type that can be obtained with such procedure is given. In particular, we restrict our attention to a special construction based on the representation of SO(2d) in terms of the elements of its Lie algebra. Explicit expressions for the filters in the case d = 2 are given, as a result of a local analysis of the parameterization obtained from perturbing the Haar system. KW - Full rank matrix filters KW - Multichannel wavelets KW - Quadrature mirror filters KW - Vector subdivision schemes Y1 - 2013 U6 - https://doi.org/10.1016/j.cam.2012.11.016 SN - 0377-0427 VL - 243 IS - 4 SP - 113 EP - 125 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Murr, Rüdiger T1 - Characterization of infinite divisibility by duality formulas application to Levy processes and random measures JF - Stochastic processes and their application N2 - Processes with independent increments are proven to be the unique solutions of duality formulas. This result is based on a simple characterization of infinitely divisible random vectors by a functional equation in which a difference operator appears. This operator is constructed by a variational method and compared to approaches involving chaos decompositions. We also obtain a related characterization of infinitely divisible random measures. KW - Duality formula KW - Integration by parts formula KW - Malliavin calculus KW - Infinite divisibility KW - Levy processes KW - Random measures Y1 - 2013 U6 - https://doi.org/10.1016/j.spa.2012.12.012 SN - 0304-4149 VL - 123 IS - 5 SP - 1729 EP - 1749 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Eichmair, Michael A1 - Metzger, Jan T1 - Large isoperimetric surfaces in initial data sets JF - Journal of differential geometry N2 - We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M, g) that are C-0-asymptotic to Schwarzschild of mass m > 0. Refining an argument due to H. Bray, we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all sufficiently large volumes, and that they are close to centered coordinate spheres. This implies that the volume-preserving stable constant mean curvature spheres constructed by G. Huisken and S.-T. Yau as well as R. Ye as perturbations of large centered coordinate spheres minimize area among all competing surfaces that enclose the same volume. This confirms a conjecture of H. Bray. Our results are consistent with the uniqueness results for volume-preserving stable constant mean curvature surfaces in initial data sets obtained by G. Huisken and S.-T. Yau and strengthened by J. Qing and G. Tian. The additional hypotheses that the surfaces be spherical and far out in the asymptotic region in their results are not necessary in our work. Y1 - 2013 SN - 0022-040X VL - 94 IS - 1 SP - 159 EP - 186 PB - International Press of Boston CY - Somerville ER - TY - JOUR A1 - Nehring, Benjamin T1 - Construction of point processes for classical and quantum gases JF - Journal of mathematical physics N2 - We propose a construction of point processes via the method of cluster expansion. The important role of the class of infinitely divisible point processes is noted. Examples are permanental and determinantal processes as well as the classical Gibbs point processes, where the interaction is given by a stable and regular pair potential. Y1 - 2013 U6 - https://doi.org/10.1063/1.4807080 SN - 0022-2488 SN - 1089-7658 VL - 54 IS - 5 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Lamm, Tobias A1 - Metzger, Jan T1 - Minimizers of the willmore functional with a small area constraint JF - ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE N2 - We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we partially classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds. KW - Willmore functional KW - Minimizers KW - Direct method Y1 - 2013 U6 - https://doi.org/10.1016/j.anihpc.2012.10.003 SN - 0294-1449 VL - 30 IS - 3 SP - 497 EP - 518 PB - Elsevier CY - Paris ER - TY - JOUR A1 - Schröter, M-A A1 - Sturm, H. A1 - Holschneider, Matthias T1 - Phase and amplitude patterns in DySEM mappings of vibrating microstructures JF - Nanotechnology N2 - We use a dynamic scanning electron microscope (DySEM) to analyze the movement of oscillating micromechanical structures. A dynamic secondary electron (SE) signal is recorded and correlated to the oscillatory excitation of scanning force microscope (SFM) cantilever by means of lock-in amplifiers. We show, how the relative phase of the oscillations modulate the resulting real part and phase pictures of the DySEM mapping. This can be used to obtain information about the underlying oscillatory dynamics. We apply the theory to the case of a cantilever in oscillation, driven at different flexural and torsional resonance modes. This is an extension of a recent work (Schroter et al 2012 Nanotechnology 23 435501), where we reported on a general methodology to distinguish nonlinear features caused by the imaging process from those caused by cantilever motion. Y1 - 2013 U6 - https://doi.org/10.1088/0957-4484/24/21/215701 SN - 0957-4484 VL - 24 IS - 21 PB - IOP Publ. Ltd. CY - Bristol ER - TY - INPR A1 - Weske, Mathias A1 - Rinderle-Ma, Stefanie A1 - Toumani, Farouk A1 - Wolf, Karsten T1 - Special section on BPM 2011 conference. - Special Issue T2 - Information systems Y1 - 2013 U6 - https://doi.org/10.1016/j.is.2013.01.003 SN - 0306-4379 VL - 38 IS - 4 SP - 545 EP - 546 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Zaourar, Naima A1 - Hamoudi, Mohamed A1 - Holschneider, Matthias A1 - Mandea, Mioara T1 - Fractal dynamics of geomagnetic storms JF - Arabian journal of geosciences N2 - We explore fluctuations of the horizontal component of the Earth's magnetic field to identify scaling behaviour of the temporal variability in geomagnetic data recorded by the Intermagnet observatories during the solar cycle 23 (years 1996 to 2005). In this work, we use the remarkable ability of scaling wavelet exponents to highlight the singularities associated with discontinuities present in the magnetograms obtained at two magnetic observatories for six intense magnetic storms, including the sudden storm commencements of 14 July 2000, 29-31 October and 20-21 November 2003. In the active intervals that occurred during geomagnetic storms, we observe a rapid and unidirectional change in the spectral scaling exponent at the time of storm onset. The corresponding fractal features suggest that the dynamics of the whole time series is similar to that of a fractional Brownian motion. Our findings point to an evident relatively sudden change related to the emergence of persistency of the fractal power exponent fluctuations precedes an intense magnetic storm. These first results could be useful in the framework of extreme events prediction studies. KW - Geomagnetic field KW - Magnetosphere KW - Geomagnetic storm KW - Multiscale analysis KW - Spectral exponent Y1 - 2013 U6 - https://doi.org/10.1007/s12517-011-0487-0 SN - 1866-7511 VL - 6 IS - 6 SP - 1693 EP - 1702 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Isotropic universe with almost scale-invariant fourth-order gravity JF - Journal of mathematical physics N2 - We study a class of isotropic cosmologies in the fourth-order gravity with Lagrangians of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars, respectively. A general discussion is given on the conditions under which this gravitational Lagrangian is scale-invariant or almost scale-invariant. We then apply this general background to the specific case L = alpha R-2 + beta Gln G with constants alpha, beta. We find closed form cosmological solutions for this case. One interesting feature of this choice of f(R) and k(G) is that for very small negative value of the parameter beta, the Lagrangian L = R-2/3 + beta Gln G leads to the replacement of the exact de Sitter solution coming from L = R-2 (which is a local attractor) to an exact, power-law inflation solution a(t) = t(p) = t(-3/beta) which is also a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of a Gln G-term. Y1 - 2013 U6 - https://doi.org/10.1063/1.4808255 SN - 0022-2488 VL - 54 IS - 6 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Nehring, Benjamin A1 - Poghosyan, Suren A1 - Zessin, Hans T1 - On the construction of point processes in statistical mechanics JF - Journal of mathematical physics N2 - We present a new approach to the construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R-d of Ginibre's Fermi-Dirac gas of such loops. This approach is based on the cluster expansion method. We obtain the existence of Gibbs perturbations of a large class of point processes. Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford, and Ruelle if the underlying potential is positive. Finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive. Y1 - 2013 U6 - https://doi.org/10.1063/1.4807724 SN - 0022-2488 VL - 54 IS - 6 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - Chiral asymmetry and the spectral action JF - Communications in mathematical physics N2 - We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter. Y1 - 2013 U6 - https://doi.org/10.1007/s00220-012-1641-6 SN - 0010-3616 SN - 1432-0916 VL - 321 IS - 2 SP - 283 EP - 310 PB - Springer CY - New York ER - TY - JOUR A1 - Namgaladze, Alexander A. A1 - Zolotov, O. V. A1 - Prokhorov, Boris E. T1 - Numerical simulation of the variations in the total electron content of the ionosphere observed before the Haiti earthquake of January 12, 2010 JF - Geomagnetism and aeronomy N2 - We present the results of a study of the abnormal variations in the total electron content (TEC) of the ionosphere observed before the earthquake of January 12, 2010, in Haiti. Global and regional maps of TEC relative (%) deviations from the quite background state are built for January 9-12, 2010. Using the UAM (Upper Atmosphere Model) global numerical model of the upper atmosphere of the Earth, the variations in the electric potential in the ionosphere and TEC are calculated using external seismic current above faults between the Earth and the ionosphere as a lower boundary condition. The numerical simulation results are compared with observations. It is shown that the simulated variations in the TEC at a specified current density of about 1 x 10(-8) A/m(2) on an area of 200 km (latitude) x 4000 km (longitude) above the focus represent all main features of the observations: prevalence of increased TEC values (positive disturbances), neighboring negative disturbances of lower magnitudes, localization, magnetic conjugacy of high-intensity effects in the Southern Hemisphere, and disappearance of disturbances around midday. Methodological recommendations are given to reveal variations in the TEC related to the preparation of seismic events. Y1 - 2013 U6 - https://doi.org/10.1134/S0016793213030122 SN - 0016-7932 SN - 1555-645X VL - 53 IS - 4 SP - 522 EP - 528 PB - Pleiades Publ. CY - New York ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - Motivic Dyson-Schwinger equations JF - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - We consider Dyson-Schwinger Equations (DSEs) in the context of Connes-Kreimer renormalization Hopf algebra of Feynman diagrams and Connes-Marcolli universal Tannakian formalism. This study leads us to formulate a family of Picard-Fuchs equations and a category of Feynman motivic sheaves with respect to each combinatorial DSE. KW - Connes-Kreimer Hopf algebra KW - Dyson-Schwinger equations KW - equi-singular connections KW - motivic Feynman rules KW - Picard-Fuchs equations KW - universal Hopf algebra of renormalization Y1 - 2013 U6 - https://doi.org/10.1142/S0217751X13501029 SN - 0217-751X VL - 28 IS - 20 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Zöller, Gert T1 - Convergence of the frequency-magnitude distribution of global earthquakes - maybe in 200 years JF - Geophysical research letters N2 - I study the ability to estimate the tail of the frequency-magnitude distribution of global earthquakes. While power-law scaling for small earthquakes is accepted by support of data, the tail remains speculative. In a recent study, Bell et al. (2013) claim that the frequency-magnitude distribution of global earthquakes converges to a tapered Pareto distribution. I show that this finding results from data fitting errors, namely from the biased maximum likelihood estimation of the corner magnitude theta in strongly undersampled models. In particular, the estimation of theta depends solely on the few largest events in the catalog. Taking this into account, I compare various state-of-the-art models for the global frequency-magnitude distribution. After discarding undersampled models, the remaining ones, including the unbounded Gutenberg-Richter distribution, perform all equally well and are, therefore, indistinguishable. Convergence to a specific distribution, if it ever takes place, requires about 200 years homogeneous recording of global seismicity, at least. KW - statistical seismology Y1 - 2013 U6 - https://doi.org/10.1002/grl.50779 SN - 0094-8276 SN - 1944-8007 VL - 40 IS - 15 SP - 3873 EP - 3877 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Rattana, Amornrat A1 - Böckmann, Christine T1 - Matrix methods for computing eigenvalues of Sturm-Liouville problems of order four JF - Journal of computational and applied mathematics N2 - This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions. Furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's methods as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods is investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated. KW - Finite difference method KW - Numerov's method KW - Boundary value methods KW - Fourth order Sturm-Liouville problem KW - Eigenvalues Y1 - 2013 U6 - https://doi.org/10.1016/j.cam.2013.02.024 SN - 0377-0427 SN - 1879-1778 VL - 249 IS - 8 SP - 144 EP - 156 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Brietzke, Gilbert B. A1 - Hinzen, Klaus-G. T1 - Comparison of deterministic and stochastic earthquake simulators for fault interactions in the Lower Rhine Embayment, Germany JF - Geophysical journal international N2 - Time-dependent probabilistic seismic hazard assessment requires a stochastic description of earthquake occurrences. While short-term seismicity models are well-constrained by observations, the recurrences of characteristic on-fault earthquakes are only derived from theoretical considerations, uncertain palaeo-events or proxy data. Despite the involved uncertainties and complexity, simple statistical models for a quasi-period recurrence of on-fault events are implemented in seismic hazard assessments. To test the applicability of statistical models, such as the Brownian relaxation oscillator or the stress release model, we perform a systematic comparison with deterministic simulations based on rate- and state-dependent friction, high-resolution representations of fault systems and quasi-dynamic rupture propagation. For the specific fault network of the Lower Rhine Embayment, Germany, we run both stochastic and deterministic model simulations based on the same fault geometries and stress interactions. Our results indicate that the stochastic simulators are able to reproduce the first-order characteristics of the major earthquakes on isolated faults as well as for coupled faults with moderate stress interactions. However, we find that all tested statistical models fail to reproduce the characteristics of strongly coupled faults, because multisegment rupturing resulting from a spatiotemporally correlated stress field is underestimated in the stochastic simulators. Our results suggest that stochastic models have to be extended by multirupture probability distributions to provide more reliable results. KW - Earthquake interaction KW - forecasting KW - and prediction KW - Seismicity and tectonics KW - Statistical seismology Y1 - 2013 U6 - https://doi.org/10.1093/gji/ggt271 SN - 0956-540X SN - 1365-246X VL - 195 IS - 1 SP - 684 EP - 694 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - The global beta-functions from solutions of dyson-schwinger equations JF - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - We apply the geometric interpretation of Dyson-Schwinger equations (DSEs) in terms of equi-singular flat connections to provide a process which relates beta-functions of a DSE under different regularization schemes. KW - Dyson-Schwinger equations KW - beta-functions KW - renormalization Hopf algebra KW - equi-singular connections Y1 - 2013 U6 - https://doi.org/10.1142/S0217732313501526 SN - 0217-7323 SN - 1793-6632 VL - 28 IS - 34 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators JF - Journal of differential equations N2 - We consider a Sturm-Liouville boundary value problem in a bounded domain D of R-n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on partial derivative D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact selfadjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types. (C) 2013 Elsevier Inc. All rights reserved. KW - Sturm-Liouville problem KW - Discontinuous Robin condition KW - Root function KW - Lipschitz domain KW - Non-coercive problem Y1 - 2013 U6 - https://doi.org/10.1016/j.jde.2013.07.029 SN - 0022-0396 SN - 1090-2732 VL - 255 IS - 10 SP - 3305 EP - 3337 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Eichmair, Michael A1 - Metzger, Jan T1 - Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions JF - Inventiones mathematicae Y1 - 2013 U6 - https://doi.org/10.1007/s00222-013-0452-5 SN - 0020-9910 SN - 1432-1297 VL - 194 IS - 3 SP - 591 EP - 630 PB - Springer CY - New York ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER EQUATIONS JF - INTERNATIONAL JOURNAL OF MODERN PHYSICS A N2 - We study Dyson-Schwinger equations (DSEs) in terms of some groups of diffeographisms to provide a new geometric formulation for their corresponding counterterms on the basis of systems of ordinary differential equations. KW - Dyson-Schwinger equations KW - Hopf algebra of Feynman diagrams KW - counterterms KW - Picard-Fuchs equations KW - equi-singular connections Y1 - 2013 U6 - https://doi.org/10.1142/S0217751X13501704 SN - 0217-751X SN - 1793-656X VL - 28 IS - 32 PB - WORLD SCIENTIFIC PUBL CO PTE LTD CY - SINGAPORE ER - TY - THES A1 - Habal, Nadia T1 - Operators on singular manifolds Y1 - 2013 CY - Potsdam ER - TY - THES A1 - Susanti, Yeni T1 - On Particular n-Clones Y1 - 2013 CY - Potsdam ER - TY - THES A1 - Rattana, Amornrat T1 - Direct and inverse sturm-liouville problems of order four Y1 - 2013 CY - Potsdam ER - TY - THES A1 - Rungrottheera, Wannarut T1 - Corner pseudo-differential operators Y1 - 2013 CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Exact radial solution in 2+1 gravity with a real scalar field N2 - In this paper we give some general considerations about circularly symmetric, static space-times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of 2+1 dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to 2+1 dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space- time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions. Y1 - 2013 UR - http://arXiv.org/abs/1212.1285 SN - 0370-2693 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Isotropic universe with almost scale-invariant fourth-order gravity N2 - We study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we discuss is the case of a very small negative value of the parameter b in the Lagrangian L = R^2 + b G ln G which leads to the replacement of the exact de Sitter solution from L = R^2 (being a local attractor) to a power-law inflation exact solution also representing a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of the G ln G-term. Y1 - 2013 UR - http://arxiv.org/abs/1212.1769 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - The tetralogy of Birkhoff theorems N2 - We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with Lambda = 0 can be expressed by the Schwarzschild metric; for Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of two- dimensional pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to two dimensions. Y1 - 2013 UR - http://arXiv.org/abs/1208.5237 SN - 0001-7701 ER - TY - THES A1 - Kröncke, Klaus T1 - Stability of Einstein Manifolds T1 - Stabilität von Einstein-Mannigfaltigkeiten N2 - This thesis deals with Einstein metrics and the Ricci flow on compact mani- folds. We study the second variation of the Einstein-Hilbert functional on Ein- stein metrics. In the first part of the work, we find curvature conditions which ensure the stability of Einstein manifolds with respect to the Einstein-Hilbert functional, i.e. that the second variation of the Einstein-Hilbert functional at the metric is nonpositive in the direction of transverse-traceless tensors. The second part of the work is devoted to the study of the Ricci flow and how its behaviour close to Einstein metrics is influenced by the variational be- haviour of the Einstein-Hilbert functional. We find conditions which imply that Einstein metrics are dynamically stable or unstable with respect to the Ricci flow and we express these conditions in terms of stability properties of the metric with respect to the Einstein-Hilbert functional and properties of the Laplacian spectrum. N2 - Die vorliegende Arbeit beschäftigt sich mit Einsteinmetriken und Ricci-Fluss auf kompakten Mannigfaltigkeiten. Wir studieren die zweite Variation des Einstein- Hilbert Funktionals auf Einsteinmetriken. Im ersten Teil der Arbeit finden wir Krümmungsbedingungen, die die Stabilität von Einsteinmannigfaltigkeiten bezüglich des Einstein-Hilbert Funktionals sicherstellen, d.h. die zweite Varia- tion des Einstein-Hilbert Funktionals ist nichtpositiv in Richtung transversaler spurfreier Tensoren. Der zweite Teil der Arbeit widmet sich dem Studium des Ricci-Flusses und wie dessen Verhalten in der Nähe von Einsteinmetriken durch das Variationsver- halten des Einstein-Hilbert Funktionals beeinflusst wird. Wir finden Bedinun- gen, die dynamische Stabilität oder Instabilität von Einsteinmetriken bezüglich des Ricci-Flusses implizieren und wir drücken diese Bedingungen in Termen der Stabilität der Metrik bezüglich des Einstein-Hilbert Funktionals und Eigen- schaften des Spektrums des Laplaceoperators aus. KW - Einstein-Mannigfaltigkeiten KW - Ricci-Fluss KW - Variationsstabilität KW - Einstein-Hilbert-Wirkung KW - Einstein manifolds KW - Ricci flow KW - variational stability KW - Einstein-Hilbert action Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-69639 ER - TY - INPR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Class of Toeplitz Operators in Several Variables N2 - We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)17 KW - Cauchy data spaces KW - Laplace-Beltrami operator KW - Toeplitz operators KW - Fredholm property Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68932 SN - 2193-6943 ER - TY - INPR A1 - Gairing, Jan A1 - Högele, Michael A1 - Kosenkova, Tetiana A1 - Kulik, Alexei Michajlovič T1 - Coupling distances between Lévy measures and applications to noise sensitivity of SDE N2 - We introduce the notion of coupling distances on the space of Lévy measures in order to quantify rates of convergence towards a limiting Lévy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Lévy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two Lévy diffusions in terms of the couping distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)16 KW - Lévy diffusion approximation KW - coupling methods KW - Skorokhod' s invariance principle KW - statistical model selection Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68886 ER - TY - INPR A1 - Wallenta, Daniel T1 - A Lefschetz fixed point formula for elliptic quasicomplexes N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)12 KW - Perturbed complexes KW - curvature KW - Lefschetz number KW - fixed point formula Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67016 ER - TY - INPR A1 - Högele, Michael A1 - Ruffino, Paulo T1 - Averaging along Lévy diffusions in foliated spaces N2 - We consider an SDE driven by a Lévy noise on a foliated manifold, whose trajectories stay on compact leaves. We determine the effective behavior of the system subject to a small smooth transversal perturbation of positive order epsilon. More precisely, we show that the average of the transversal component of the SDE converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to the invariant measures on the leaves (of the unpertubed system) as epsilon goes to 0. In particular we give upper bounds for the rates of convergence. The main results which are proved for pure jump Lévy processes complement the result by Gargate and Ruffino for Stratonovich SDEs to Lévy driven SDEs of Marcus type. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)10 KW - Averaging principle KW - foliated diffusion KW - Lévy diffusions on manifolds KW - canonical Marcus integration Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64926 SN - 2193-6943 ER - TY - INPR A1 - Méléard, Sylvie A1 - Roelly, Sylvie T1 - Evolutive two-level population process and large population approximations N2 - We are interested in modeling the Darwinian evolution of a population described by two levels of biological parameters: individuals characterized by an heritable phenotypic trait submitted to mutation and natural selection and cells in these individuals influencing their ability to consume resources and to reproduce. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We are looking for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 8 KW - Two-level interacting process KW - birth-death-mutation-competition point process KW - non-linear integro-differential equations Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64604 SN - 2193-6943 ER - TY - INPR A1 - Makhmudov, Olimdjan A1 - Tarkhanov, Nikolai Nikolaevich T1 - An extremal problem related to analytic continuation N2 - We show that the usual variational formulation of the problem of analytic continuation from an arc on the boundary of a plane domain does not lead to a relaxation of this overdetermined problem. To attain such a relaxation, we bound the domain of the functional, thus changing the Euler equations. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 4 KW - Extremal problem KW - Euler equations KW - p-Laplace operator KW - mixed problems Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63634 ER - TY - INPR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - A quasi-random-walk to model a biological transport process N2 - Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 3 KW - Markov chain KW - random walk KW - molecular motor KW - step process Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63582 ER - TY - INPR A1 - Bagderina, Yulia Yu. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Differential invariants of a class of Lagrangian systems with two degrees of freedom N2 - We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 2 KW - equivalence KW - invariant KW - Euler-Lagrange equations Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63129 ER -