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 - 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 - 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 - 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 - 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 - Cierjacks, Arne A1 - Kowarik, Ingo A1 - Joshi, Jasmin Radha A1 - Hempel, Stefan A1 - Ristow, Michael A1 - von der Lippe, Moritz A1 - Weber, Ewald T1 - Biological flora of the british isles: robinia pseudoacacia T2 - The journal of ecology N2 - This account presents information on all aspects of the biology of Robinia pseudoacacia L. that are relevant to understanding its ecological characteristics and behaviour. The main topics are presented within the standard framework of the Biological Flora of the British Isles: distribution, habitat, communities, responses to biotic factors, responses to environment, structure and physiology, phenology, floral and seed characters, herbivores and disease, and history and conservation.Robinia pseudoacacia, false acacia or black locust, is a deciduous, broad-leaved tree native to North America. The medium-sized, fast-growing tree is armed with spines, and extensively suckering. It has become naturalized in grassland, semi-natural woodlands and urban habitats. The tree is common in the south of the British Isles and in many other regions of Europe.Robinia pseudoacacia is a light-demanding pioneer species, which occurs primarily in disturbed sites on fertile to poor soils. The tree does not tolerate wet or compacted soils. In contrast to its native range, where it rapidly colonizes forest gaps and is replaced after 15-30years by more competitive tree species, populations in the secondary range can persist for a longer time, probably due to release from natural enemies.Robinia pseudoacacia reproduces sexually, and asexually by underground runners. Disturbance favours clonal growth and leads to an increase in the number of ramets. Mechanical stem damage and fires also lead to increased clonal recruitment. The tree benefits from di-nitrogen fixation associated with symbiotic rhizobia in root nodules. Estimated symbiotic nitrogen fixation rates range widely from 23 to 300kgha(-1)year(-1). The nitrogen becomes available to other plants mainly by the rapid decay of nitrogen-rich leaves.Robinia pseudoacacia is host to a wide range of fungi both in the native and introduced ranges. Megaherbivores are of minor significance in Europe but browsing by ungulates occurs in the native range. Among insects, the North American black locust gall midge (Obolodiplosis robiniae) is specific to Robinia and is spreading rapidly throughout Europe. In parts of Europe, Robinia pseudoacacia is considered an invasive non-indigenous plant and the tree is controlled. Negative impacts include shading and changes of soil conditions as a result of nitrogen fixation. KW - climatic limitation KW - ecophysiology KW - geographical and altitudinal distribution KW - germination KW - invasive KW - mycorrhiza KW - nitrogen fixation KW - parasites and diseases KW - reproductive biology KW - soils Y1 - 2013 U6 - https://doi.org/10.1111/1365-2745.12162 SN - 0022-0477 SN - 1365-2745 VL - 101 IS - 6 SP - 1623 EP - 1640 PB - Wiley-Blackwell CY - Hoboken 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 - 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 - TY - INPR A1 - Kaufmann, Liane A1 - Mazzocco, Michele M. A1 - Dowker, Ann A1 - von Aster, Michael G. A1 - Goebel, Silke M. A1 - Grabner, Roland H. A1 - Henik, Avishai A1 - Jordan, Nancy C. A1 - Karmiloff-Smith, Annette D. A1 - Kucian, Karin A1 - Rubinsten, Orly A1 - Szucs, Denes A1 - Shalev, Ruth A1 - Nuerk, Hans-Christoph T1 - Dyscalculia from a developmental and differential perspective T2 - Frontiers in psychology Y1 - 2013 U6 - https://doi.org/10.3389/fpsyg.2013.00516 SN - 1664-1078 VL - 4 IS - 2 PB - Frontiers Research Foundation CY - Lausanne 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 -