TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Cercignani, C., Scaling limits and models in physical process; Basel, Birkhäuser, 1998 BT - Scaling limits and models in physical process Y1 - 1999 ER - TY - JOUR A1 - Lledó, Fernando T1 - Contributions to operator theory in spaces with an indefinite metric, the Heinz Langer anniversary volume, A. S. Dijksma ... eds.; Basel [u.a.], Birkhäuser, 1998, ISBN 3-7643-6003-8 Y1 - 1999 ER - TY - JOUR A1 - Becker, Christian A1 - Schenkel, Alexander A1 - Szabo, Richard J. T1 - Differential cohomology and locally covariant quantum field theory JF - Reviews in Mathematical Physics N2 - We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fréchet–Lie group structure on differential cohomology groups. KW - Algebraic quantum field theory KW - generalized Abelian gauge theory KW - differential cohomology Y1 - 2017 U6 - https://doi.org/10.1142/S0129055X17500039 SN - 0129-055X SN - 1793-6659 VL - 29 IS - 1 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Jahnke, Thomas T1 - Führer, L., Pädagogik des Mathematikunterrichts, eine Einführung in die Fachdidaktik; Braunschweig, Vieweg, 1997 BT - Pädagogik des Mathematikunterrichts : eine Einführung in die Fachdidaktik Y1 - 1998 ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Golusin-Krylov formulas in complex analysis JF - Complex variables and elliptic equations N2 - This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces. KW - Analytic continuation KW - inegral formulas KW - Cauchy problem Y1 - 2017 U6 - https://doi.org/10.1080/17476933.2017.1395872 SN - 1747-6933 SN - 1747-6941 VL - 63 IS - 7-8 SP - 1142 EP - 1167 PB - Routledge CY - Abingdon ER - TY - JOUR A1 - Bölling, Reinhard T1 - Guzevic, D., Petr Petrovic Bazen, 1786 - 1838; Sankt-Peterburg, Nauka, 1995 BT - Petr Petrovic Bazen Y1 - 1997 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Karsinski, A., Inhomogeneous cosmological models; Cambridge, Univ. Press, 1997 BT - Inhomogeneous cosmological models Y1 - 1998 ER - TY - JOUR A1 - Schrohe, Elmar T1 - Lesch, M., Operators of Fuchs type, conical singularities, and asymptotic methods BT - Operators of Fuchs type, conical singularities, and asymptotic methods Y1 - 1998 ER - TY - JOUR A1 - Schrohe, Elmar T1 - Lesch, M., Operators of Fuchs type, conical singularities, and asymptotic methods BT - Operators of Fuchs type, conical singularities, and asymptotic methods Y1 - 1999 ER - TY - JOUR A1 - Bölling, Reinhard T1 - Mathematics of the 19th century, geometry, analytic function theory / ed. by A. N. Kolmogorov ... ;Basel [u.a.], Birkhäuser, 1996 Y1 - 1997 SN - 0036-6978 ER - TY - JOUR A1 - Bölling, Reinhard T1 - Neuenschwander, E., Riemanns Einführung in die Funktionentheorie, eine quellenkritische Edition seiner Vorlesungen mit einer Bibliographie zur Wirkungsgeschichte der Riemannschen Funktionentheorie; Göttingen, Vandenhoeck und Ruprecht, 1996 BT - Riemanns Einführung in die Funktionentheorie:eine quellenkritische Edition seiner Vorlesungen mit einer Bibliographie zur Wirkungsgeschichte der Riemannschen Funktionentheorie Y1 - 1998 SN - 0036-6978 ER - TY - JOUR A1 - van Leeuwen, Peter Jan A1 - Kunsch, Hans R. A1 - Nerger, Lars A1 - Potthast, Roland A1 - Reich, Sebastian T1 - Particle filters for high-dimensional geoscience applications: A review JF - Quarterly journal of the Royal Meteorological Society N2 - 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. KW - hybrids KW - localization KW - nonlinear data assimilation KW - particle filters KW - proposal densities Y1 - 2019 U6 - https://doi.org/10.1002/qj.3551 SN - 0035-9009 SN - 1477-870X VL - 145 IS - 723 SP - 2335 EP - 2365 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Schrohe, Elmar T1 - Schulze, B.-W., Pseudo-Differential Boundary Value Problems, Conical Singularities, and Asymptotics; Berlin, Akademie-Verl., 1995 BT - Pseudo-Differential Boundary Value Problems, Conical Singularities and Asymptotics Y1 - 1995 ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - The tunneling effect for a class of difference operators JF - Reviews in Mathematical Physics N2 - We analyze a general class of self-adjoint difference operators H-epsilon = T-epsilon + V-epsilon on l(2)((epsilon Z)(d)), where V-epsilon is a multi-well potential and v(epsilon) is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]). Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H-epsilon is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H-epsilon, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H-epsilon converge to the first n eigenvalues of the direct sum of harmonic oscillators on R-d located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H-epsilon. These are obtained from eigenfunctions or quasimodes for the operator H-epsilon acting on L-2(R-d), via restriction to the lattice (epsilon Z)(d). Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrodinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted l(2)-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two "wells" (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrodinger operator in [22]. KW - Semiclassical difference operator KW - tunneling KW - interaction matrix KW - asymptotic expansion KW - multi-well potential KW - Finsler distance KW - Agmon estimates Y1 - 2018 U6 - https://doi.org/10.1142/S0129055X18300029 SN - 0129-055X SN - 1793-6659 VL - 30 IS - 4 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Bölling, Reinhard T1 - Tuschmann, W., Hawig, P., Sofia Kowalewskaja, ein Leben für Mathematik und Emanzipation; Basel [u.a.], Birkhäuser, 1993 BT - Sofia Kowalewskaja, ein Leben für Mathematik und Emanzipation Y1 - 1995 ER - TY - JOUR A1 - Schrohe, Elmar T1 - Wloka, J. T. [u.a.], Boundary value problems for eliptic systems BT - Boundary value problems for eliptic systems Y1 - 1998 ER -