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- ItemArbeitsgemeinschaft mit aktuellem Thema: Polylogarithms(Zürich : EMS Publ. House, 2004) Kings, Guido; Wildeshaus, Jörg[no abstract available]
- ItemThe Mathematical, Computational and Biological Study of Vision(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2001) von der Malsburg, Christoph; Mumford, David[no abstract available]
- ItemStratifying modular representations of finite groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Benson, Dave; Iyengar, Srikanth B.; Krause, HenningWe classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Along the way we establish similar classifications for differential graded modules over graded polynomial rings, and over graded exterior algebras.
- ItemSimulations of 3D/4D precipitation processes in a turbulent flow field(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) John, Volker; Roland, MichaelPrecipitation processes are modeled by population balance systems. A very expensive part of the simulation of population balance systems is the solution of the equation for the particle size distribution (PSD) since this equation is defined in a higher dimensional domain than the other equations in the system. This paper studies different approaches for the solution of this equation: two finite difference upwind schemes and a linear finite element flux--corrected transport method. It is shown that the different schemes lead to qualitatively different solutions for an output of interest.
- ItemPlasma induced pulse breaking in filamentary self-compression(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Brée, Carsten; Demircan, Ayhan; Skupin, Stefan; Berg´e, Luc; Steinmeyer, GünterA plasma induced temporal break-up in filamentary propagation has recently been identified as one of the key events in the temporal self-compression of femtosecond laser pulses. An analysis of the Nonlinear Schrödinger Equation coupled to a noninstantaneous plasma response yields a set of stationary states. This analysis clearly indicates that the emergence of double-hump, characteristically asymmetric temporal on-axis intensity profiles in regimes where plasma defocusing saturates the optical collapse caused by Kerr self-focusing is an inherent property of the underlying dynamical model.
- ItemAdaptive Numerical Methods for PDEs(Zürich : EMS Publ. House, 2007) Süli, Endre; Verfürth, RüdigerThis collection contains the extended abstracts of the talks given at the Oberwolfach Conference on “Adaptive Numerical Methods for PDEs”, June 10th - June 16th, 2007. These talks covered various aspects of a posteriori error estimation and mesh as well as model adaptation in solving partial differential equations. The topics ranged from the theoretical convergence analysis of self-adaptive methods, over the derivation of a posteriori error estimates for the finite element Galerkin discretization of various types of problems to the practical implementation and application of adaptive methods.
- ItemApplications of Asymptotic Analysis(Zürich : EMS Publ. House, 2006) Palencia, E. Sanchez; Sokolowski, Jan; Wagner, BarbaraThis workshop focused on asymptotic analysis and its fundamental role in the derivation and understanding of the nonlinear structure of mathematical models in various fields of applications, its impact on the development of new numerical methods and on other fields of applied mathematics such as shape optimization. This was complemented by a review as well as the presentation of some of the latest developments of singular perturbation methods.
- ItemPositivität von Polynomen(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2002) Berg, Christian; Prestel, Alexander[no abstract available]
- ItemLinear stability analysis of ta sharp-interface model for dewetting thin films(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) King, John R.; Münch, Andreas; Wagner, BarbaraThe topic of this study concerns the stability of the three-phase contact-line of a dewetting thin liquid film on a hydrophobised substrate driven by van der Waals forces. The role of slippage in the emerging instability at the three-phase contact-line is studied by deriving a sharp-interface model for the dewetting thin film via matched asymptotic expansions. This allows for a derivation of travelling waves and their linear stability via eigenmode analysis. In contrast to the dispersion relations typically encountered for the finger-instabilty, where the dependence of the growth rate on the wave number is quadratic, here it is linear. Using the separation of time scales of the slowly growing rim of the dewetting film and time scale on which the contact line destabilises, the sharp-interface results are compared to earlier results for the full lubrication model and good agreement for the most unstable modes is obtained.
- ItemMaximal convergence theorems for functions of squared modulus holomorphic type and various applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Kraus, ChristianeIn this paper we extend the theory of maximal convergence introduced by Walsh to functions of squared modulus holomorphic type. We introduce in accordance to the well-known complex maximal convergence number for holomorphic functions a real maximal convergence number for functions of squared modulus holomorphic type and prove several maximal convergence theorems. We achieve that the real maximal convergence number for F is always greater or equal than the complex maximal convergence number for g and equality occurs if L is a closed disk in R^2. Among other various applications of the resulting approximation estimates we show that for functions F of squared holomorphic type which have no zeros in a closed disk B_r the relation limsupntoinftysqrt[n]En(Br,F)=limsupntoinftysqrt[n]En(partialBr,F) is valid, where E_n is the polynomial approximation error.