470 results
Search Results
Now showing 1 - 10 of 470
- ItemDiffraction of stochastic point sets : exactly solvable examples(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Baake, Michael; Birkner, Matthias; Moody, Robert V.Stochastic point sets are considered that display a diffraction spectrum of mixed type, with special emphasis on explicitly computable cases together with a unified approach of reasonable generality. Several pairs of autocorrelation and diffraction measures are discussed that show a duality structure that may be viewed as analogues of the Poisson summation formula for lattice Dirac combs.
- ItemDiscretisation of the Maxwell equations on tetrahedral grids(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2003) Schefter, JürgenThe aim of this report is to describe the discretisation of the Maxwell equations on tetrahedral grids with corresponding dual Voronoi cells to explain the resulting program. The symmetry of the coefficients of the matrix is proven. A small example shows an input file and same other details.
- ItemSimple vector bundles on plane degenerations of an elliptic curve(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Bodnarchuk, Lesya; Drozd, Yuriy; Greuel, Gert-MartinIn 1957 Atiyah classifed simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classifcation by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that a simple vector bundle on such a curve is completely determined by its rank, multidegree and determinant. Our approach, based on the representation theory of boxes, also yields an explicit description of the corresponding universal families of simple vector bundles.
- ItemHeuristic parameter selection based on functional minimization : optimality and model function approach(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Lu, Shuai; Mathé, KarstenWe analyze some parameter choice strategies in regularization of inverse problems, in particular the (modified) L-curve method and a variant of the Hanke-Raus rule. These are heuristic rules, free of the noise level, and they are based on minimization of some functional. We analyze these functionals, and we prove some optimality results under general smoothness conditions. We also devise some numerical approach for finding the minimizers, which uses model functions. Numerical experiments indicate that this is an efficient numerical procedure.
- ItemHomological properties of piecewise hereditary algebras(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Happel, Dieter; Zacharia, DanLet Delta be a finite dimensional algebra over an algebraically closed field k. We will investigate homological properties of piecewise hereditary algebras Delta. In particular we give lower and upper bounds of the strong global dimension, show the behavior of the strong global under one point extensions and tilting. Moreover we show that the pieces of mod Delta have Auslander-Reiten sequence.
- ItemHölder-differentiability of Gibbs distribution functions(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Kesseböhmer, Marc; Stratmann, Bernd O.In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil’s staircases) supported on limit sets of finitely generated conformal iterated function systems in R. For a large class of these Gibbs states we determine the Hausdorff dimension of the set of points at which the distribution function of these measures is not a-Hölder-differentiable. The obtained results give significant extensions of recent work by Darst, Dekking, Falconer, Li, Morris, and Xiao. In particular, our results clearly show that the results of these authors have their natural home within thermodynamic formalism.
- ItemFinite element error analysis for state-constrained optimal control of the Stokes equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Reyes, Juan Carlos de los; Meyer, Christian; Vexler, BorisAn optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerened with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the $L^infty$-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the $L^infty$-finite-element-error can be verified for different numerical settings. The theoretical results are confirmed by numerical examples.
- ItemLarge time asymptotics of growth models on space-like paths II: PNG and parallel TASEP(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Borodin, Alexei; Ferrari, Patrik; Sasamoto, TomohiroWe consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy$_1$ process. This result holds more generally for the observation points located along any space-like path in the space-time plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update.
- ItemExistence and stability of solutions with periodically moving weak internal layers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Butuzov, V.F.; Nefedpv, N.N.; Recke, L.; Schneider, K.R.We consider the periodic parabolic differential equation $ep^2 Big( fracpartial^2 upartial x^2 -fracpartial upartial t Big)=f(u,x,t,ep)$ under the assumption that $ve$ is a small positive parameter and that the degenerate equation $f(u,x,t,0) =0$ has two intersecting solutions. We derive conditions such that there exists an asymptotically stable solution $u_p(x,t,ep)$ which is $T$-periodic in $t$, satisfies no-flux boundary conditions and tends to the stable composed root of the degenerate equation as $eprightarrow 0$.
- ItemElastic half plane under random boundary excitations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Shalimova, Irina; Sabel'fel'd, Karl K.We study in this paper a respond of an elastic half-plane to random boundary excitations. We treat both the white noise excitations and more generally, homogeneous random fluctuations of displacements prescribed on the boundary. Solutions to these problems are inhomogeneous random fields which are however homogeneous with respect to the longitudinal coordinate. This is used to represent the displacements as series expansions involving a complete set of deterministic functions with corresponding random coefficients. We construct the Karhunen-Loève (K-L) series expansion which is based on the eigen-decomposition of the correlation operator. The K-L expansion can be used to calculate the statistical characteristics of other functionals of interest, in particular, the strain and stress tensors and the elastic energy tensor.