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- Zustandsschätzung (1)
- Zählprozesse (1)
- a posteriori stopping rule (1)
- absorbing boundary (1)
- absorbing set (1)
- absorption (1)
- accelerated life time model (1)
- accelerated small (1)
- accuracy (1)
- acute severe (1)
- adaptive (1)
- adaptivity (1)
- adipose tissue (1)
- adrenal insufficiency (1)
- aerosol (1)
- aerosol distribution (1)
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- aerosols (1)
- affine (1)
- affine invariance (1)
- algebra (1)
- algebra of rank n (1)
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- algebras (1)
- alignment (1)
- alternating direction implicit (1)
- alternative variety (1)
- amoeboid motion (1)
- amöboide Bewegung (1)
- analytic functional (1)
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- asymptotic (1)
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- asymptotic expansions (1)
- asymptotic methods (1)
- asymptotic properties of eigenfunctions (1)
- asymptotic stable (1)
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- asymptotics (1)
- asymptotics of solutions (1)
- asymptotische Entwicklung (1)
- asymptotische Normalverteilung (1)
- attenuated Radon transform (1)
- aurora (1)
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- b-value (1)
- backtrajectories; (1)
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- balanced dynamics (1)
- bar with variable cross-section (1)
- basic ideas ('Grundvorstellungen') (1)
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- bedingter Erwartungswert (1)
- behavior (1)
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- compressible Euler equations (1)
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- conditioned (1)
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- conditions (1)
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- congenital adrenal hyperplasia (1)
- congruence (1)
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- convergence assessment (1)
- convergence rate (1)
- corner parametrices (1)
- corona virus (1)
- correlated noise (1)
- cortisol (1)
- coupled solution (1)
- covering (1)
- critical and subcritical Dawson-Watanabe process (1)
- criticality theorem (1)
- criticality theory (1)
- critically ill (1)
- crohn's disease (1)
- crossed product (1)
- curvature varifold (1)
- cusp (1)
- cusped bar (1)
- das Cauchyproblem (1)
- das Goursatproblem (1)
- das charakteristische Cauchyproblem (1)
- data-driven (1)
- dbar-Neumann problem (1)
- de Sitter model ; Fundamental solutions ; Decay estimates (1)
- decay of eigenfunctions (1)
- decomposition (1)
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- degenerate elliptic equations (1)
- degenerate elliptic systems (1)
- delaney-dress tiling theory (1)
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- disagreement percolation (1)
- discontinuous Robin condition (1)
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- discrete Schrodinger (1)
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- diskreter Witten-Laplace-Operator (1)
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- distribution (1)
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- distributions with one-sided support (1)
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- doppelsemigroup (1)
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- edge Sobolev spaces (1)
- edge algebra (1)
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- edge quantizations (1)
- edge spaces (1)
- edge symbol (1)
- edge- and corner-degenerate symbols (1)
- eigenfunction (1)
- eigenvalue asymptotics (1)
- eigenvalue decay (1)
- eigenvalues (1)
- elastic bar (1)
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- elliptic boundary (1)
- elliptic boundary conditions (1)
- elliptic complex (1)
- elliptic differential operators of firstorder (1)
- elliptic equation (1)
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- elliptic morphism (1)
- elliptic operators in subspaces (1)
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- elliptic problem (1)
- elliptic problems (1)
- elliptic quasicomplexes (1)
- elliptic systems (1)
- ellipticity in the edge calculus (1)
- ellipticity of cone operators (1)
- ellipticity of corners operators (1)
- ellipticity with interface conditions (1)
- ellipticity with parameter (1)
- ellipticity with respect to interior and edge symbols (1)
- elliptische Gleichungen (1)
- elliptische Quasi-Komplexe (1)
- embedded Markov chain (1)
- embeddings (1)
- empirical Wasserstein distance (1)
- endomorphism semigroup (1)
- energetic space (1)
- enlargement of filtration (1)
- ensembles (1)
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- equatorial ionosphere (1)
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- equivalence (1)
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- error diagram (1)
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- essential position in terms (1)
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- expansion (1)
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- exponential function (1)
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- exterior tensor product (1)
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- fat-free mass (1)
- feedback (1)
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- fibration (1)
- fibre coordinates (1)
- fibroblasts (1)
- field-aligned currents (1)
- filtering (1)
- finite transformation semigroup (1)
- finiteness theorem (1)
- finsler distance (1)
- first exit location (1)
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- illposed problem (1)
- indecomposable varifold (1)
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- inegral formulas (1)
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- invariance (1)
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- manifold (1)
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- minor planets, asteroids: individual: (162173) Ryugu (1)
- mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung (1)
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Institute
- Institut für Mathematik (2160) (remove)
Our work goes in two directions. At first we want to transfer definitions, concepts and results of the theory of hyperidentities and solid varieties from the total to the partial case. (1) We prove that the operators chi^A_RNF and chi^E_RNF are only monotone and additive and we show that the sets of all fixed points of these operators are characterized only by three instead of four equivalent conditions for the case of closure operators. (2) We prove that V is n − SF-solid iff clone^SF V is free with respect to itself, freely generated by the independent set {[fi(x_1, . . . , x_n)]Id^SF_n V | i \in I}. (3) We prove that if V is n-fluid and ~V |P(V ) =~V −iso |P(V ) then V is kunsolid for k >= n (where P(V ) is the set of all V -proper hypersubstitutions of type \tau ). (4) We prove that a strong M-hyperquasi-equational theory is characterized by four equivalent conditions. The second direction of our work is to follow ideas which are typical for the partial case. (1) We characterize all minimal partial clones which are strongly solidifyable. (2)We define the operator Chi^A_Ph where Ph is a monoid of regular partial hypersubstitutions.Using this concept, we define the concept of a Phyp_R(\tau )-solid strong regular variety of partial algebras and we prove that a PHyp_R(\tau )-solid strong regular variety satisfies four equivalent conditions.
Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity
(2006)
We consider scattering in $\R^n$, $n\ge 2$, described by the Schr\"odinger operator $P(h)=-h^2\Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\to 0$ of the scattering amplitude $f(\omega_-,\omega_+;\lambda,h)$ $\omega_+\neq\omega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.
We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time.
We analyze the asymptotic behavior in the limit epsilon to zero for a wide class of difference operators H_epsilon = T_epsilon + V_epsilon with underlying multi-well potential. They act on the square summable functions on the lattice (epsilon Z)^d. We start showing the validity of an harmonic approximation and construct WKB-solutions at the wells. Then we construct a Finslerian distance d induced by H and show that short integral curves are geodesics and d gives the rate for the exponential decay of Dirichlet eigenfunctions. In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix.
We consider a system of infinitely many hard balls in R<sup>d undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.
We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.
Ergodicity of PCA
(2004)
For a general attractive Probabilistic Cellular Automata on S-Zd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {1,+1}(Zd), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths C[0; 1]; R-d) Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov.
We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field.