Filtern
Erscheinungsjahr
- 2016 (71) (entfernen)
Dokumenttyp
- Wissenschaftlicher Artikel (48)
- Preprint (11)
- Dissertation (10)
- Monographie/Sammelband (1)
- Masterarbeit (1)
Sprache
- Englisch (71)
Gehört zur Bibliographie
- ja (71) (entfernen)
Schlagworte
- Cox model (2)
- Scientific discovery learning (2)
- conjugate gradient (2)
- geodesic distance (2)
- index (2)
- local time (2)
- minimax convergence rates (2)
- partial least squares (2)
- reproducing kernel Hilbert space (2)
- stochastic differential equations (2)
- (generalised) wealdy differentiable function (1)
- (sub-) tropical Africa (1)
- (sub-) tropisches Afrika (1)
- AFM (1)
- Aerosole (1)
- Asymptotic variance of maximum partial likelihood estimate (1)
- Asymptotics of solutions (1)
- Bivariant K-theory (1)
- Brownian motion with discontinuous drift (1)
- Calculation (1)
- Case-Cohort-Design (1)
- Cauchy problem (1)
- Cheeger inequalities (1)
- Classification (1)
- Clifford algebra (1)
- Computer simulations (1)
- Conceptual change (1)
- Cone and edge pseudo-differential operators (1)
- Cox-Modell (1)
- Critical mathematics education (1)
- Critique (1)
- Data assimilation (1)
- Definitions (1)
- Detektion multipler Übergänge (1)
- Determinante (1)
- Diagrams (1)
- Dichte eines Maßes (1)
- Digital technology (1)
- Dirac operator (1)
- Dirichlet-to-Neumann operator (1)
- DySEM (1)
- Edge degenerate operators (1)
- Ellipticity of edge-degenerate operators (1)
- Ensemble Kalman filter (1)
- Estimability (1)
- FIB patterning (1)
- Fitness (1)
- Foucault (1)
- Fourier transform (1)
- Fredholm operator (1)
- Fredholm property (1)
- Fuzzy logic (1)
- Geomagnetic field (1)
- Geomagnetic models (1)
- Geometry (1)
- Gestures (1)
- Gibbs processes (1)
- Goal specificity (1)
- Graph Laplacians (1)
- HIV (1)
- HIV Erkrankung (1)
- Hodge theory (1)
- Holder-type source condition (1)
- Integrability (1)
- Intrinsic metrics for Dirichlet forms (1)
- Inversion (1)
- Ionospheric current (1)
- Kombinationstherapie (1)
- Laplace expansion (1)
- Lidar (1)
- Linearized equation (1)
- Lyapunov function (1)
- Lévy type processes (1)
- Markov-field property (1)
- Marx (1)
- Mellin and Green operators edge symbols (1)
- Mellin operators (1)
- Mellin oscillatory integrals (1)
- Mellin-Symbole (1)
- Mellin-Symbols (1)
- Meromorphic operator-valued symbols (1)
- Mikrophysik (1)
- Misconceptions (1)
- Moduli space (1)
- Multiple problem spaces (1)
- Navier-Stokes equations (1)
- Neumann problem (1)
- Nonlinear ill-posed problems (1)
- Nonparametric regression (1)
- Operator algebras (1)
- Ordnungs-Filtrierung (1)
- Paleoclimate reconstruction (1)
- Papangelou processes (1)
- Pfadintegrale (1)
- Pharmakokinetik (1)
- Physics concepts (1)
- Plio-Pleistocene (1)
- Plio-Pleistozän (1)
- Poincare inequality (1)
- Positive mass theorem (1)
- Problem solving (1)
- Proving (1)
- Proxy forward modeling (1)
- Pseudo-differential operators (1)
- Quasilinear equations (1)
- Rectifiable varifold (1)
- Regularisierung (1)
- Removable sets (1)
- Retrieval (1)
- Rho invariants (1)
- Ricci solitons (1)
- Riemann-Hilbert problem (1)
- Runge-Kutta methods (1)
- Skew Diffusionen (1)
- Sobolev Poincare inequality (1)
- Spectral theory of graphs (1)
- Stability selection (1)
- Subsampling (1)
- Surgery (1)
- Symplectic manifold (1)
- Technology (1)
- Three-space theory (1)
- Variable selection (1)
- Varifaltigkeit (1)
- Visuospatial reasoning (1)
- Wasserstein distance (1)
- Wiener measure (1)
- Wärmekern (1)
- Wärmeleitungsgleichung (1)
- Yamabe operator (1)
- aerosols (1)
- approximate differentiability (1)
- asymptotic expansion (1)
- asymptotische Entwicklung (1)
- boundary value problems (1)
- calculus of variations (1)
- characterization of point processes (1)
- clone (1)
- coarea formula (1)
- composition of terms (1)
- consistency (1)
- curvature varifold (1)
- decomposition (1)
- density of a measure (1)
- determinant (1)
- direct and indirect climate observations (1)
- direkte und indirekte Klimaobservablen (1)
- discontinuous drift (1)
- discrete spectrum (1)
- diskontinuierliche Drift (1)
- distributional boundary (1)
- division of spaces (1)
- eigenvalue asymptotics (1)
- elliptic complex (1)
- elliptic complexes (1)
- enlargement of filtration (1)
- erste Variation (1)
- essential position in terms (1)
- exact simulation (1)
- exact simulation method (1)
- exakte Simulation (1)
- exit calculus (1)
- first variation (1)
- generating sets (1)
- geodätischer Abstand (1)
- hard core interaction (1)
- heat asymptotics (1)
- heat equation (1)
- heat kernel (1)
- heavy-tailed distributions (1)
- ill-posed (1)
- indecomposable varifold (1)
- independent splittings (1)
- integral representation method (1)
- intrinsic diameter (1)
- intrinsischer Diameter (1)
- inversion (1)
- isoperimetric estimates (1)
- isoperimetric inequality (1)
- isoperimetrische Ungleichung (1)
- kernel method (1)
- kernel-based Bayesian inference (1)
- kernel-basierte Bayes'sche Inferenz (1)
- label noise (1)
- lattice packing and covering (1)
- lidar (1)
- linear hyperidentity (1)
- linear hypersubstitution (1)
- linear identity (1)
- linear term (1)
- logistic regression analysis (1)
- logistische Regression (1)
- manifold with boundary (1)
- mathematical modelling (1)
- mathematische Modellierung (1)
- mean curvature (1)
- microphysics (1)
- minimax rate (1)
- mittlere Krümmung (1)
- mixture proportion estimation (1)
- modal analysis (1)
- model selection (1)
- multi-change point detection (1)
- multilevel Monte Carlo (1)
- multiplicative Lévy noise (1)
- nonparametric regression (1)
- normal reflection (1)
- operator valued symbols (1)
- optimal transport (1)
- order filtration (1)
- p-Laplace equation (1)
- p-Laplace operator (1)
- parameter estimation (1)
- partial clone (1)
- path integral (1)
- periodic Gaussian process (1)
- periodic Ornstein-Uhlenbeck process (1)
- pharmacokinetics (1)
- polyhedra and polytopes (1)
- rectifiable varifold (1)
- regular figures (1)
- regularization (1)
- regularization methods (1)
- rektifizierbare Varifaltigkeit (1)
- relative isoperimetric inequality (1)
- relative ranks (1)
- restricted range (1)
- retrieval (1)
- reversible measure (1)
- schlecht gestellt (1)
- sequential data assimilation (1)
- singular manifolds (1)
- singuläre Mannigfaltigkeiten (1)
- skew Brownian motion (1)
- skew diffusion (1)
- skew diffusions (1)
- stable variety (1)
- star product (1)
- statistical inverse problem (1)
- stochastic completeness (1)
- stopping rules (1)
- structured cantilever (1)
- surrogate loss (1)
- survival analysis (1)
- terrigener Staub (1)
- terrigenous dust (1)
- time series (1)
- trace (1)
- transformation semigroups (1)
- unzerlegbare Varifaltigkeit (1)
- varifold (1)
- viral fitness (1)
- weighted Hölder spaces (1)
- weighted Sobolev spaces (1)
Institut
- Institut für Mathematik (71) (entfernen)
We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed
problems, and construct an explicit formula for approximate solutions.
Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.
We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.
Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved.
We analyze a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2)(((epsilon)Z)(d)), where V-epsilon is a multi-well potential and epsilon is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted l(2)-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators.
We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed Hölder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fréchet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of Hölder spaces.
Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving.
We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles.
We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.
The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.