Refine
Year of publication
Document Type
- Preprint (566) (remove)
Language
- English (528)
- German (35)
- Multiple languages (2)
- French (1)
Keywords
- index (11)
- boundary value problems (9)
- elliptic operators (9)
- Fredholm property (8)
- K-theory (7)
- manifolds with singularities (6)
- pseudodifferential operators (6)
- relative index (6)
- Atiyah-Patodi-Singer theory (5)
- index theory (5)
- Boundary value problems (4)
- Cauchy problem (4)
- Toeplitz operators (4)
- cluster expansion (4)
- elliptic operator (4)
- manifold with singularities (4)
- mental number line (4)
- numerical cognition (4)
- reversible measure (4)
- surgery (4)
- 'eta' invariant (3)
- Atiyah-Bott condition (3)
- Fredholm operators (3)
- Hodge theory (3)
- Lefschetz number (3)
- Stochastic Differential Equation (3)
- boundary value problem (3)
- conical singularities (3)
- conormal symbol (3)
- differential operators (3)
- elliptic complexes (3)
- ellipticity (3)
- eta invariant (3)
- hard core potential (3)
- index of elliptic operators in subspaces (3)
- local time (3)
- reciprocal class (3)
- regularization (3)
- spectral flow (3)
- star product (3)
- Atiyah-Bott obstruction (2)
- Brownian bridge (2)
- Brownian motion (2)
- Canonical Gibbs measure (2)
- Carleman matrix (2)
- Chemotaxis (2)
- Climate change (2)
- Dirac operator (2)
- Gibbs measure (2)
- Heat equation (2)
- Laplace equation (2)
- Lefschetz fixed point formula (2)
- Markov chain (2)
- Markov processes (2)
- Mellin transform (2)
- Navier-Stokes equations (2)
- Neumann problem (2)
- Perturbed complexes (2)
- Probabilistic Cellular Automata (2)
- Riemann-Hilbert problem (2)
- Riemannian manifold (2)
- WKB method (2)
- Zaremba problem (2)
- aerosol size distribution (2)
- analytic continuation (2)
- attention (2)
- birth-death-mutation-competition point process (2)
- counting process (2)
- curvature (2)
- detailed balance equation (2)
- duality formula (2)
- edge singularities (2)
- edge-degenerate operators (2)
- elliptic boundary value problems (2)
- elliptic families (2)
- elliptic family (2)
- elliptic system (2)
- eta-invariant (2)
- holomorphic solution (2)
- homotopy classification (2)
- ill-posed problem (2)
- index formulas (2)
- integral formulas (2)
- inversion (2)
- linking coefficients (2)
- manifolds with conical singularities (2)
- manifolds with edges (2)
- maximum likelihood estimator (2)
- modn-index (2)
- molecular motor (2)
- monodromy matrix (2)
- non-Markov drift (2)
- p-Laplace operator (2)
- pseudo-differential boundary value problems (2)
- pseudodiferential operators (2)
- pseudodifferential operator (2)
- quantization (2)
- reciprocal processes (2)
- regularizer (2)
- regularizers (2)
- root functions (2)
- singular partial differential equation (2)
- singular perturbation (2)
- skew Brownian motion (2)
- spatial cognition (2)
- spectral theorem (2)
- star-product (2)
- stochastic differential equations (2)
- symmetry conditions (2)
- the Cauchy problem (2)
- time duality (2)
- weighted edge spaces (2)
- weighted spaces (2)
- (co)boundary operator (1)
- 2AFC (1)
- APS problem (1)
- Adaptive evolution (1)
- Agrarwissenschaft (1)
- Agricultural Science (1)
- Air showers (1)
- Alan Kennedy (1)
- Anti-doping (1)
- Approximate likelihood (1)
- Artificial selection (1)
- Athlete (1)
- Atiyah-Singer theorem (1)
- Attitude (1)
- Attractive Dynamics (1)
- Automatisches Beweisen (1)
- Averaging principle (1)
- Beltrami equation (1)
- Betriebssysteme (1)
- Bibel (1)
- Bose-Einstein condensation (1)
- Botanic gardens (1)
- Boundary value methods (1)
- Boundary value problems for first order systems (1)
- Boundary-contact problems (1)
- Brownian motion with discontinuous drift (1)
- C0−semigroup (1)
- CCR-algebra (1)
- Calculus of conormal symbols (1)
- Calderón projections (1)
- Capture into resonance (1)
- Carbon (1)
- Carleman formulas (1)
- Carrera Digital D132 (1)
- Casped plates (1)
- Categories of stratified spaces (1)
- Cauchy Riemann operator (1)
- Cauchy data spaces (1)
- Censoring (1)
- Cherenkov Telescopes (1)
- Chern character (1)
- Clifford algebra (1)
- Climate variability (1)
- Clonal plants (1)
- Corner boundary value problems (1)
- Coupling (1)
- Crack theory (1)
- Cross-effects (1)
- Cycling (1)
- DLR equation (1)
- DPLL (1)
- Data Protection (1)
- Database (1)
- Datenschutz (1)
- Decoupling (1)
- Delphi study (1)
- Diophantine Approximation (1)
- Dirac operators (1)
- Dirac-type operator (1)
- Dirichlet form (1)
- Dirichlet problem (1)
- Dirichlet to Neumann operator (1)
- Dirichlet-to-Neumann operator (1)
- Dispersal (1)
- Drug (1)
- Dtn. 6:18 (1)
- Duality formula (1)
- Earth Sciences (1)
- Echtzeit (1)
- Ecosystem function (1)
- Edge-degenerate operators (1)
- Editorial policies (1)
- Eigenvalues (1)
- Elliptic equation with order degeneration (1)
- Elliptic operators (1)
- Elliptic operators in domains with edges (1)
- Environmental Sciences (1)
- Erfahrungsbericht (1)
- Euler equations (1)
- Euler operator (1)
- Euler's theta functions (1)
- Euler-Lagrange equations (1)
- Evidence-based policy making (1)
- Ex situ conservation (1)
- Extremal problem (1)
- Eye movements (1)
- Eyemind assumption (1)
- Feynman-Kac formula (1)
- Finite difference method (1)
- Fischer-Riesz equations (1)
- Foot orthoses (1)
- Form (1)
- Forschungsdaten (1)
- Fourth order Sturm-Liouville problem (1)
- Fredholm operator (1)
- Functional diversity (1)
- Functional traits (1)
- G-index (1)
- G-trace (1)
- Genetic drift (1)
- Geowissenschaften (1)
- Gevrey classes (1)
- Gibbs perturbation (1)
- Gibbs point processes (1)
- Gibbs state (1)
- Girsanov formula (1)
- Goursat problem (1)
- Green and Mellin edge operators (1)
- Green formula (1)
- Green operator (1)
- Green's operator (1)
- Grushin operator (1)
- Gutzwiller formula (1)
- Halacha (1)
- Halakhah (1)
- Hamilton-Jacobi theory (1)
- Hamiltonian group action (1)
- Hardy‘s inequality (1)
- Hyperbolic-parabolic system (1)
- Hypoelliptic operators (1)
- Hypoellipticity (1)
- Hölder-type source condition (1)
- Ill-posed problem (1)
- In-shoe measurement (1)
- Infinite-dimensional SDE (1)
- Integrability (1)
- Interacting Particle Systems (1)
- Judaism (1)
- Judentum (1)
- KS model (1)
- Klausellernen (1)
- Knowledge creep (1)
- Knowledge utilization (1)
- Kolmogorov-Smirnov type tests (1)
- Korn’s weighted inequality (1)
- LEGO Mindstorms EV3 (1)
- Lagrangian system (1)
- Lame system (1)
- Lamé system (1)
- Land use (1)
- Landscape (1)
- Laplace-Beltrami operator (1)
- Levy measure (1)
- Levy process (1)
- Liouville theorem (1)
- Lipschitz domains (1)
- Logarithmic Sobolev inequality (1)
- Logikkalkül (1)
- Logrank test (1)
- Loop space (1)
- Lévy diffusion approximation (1)
- Lévy diffusions on manifolds (1)
- Lévy measure (1)
- Lévy type processes (1)
- Lφ spectrum (1)
- MHD-equations (1)
- Malliavin calculus (1)
- Management (1)
- Markov-field property (1)
- Martin-Dynkin boundary (1)
- Maslov and Conley–Zehnder index (1)
- Meromorphic operator functions (1)
- Modality (1)
- Modelling (1)
- Montel theorem (1)
- Morse-Smale property (1)
- Multidimensional nonisentropic hydrodynamic model (1)
- Multiwavelength LIDAR (1)
- Newton method (1)
- Non-linear (1)
- Non-proportional hazards (1)
- Nonlinear (1)
- Nonlinear Laplace operator (1)
- Numerov's method (1)
- Operators on manifolds with conical singularities (1)
- Operators on manifolds with edge (1)
- Operators on manifolds with edge and conical exit to infinity (1)
- Operators on manifolds with second order singularities (1)
- Organizational epistemology (1)
- Orthoptera (1)
- Peano phenomena (1)
- Perron's method (1)
- Planetary Rings (1)
- Plant growth (1)
- Plantar Pressure Distribution (1)
- Point process (1)
- Poisson bridge (1)
- Pontrjagin duality (1)
- Prohibited performance enhancement (1)
- Proportional hazards (1)
- Pseudo-differential operators (1)
- Pseudodifferential operators (1)
- Punctuated equilibrium theory (1)
- Quasiconformal mapping (1)
- Quasilinear equations (1)
- Quasilinear hyperbolic system (1)
- ROC curve (1)
- RT_PREEMT patch (1)
- RT_PREEMT-Patch (1)
- Ramified Cauchy problem (1)
- Reading (1)
- Reciprocal process (1)
- Renormalized integral (1)
- Research Data (1)
- Riemann-Roch theorem (1)
- Runge-Kutta methods (1)
- SAT (1)
- SNARC (1)
- SNARC effect (1)
- SPECT (1)
- Saturation model (1)
- Scene perception (1)
- Schrödinger problem (1)
- Second order elliptic equations (1)
- Serial and parallel (1)
- Skorokhod' s invariance principle (1)
- Sobolev problem (1)
- Sobolev spaces with double weights on singular cones (1)
- Statistics (1)
- Stochastic Ordering (1)
- Stochastic differential equations (1)
- Sturm-Liouville problems (1)
- Surface potentials with asymptotics (1)
- Survival models with covariates (1)
- System of nonlocal PDE of first order (1)
- TOP-Guidelines (1)
- TeV gamma-ray astronomy (1)
- Tikhonov regularization (1)
- Two-level interacting process (1)
- Two-sample tests (1)
- Umweltwissenschaften (1)
- Viscosity solutions (1)
- Vitali theorem (1)
- Volterra symbols (1)
- Wasserstein distance (1)
- Wave operator (1)
- Weak Mixing Condition (1)
- Weyl algebras bundle (1)
- Weyl symbol (1)
- Wiener measure (1)
- absorbing boundary (1)
- absorbing set (1)
- absorption (1)
- aerosol distribution (1)
- aggression (1)
- analytic index (1)
- ancient DNA (1)
- anisotropic spaces (1)
- anniversary issue (1)
- applied classical electromagnetism (1)
- approximate inertial manifolds (1)
- asymptotic behavior (1)
- asymptotic expansion (1)
- asymptotic methods (1)
- asymptotic stable (1)
- asymptotics (1)
- asymptotics of solutions (1)
- attenuated Radon transform (1)
- automated theorem proving (1)
- automatic processing (1)
- bar with variable cross-section (1)
- bending of an orthotropic cusped plate (1)
- boun- dedness (1)
- boundary layer (1)
- boundary regularity (1)
- boundary values problems (1)
- bridge (1)
- bridges of random walks (1)
- bundles (1)
- calculus of variations (1)
- canonical Marcus integration (1)
- censoring (1)
- characteristic boundary point (1)
- characteristic points (1)
- children (1)
- classical and quantum reduction (1)
- classical solution (1)
- clause learning (1)
- climatic limitation (1)
- coated and absorbing aerosols (1)
- coercivity (1)
- cohomology (1)
- comparison principle (1)
- completeness (1)
- composition operator (1)
- compound Poisson processes (1)
- compound detection or discrimination (1)
- compressible Euler equations (1)
- computer security (1)
- conditional Wiener measure (1)
- conjugate gradient (1)
- connections (1)
- conormal asymptotic expansions (1)
- conormal asymptotics (1)
- conormal symbols (1)
- conservation laws (1)
- consistency (1)
- contact transformations (1)
- continuity in Sobolev spaces with double weights (1)
- continuous time Markov chain (1)
- corner Sobolev spaces with double weights (1)
- coupled solution (1)
- coupling (1)
- coupling methods (1)
- covering (1)
- cross-cultural (1)
- cusp (1)
- cusped bar (1)
- dbar-Neumann problem (1)
- de Rham complex (1)
- de Sitter model ; Fundamental solutions ; Decay estimates (1)
- decay of eigenfunctions (1)
- decomposition (1)
- definition (1)
- deformation quantization (1)
- degenerate elliptic equations (1)
- degenerate elliptic systems (1)
- derivational affixes (1)
- design options (1)
- determinantal point processes (1)
- developmental dyscalculia (1)
- dimension functional (1)
- discontinuous Robin condition (1)
- discrete saymptotic types (1)
- distorted Brownian motion (1)
- division algebras (1)
- division of spaces (1)
- divisors (1)
- domains with singularities (1)
- dynamical system (1)
- dynamical system representation (1)
- ecophysiology (1)
- edge Sobolev spaces (1)
- edge algebra (1)
- edge quantizations (1)
- edge spaces (1)
- edge symbol (1)
- eingebettete Systeme (1)
- elastic bar (1)
- elliptic boundary conditions (1)
- elliptic complex (1)
- elliptic functions (1)
- elliptic morphism (1)
- elliptic operators in subspaces (1)
- elliptic operators on non-compact manifolds (1)
- elliptic problem (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)
- embedded systems (1)
- embodied cognition (1)
- embodied numerical cognition (1)
- empirical Wasserstein distance (1)
- energetic space (1)
- enlargement of filtration (1)
- environmental policy (1)
- equivalence (1)
- estimation of regression (1)
- evolution equation (1)
- exact simulation (1)
- exact simulation method (1)
- experience report (1)
- experiments (1)
- exponential function (1)
- exponential stability (1)
- exterior tensor product (1)
- fibre coordinates (1)
- finiteness theorem (1)
- finsler distance (1)
- first boundary value problem (1)
- fixed point formula (1)
- fluctuation phenomena (1)
- foliated diffusion (1)
- force unification (1)
- fully non-linear degenerate parabolic equations (1)
- fundamental solution (1)
- gauge group (1)
- generalized Laplace operator (1)
- geodesics (1)
- geographical and altitudinal distribution (1)
- geometric optics approximation (1)
- germination (1)
- gestures (1)
- global exact boundary controllability (1)
- global solution (1)
- global solutions (1)
- globally hyperbolic spacetime (1)
- good-inner function (1)
- goodness of fit (1)
- goodness-of-fit (1)
- hard core interaction (1)
- heat equation (1)
- heavy-tailed distributions (1)
- hitting times (1)
- host-parasite stochastic particle system (1)
- human evolutionary genetics (1)
- hyperbolic dynamical system (1)
- hyperbolic operators (1)
- hypoelliptic estimate (1)
- ill-posed problems (1)
- illposed problem (1)
- index formula (1)
- index of elliptic operator (1)
- index of stability (1)
- infinite divisibility (1)
- infinite-dimensional Brownian diffusion (1)
- infinite-dimensional diffusion (1)
- infinitely divisible point processes (1)
- innate number sense (1)
- integral representation method (1)
- integration by parts on path space (1)
- interaction matrix (1)
- interfaces with conical singularities (1)
- invariant (1)
- invasive (1)
- inverse ill-posed problem (1)
- jump process (1)
- jump processes (1)
- kernel estimator of the hazard rate (1)
- kernel method (1)
- lattice packing and covering (1)
- lattice point (1)
- learning disability (1)
- least squares estimator (1)
- lifespan (1)
- limit theorem for integrated squared difference (1)
- literature review (1)
- logarithmic residue (1)
- logical calculus (1)
- long-term policy (1)
- m-commerce (1)
- machine learning (1)
- manifold with boundary (1)
- manifold with edge (1)
- manifolds with cusps (1)
- mapping degree (1)
- matching of asymptotic expansions (1)
- mathematical cognition (1)
- mechanical effects of light (1)
- media violence (1)
- mediation (1)
- meromorphic family (1)
- metaplectic operators (1)
- minimax convergence rates (1)
- minimax rate (1)
- mixed elliptic problems (1)
- mixed problems (1)
- mobile commerce research (1)
- mod k index (1)
- model selection (1)
- moduli space of flat connections (1)
- modulo n index (1)
- mollifier method (1)
- moment map (1)
- monotone coupling (1)
- monotone method (1)
- monotone random (1)
- monotonicity conditions (1)
- morphological processing (1)
- multilayered coated and absorbing aerosol (1)
- multiple characteristics (1)
- multiplicative Lévy noise (1)
- multiplicative noise (1)
- multiwavelength Lidar (1)
- multiwavelength lidar (1)
- mycorrhiza (1)
- new recursive algorithm (1)
- nitrogen fixation (1)
- noise (1)
- non-coercive boundary conditions (1)
- non-linear integro-differential equations (1)
- non-native speakers (1)
- non-probability samples (1)
- non-regular drift (1)
- non-uniqueness (1)
- nondegenerate condition (1)
- nonhomogeneous boundary value problems (1)
- nonlinear equations (1)
- nonlinear invers problem (1)
- nonlinear optimization (1)
- nonlinear semigroup (1)
- nonlocal problem (1)
- nonparametric regression (1)
- nonsmooth curves (1)
- norm estimates with respect to a parameter (1)
- normal reflection (1)
- number line (1)
- numeracy training (1)
- operating systems (1)
- operational momentum (1)
- operator algebras on manifolds with singularities (1)
- operators on manifolds with conical and edge singularities (1)
- operators on manifolds with edges (1)
- operators on manifolds with singularities (1)
- order reduction (1)
- p-Laplace Operator (1)
- palaeogenomics (1)
- parallelizable spheres (1)
- parameter-dependent cone operators (1)
- parameter-dependent ellipticity (1)
- parameter-dependent pseudodifferential operators (1)
- parasites and diseases (1)
- parity condition (1)
- parity conditions (1)
- partial least squares (1)
- partial ordering (1)
- path integral (1)
- periodic Gaussian process (1)
- periodic Ornstein-Uhlenbeck process (1)
- permanental- (1)
- polydisc (1)
- polyhedra and polytopes (1)
- porous medium equation (1)
- principal symbolic hierarchies (1)
- probability summation (1)
- problem of classification (1)
- profile likelihood (1)
- propor-tional hazard mode (1)
- pseudo-diferential operators (1)
- pseudo-differential operators (1)
- pseudo-differentialboundary value problems (1)
- pseudodifferential boundary value problems (1)
- pseudodifferential subspace (1)
- pseudodifferential subspaces (1)
- psychometric functions (1)
- quasilinear Fredholm operator (1)
- quasilinear equation (1)
- random number generation (1)
- random processes (1)
- random walk (1)
- random walk on Abelian group (1)
- random walks on graphs (1)
- real-time (1)
- reciprocal characteristics (1)
- redundancy gain (1)
- regular figures (1)
- regularisation (1)
- regularization methods (1)
- rejection sampling (1)
- relative cohomology (1)
- relative index formulas (1)
- relative η-invariant (1)
- removable set (1)
- removable sets (1)
- reproducing kernel Hilbert space (1)
- reproductive biology (1)
- residue (1)
- response selection (1)
- semi-classical difference operator (1)
- semiconductors (1)
- semipermeable barriers (1)
- semiprocess (1)
- shock wave (1)
- singular drifts (1)
- singular integral equations (1)
- singular point (1)
- skew diffusion (1)
- small noise asymptotic (1)
- small parameter (1)
- socialization effects (1)
- soils (1)
- spatial numerical associations (1)
- spatial-nunmerical association (1)
- specific entropy (1)
- spectral boundary value problems (1)
- spectral independence (1)
- spectral kernel function (1)
- spectral resolution (1)
- spirallike function (1)
- stable limit cycle (1)
- statistical inverse problem (1)
- statistical model selection (1)
- step process (1)
- stochastic bridge (1)
- stochastic bridges (1)
- stochastic ordering (1)
- stopping rules (1)
- strongly pseudoconvex domains (1)
- subRiemannian geometry (1)
- symbolic calculation (1)
- symmetry group (1)
- symplectic (canonical) transformations (1)
- symplectic manifold (1)
- symplectic reduction (1)
- system Lame (1)
- systems of partial differential equations (1)
- the Dirichlet problem (1)
- the first boundary value problem (1)
- time series (1)
- time series with heavy tails (1)
- time symmetry (1)
- tomogrphy (1)
- trace (1)
- transition path theory (1)
- tunneling (1)
- two-level interacting processes (1)
- ultracontractivity (1)
- uniform compact attractor (1)
- variable projection method (1)
- variational principle (1)
- vibration (1)
- visual perception (1)
- weak boundary values (1)
- weighted Hölder spaces (1)
- weighted Sobolev space (1)
- weighted Sobolev spaces with discrete saymptotics (1)
- weighted spaces with asymptotics (1)
- zero-noise limit (1)
- η-invariant (1)
- ∂-operator (1)
Institute
- Institut für Mathematik (378)
- Interdisziplinäres Zentrum für Dynamik komplexer Systeme (52)
- Institut für Physik und Astronomie (44)
- Department Psychologie (20)
- Institut für Anglistik und Amerikanistik (20)
- Institut für Biochemie und Biologie (20)
- Institut für Geowissenschaften (17)
- Department Sport- und Gesundheitswissenschaften (8)
- Institut für Chemie (8)
- Extern (7)
Der Beitrag setzt sich mit der halachischen Bedeutung von Dtn. 6,18 im Kontext der heutigen Zeit auseinander.
Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einführung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen Überschreitungszeit der Brown- schen Bewegung 2.9 Waldidentitäten für die Überschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentität 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentität für die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentität 3.4 Stärkere Verfeinerung der ersten Waldidentität für die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele für lokale Martingale für die Verfeinerung der ersten Waldidentität 3.7 Überschreitungszeiten der Brownschen Bewegung für nichtlineare Schranken 4 Zweite Waldidentität 4.1 Zweite Waldidentität für die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentität für die Brown- schen Bewegung 5 Dritte Waldidentität 5.1 Dritte Waldidentität für die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentität 5.3 Eine wichtige Voraussetzung für die Verfeinerung der drittenWal- didentität 5.4 Verfeinerung der dritten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentitäten im Mehrdimensionalen 6.1 Erste Waldidentität im Mehrdimensionalen 6.2 Zweite Waldidentität im Mehrdimensionalen 6.3 Dritte Waldidentität im Mehrdimensionalen 7 Appendix
Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.
This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.
Many perceptual and cognitive tasks permit or require the integrated cooperation of specialized sensory channels, detectors, or other functionally separate units. In compound detection or discrimination tasks, 1 prominent general mechanism to model the combination of the output of different processing channels is probability summation. The classical example is the binocular summation model of Pirenne (1943), according to which a weak visual stimulus is detected if at least 1 of the 2 eyes detects this stimulus; as we review briefly, exactly the same reasoning is applied in numerous other fields. It is generally accepted that this mechanism necessarily predicts performance based on 2 (or more) channels to be superior to single channel performance, because 2 separate channels provide "2 chances" to succeed with the task. We argue that this reasoning is misleading because it neglects the increased opportunity with 2 channels not just for hits but also for false alarms and that there may well be no redundancy gain at all when performance is measured in terms of receiver operating characteristic curves. We illustrate and support these arguments with a visual detection experiment involving different spatial uncertainty conditions. Our arguments and findings have important implications for all models that, in one way or another, rest on, or incorporate, the notion of probability summation for the analysis of detection tasks, 2-alternative forced-choice tasks, and psychometric functions.
We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein{Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. In order to achieve our goals we are enforced, by the complexity of the problem, to deal with these equations in a new type of weighted Sobolev spaces of fractional order. Beside their construction, we develop tools for PDEs and techniques for hyperbolic and elliptic equations in these spaces. The well posedness is obtained in these spaces.
We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.
Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.
Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}
Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.
Preclinical work indicates that calcitriol restores vascular function by normalizing the endothelial expression of cyclooxygenase-2 and thromboxane-prostanoid receptors in conditions of estrogen deficiency and thus prevents the thromboxane-prostanoid receptor activation-induced inhibition of nitric oxide synthase. Since endothelial dysfunction is a key factor in the pathogenesis of cardiovascular diseases, this finding may have an important translational impact. It provides a clear rationale to use endothelial function in clinical trials aiming to find the optimal dose of vitamin D for the prevention of cardiovascular events in postmenopausal women.
In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].
Untitled
(2011)
In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.
We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Lévy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.
Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
(2003)
Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.
This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved.
Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too.
Think local sell global
(2010)
We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y , i.e., Au = f in int X, T±u = g± on int Y±, where Y is subdivided into subsets Y± with an interface Z and boundary conditions T± on Y± that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z ⊂ Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T− Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in [3]. With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z \ {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.
Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.
We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.
We study an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A )-¹ exists in a sector of the complex plane and decays like 1/|λ| as |λ| -> ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with striaght conical degeneracy and establish maximal regularity for the Cauchy problem u - Δu = f, u(0) = 0.
The queerness of things not queer - entgrenzungen - Affekte und Materialitäten - Interventionen
(2012)
The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times.
The role of knowledge in the policy process remains a central theoretical puzzle in policy analysis and political science. This article argues that an important yet missing piece of this puzzle is the systematic exploration of the political use of policy knowledge. While much of the recent debate has focused on the question of how the substantive use of knowledge can improve the quality of policy choices, our understanding of the political use of knowledge and its effects in the policy process has remained deficient in key respects. A revised conceptualization of the political use of knowledge is introduced that emphasizes how conflicting knowledge can be used to contest given structures of policy authority. This allows the analysis to differentiate between knowledge creep and knowledge shifts as two distinct types of knowledge effects in the policy process. While knowledge creep is associated with incremental policy change within existing policy structures, knowledge shifts are linked to more fundamental policy change in situations when the structures of policy authority undergo some level of transformation. The article concludes by identifying characteristics of the administrative structure of policy systems or sectors that make knowledge shifts more or less likely.
When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for
the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on
a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.
We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.
We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.
For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.