Refine
Year of publication
Document Type
- Preprint (569) (remove)
Language
- English (531)
- 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)
- age (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)
- dating (1)
- dbar-Neumann problem (1)
- de Rham complex (1)
- de Sitter model ; Fundamental solutions ; Decay estimates (1)
- decarbonization (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)
- digitization (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)
- energy efficiency (1)
- enlargement of filtration (1)
- environmental policy (1)
- equivalence (1)
- estimation of regression (1)
- ethnicity (1)
- evidence-based policy (1)
- evolution equation (1)
- exact simulation (1)
- exact simulation method (1)
- experience report (1)
- experiment (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)
- gender (1)
- gender social inequality (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 demand (1)
- heat equation (1)
- heavy-tailed distributions (1)
- hitting times (1)
- host-parasite stochastic particle system (1)
- housing sector (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)
- marriage (1)
- matching of asymptotic expansions (1)
- mathematical cognition (1)
- mating (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)
- observational data (1)
- occupational gender segregation (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)
- partnership (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)
- social inequality (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)
- stereotypes (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)
In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.
The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.
One of the fundamental challenges in anti-doping is identifying athletes who use, or are at risk of using, prohibited performance enhancing substances. The growing trend to employ a forensic approach to doping control aims to integrate information from social sciences (e.g., psychology of doping) into organised intelligence to protect clean sport. Beyond the foreseeable consequences of a positive identification as a doping user, this task is further complicated by the discrepancy between what constitutes a doping offence in the World Anti-Doping Code and operationalized in doping research. Whilst psychology plays an important role in developing our understanding of doping behaviour in order to inform intervention and prevention, its contribution to the array of doping diagnostic tools is still in its infancy. In both research and forensic settings, we must acknowledge that (1) socially desirable responding confounds self-reported psychometric test results and (2) that the cognitive complexity surrounding test performance means that the response-time based measures and the lie detector tests for revealing concealed life-events (e.g., doping use) are prone to produce false or non-interpretable outcomes in field settings. Differences in social-cognitive characteristics of doping behaviour that are tested at group level (doping users vs. non-users) cannot be extrapolated to individuals; nor these psychometric measures used for individual diagnostics. In this paper, we present a position statement calling for policy guidance on appropriate use of psychometric assessments in the pursuit of clean sport. We argue that, to date, both self-reported and response-time based psychometric tests for doping have been designed, tested and validated to explore how athletes feel and think about doping in order to develop a better understanding of doping behaviour, not to establish evidence for doping. A false 'positive' psychological profile for doping affects not only the individual 'clean' athlete but also their entourage, their organisation and sport itself. The proposed policy guidance aims to protect the global athletic community against social, ethical and legal consequences from potential misuse of psychological tests, including erroneous or incompetent applications as forensic diagnostic tools in both practice and research. (C) 2015 Elsevier B.V. All rights reserved.
We consider a class of ergodic Hamilton-Jacobi-Bellman (HJB) equations, related to large time asymptotics of non-smooth multiplicative functional of difusion processes. Under suitable ergodicity assumptions on the underlying difusion, we show existence of these asymptotics, and that they solve the related HJB equation in the viscosity sense.
For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails.
A function has vanishing mean oscillation (VMO) on R up(n) if its mean oscillation - the local average of its pointwise deviation from its mean value - both is uniformly bounded over all cubes within R up(n) and converges to zero with the volume of the cube. The more restrictive class of functions with vanishing lower oscillation (VLO) arises when the mean value is replaced by the minimum value in this definition. It is shown here that each VMO function is the difference of two functions in VLO.
We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.