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- elliptic operators (9)
- boundary value problems (8)
- index (8)
- K-theory (7)
- manifolds with singularities (6)
- pseudodifferential operators (6)
- relative index (6)
- Atiyah-Patodi-Singer theory (5)
- Fredholm property (5)
- index theory (5)
- Boundary value problems (4)
- elliptic operator (4)
- manifold with singularities (4)
- surgery (4)
- 'eta' invariant (3)
- Atiyah-Bott condition (3)
- boundary value problem (3)
- conical singularities (3)
- conormal symbol (3)
- differential operators (3)
- ellipticity (3)
- eta invariant (3)
- index of elliptic operators in subspaces (3)
- spectral flow (3)
- Atiyah-Bott obstruction (2)
- Carleman matrix (2)
- Chemotaxis (2)
- Fredholm operators (2)
- Hodge theory (2)
- Laplace equation (2)
- Lefschetz fixed point formula (2)
- Mellin transform (2)
- Probabilistic Cellular Automata (2)
- Toeplitz operators (2)
- Zaremba problem (2)
- aerosol size distribution (2)
- cluster expansion (2)
- edge singularities (2)
- edge-degenerate operators (2)
- elliptic boundary value problems (2)
- elliptic complexes (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)
- inversion (2)
- linking coefficients (2)
- manifolds with conical singularities (2)
- manifolds with edges (2)
- maximum likelihood estimator (2)
- modn-index (2)
- monodromy matrix (2)
- pseudo-differential boundary value problems (2)
- pseudodiferential operators (2)
- quantization (2)
- regularization (2)
- regularizer (2)
- regularizers (2)
- reversible measure (2)
- singular partial differential equation (2)
- star-product (2)
- symmetry conditions (2)
- the Cauchy problem (2)
- weighted edge spaces (2)
- weighted spaces (2)
- (co)boundary operator (1)
- APS problem (1)
- Approximate likelihood (1)
- Atiyah-Singer theorem (1)
- Attractive Dynamics (1)
- Automatisches Beweisen (1)
- Beltrami equation (1)
- Boundary-contact problems (1)
- Brownian bridge (1)
- C0−semigroup (1)
- Calculus of conormal symbols (1)
- Calderón projections (1)
- Canonical Gibbs measure (1)
- Capture into resonance (1)
- Casped plates (1)
- Categories of stratified spaces (1)
- Cauchy Riemann operator (1)
- Cauchy problem (1)
- Chern character (1)
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- Coupling (1)
- Crack theory (1)
- DLR equation (1)
- DPLL (1)
- Dirac operators (1)
- Dirichlet to Neumann operator (1)
- Edge-degenerate operators (1)
- Elliptic equation with order degeneration (1)
- Elliptic operators in domains with edges (1)
- Euler operator (1)
- Euler's theta functions (1)
- G-index (1)
- G-trace (1)
- Gevrey classes (1)
- Gibbs perturbation (1)
- Girsanov formula (1)
- Goursat problem (1)
- Green and Mellin edge operators (1)
- Green operator (1)
- Grushin operator (1)
- Gutzwiller formula (1)
- Hamilton-Jacobi theory (1)
- Hamiltonian group action (1)
- Hardy‘s inequality (1)
- Hyperbolic-parabolic system (1)
- Ill-posed problem (1)
- Interacting Particle Systems (1)
- KS model (1)
- Klausellernen (1)
- Korn’s weighted inequality (1)
- Lame system (1)
- Lefschetz number (1)
- Levy measure (1)
- Logarithmic Sobolev inequality (1)
- Logikkalkül (1)
- Lφ spectrum (1)
- Markov chain (1)
- Markov processes (1)
- Maslov and Conley–Zehnder index (1)
- Meromorphic operator functions (1)
- Multidimensional nonisentropic hydrodynamic model (1)
- Multiwavelength LIDAR (1)
- Neumann problem (1)
- Non-linear (1)
- Nonlinear (1)
- Nonlinear Laplace operator (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)
- Perron's method (1)
- Poisson bridge (1)
- Pontrjagin duality (1)
- Pseudo-differential operators (1)
- Pseudodifferential operators (1)
- Quasiconformal mapping (1)
- Quasilinear hyperbolic system (1)
- Ramified Cauchy problem (1)
- Reciprocal process (1)
- Riemann-Roch theorem (1)
- SAT (1)
- SPECT (1)
- Saturation model (1)
- Second order elliptic equations (1)
- Sobolev problem (1)
- Sobolev spaces with double weights on singular cones (1)
- Stochastic Differential Equation (1)
- Stochastic Ordering (1)
- Stochastic differential equations (1)
- Surface potentials with asymptotics (1)
- Survival models with covariates (1)
- System of nonlocal PDE of first order (1)
- Tikhonov regularization (1)
- Viscosity solutions (1)
- Volterra symbols (1)
- WKB method (1)
- Weak Mixing Condition (1)
- Weyl algebras bundle (1)
- Weyl symbol (1)
- absorbing set (1)
- absorption (1)
- aerosol distribution (1)
- analytic continuation (1)
- analytic index (1)
- anisotropic spaces (1)
- asymptotic behavior (1)
- asymptotic stable (1)
- asymptotics of solutions (1)
- attenuated Radon transform (1)
- automated theorem proving (1)
- bar with variable cross-section (1)
- bending of an orthotropic cusped plate (1)
- boun- dedness (1)
- boundary values problems (1)
- bundles (1)
- censoring (1)
- classical and quantum reduction (1)
- clause learning (1)
- coated and absorbing aerosols (1)
- cohomology (1)
- comparison principle (1)
- compressible Euler equations (1)
- computer security (1)
- connections (1)
- conormal asymptotic expansions (1)
- conormal asymptotics (1)
- conormal symbols (1)
- conservation laws (1)
- consistency (1)
- contact transformations (1)
- corner Sobolev spaces with double weights (1)
- coupled solution (1)
- covering (1)
- cusped bar (1)
- de Rham complex (1)
- de Sitter model ; Fundamental solutions ; Decay estimates (1)
- deformation quantization (1)
- degenerate elliptic equations (1)
- degenerate elliptic systems (1)
- detailed balance equation (1)
- dimension functional (1)
- discrete saymptotic types (1)
- division algebras (1)
- divisors (1)
- domains with singularities (1)
- duality formula (1)
- edge Sobolev spaces (1)
- edge algebra (1)
- edge spaces (1)
- edge symbol (1)
- elastic bar (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 respect to interior and edge symbols (1)
- energetic space (1)
- estimation of regression (1)
- exponential function (1)
- exponential stability (1)
- exterior tensor product (1)
- fibre coordinates (1)
- finiteness theorem (1)
- force unification (1)
- fully non-linear degenerate parabolic equations (1)
- fundamental solution (1)
- gauge group (1)
- geodesics (1)
- geometric optics approximation (1)
- global exact boundary controllability (1)
- global solution (1)
- global solutions (1)
- good-inner function (1)
- goodness of fit (1)
- hard core interaction (1)
- hard core potential (1)
- hyperbolic operators (1)
- illposed problem (1)
- index formula (1)
- index of elliptic operator (1)
- infinite-dimensional diffusion (1)
- integral formulas (1)
- interfaces with conical singularities (1)
- inverse ill-posed problem (1)
- kernel estimator of the hazard rate (1)
- least squares estimator (1)
- lifespan (1)
- limit theorem for integrated squared difference (1)
- local time (1)
- logical calculus (1)
- machine learning (1)
- manifold with edge (1)
- manifolds with cusps (1)
- matching of asymptotic expansions (1)
- meromorphic family (1)
- metaplectic operators (1)
- mixed elliptic problems (1)
- mod k index (1)
- moduli space of flat connections (1)
- modulo n index (1)
- molecular motor (1)
- mollifier method (1)
- moment map (1)
- monotone coupling (1)
- monotone method (1)
- multilayered coated and absorbing aerosol (1)
- multiple characteristics (1)
- multiwavelength Lidar (1)
- multiwavelength lidar (1)
- new recursive algorithm (1)
- non-Markov drift (1)
- non-coercive boundary conditions (1)
- nondegenerate condition (1)
- nonhomogeneous boundary value problems (1)
- nonlinear invers problem (1)
- nonlinear optimization (1)
- nonlocal problem (1)
- norm estimates with respect to a parameter (1)
- normal reflection (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)
- parallelizable spheres (1)
- parameter-dependent cone operators (1)
- parameter-dependent ellipticity (1)
- parameter-dependent pseudodifferential operators (1)
- parity condition (1)
- parity conditions (1)
- polydisc (1)
- principal symbolic hierarchies (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 operator (1)
- pseudodifferential subspace (1)
- pseudodifferential subspaces (1)
- reciprocal processes (1)
- relative cohomology (1)
- relative index formulas (1)
- relative η-invariant (1)
- residue (1)
- root functions (1)
- semiconductors (1)
- semiprocess (1)
- shock wave (1)
- small parameter (1)
- spectral boundary value problems (1)
- spectral independence (1)
- spectral resolution (1)
- spectral theorem (1)
- star product (1)
- stochastic ordering (1)
- subRiemannian geometry (1)
- symmetry group (1)
- symplectic (canonical) transformations (1)
- symplectic reduction (1)
- system Lame (1)
- systems of partial differential equations (1)
- time duality (1)
- time symmetry (1)
- tomogrphy (1)
- transition path theory (1)
- ultracontractivity (1)
- uniform compact attractor (1)
- variable projection method (1)
- vibration (1)
- weighted Sobolev space (1)
- weighted Sobolev spaces with discrete saymptotics (1)
- weighted spaces with asymptotics (1)
- η-invariant (1)
- ∂-operator (1)
Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics
The paper presents a method that determines, by standard numerical means, the type of mutual relations of fold and flip bifurcations (configured as a so-called communication area) of a map. Equation systems are developed for the computation of points where a transition between areas of different types occurs. Furthermore, it is shown that saddle area<->spring area transitions can exist which have not yet been considered in the literature. Analytical conditions of that transition are derived.
Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.
We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.
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}
We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field.
We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x1=0 and 1. Periodic boundary conditions are assumed in the x2 and x3 directions and the magnetofluid is driven by an electric field in the x3 direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,J3). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L2 and L3 in the x2 and x3 directions, and the mean values B¯2 and B¯3 of the magnetic-field components in these directions.
It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.
The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.
The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.