Filtern
Volltext vorhanden
- ja (446) (entfernen)
Erscheinungsjahr
Dokumenttyp
- Preprint (446) (entfernen)
Sprache
- Englisch (425)
- Deutsch (18)
- Mehrsprachig (2)
- Französisch (1)
Schlagworte
- 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)
- surgery (4)
- 'eta' invariant (3)
- Atiyah-Bott condition (3)
- Fredholm operators (3)
- Hodge theory (3)
- Lefschetz number (3)
- boundary value problem (3)
- conical singularities (3)
- conormal symbol (3)
- differential operators (3)
- elliptic complexes (3)
- ellipticity (3)
- eta invariant (3)
- index of elliptic operators in subspaces (3)
- reciprocal class (3)
- regularization (3)
- reversible measure (3)
- spectral flow (3)
- star product (3)
- Atiyah-Bott obstruction (2)
- Brownian bridge (2)
- Canonical Gibbs measure (2)
- Carleman matrix (2)
- Chemotaxis (2)
- Dirac operator (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)
- Stochastic Differential Equation (2)
- WKB method (2)
- Zaremba problem (2)
- aerosol size distribution (2)
- analytic continuation (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)
- hard core potential (2)
- holomorphic solution (2)
- homotopy classification (2)
- ill-posed problem (2)
- index formulas (2)
- integral formulas (2)
- inversion (2)
- linking coefficients (2)
- local time (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)
- 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)
- APS problem (1)
- Agrarwissenschaft (1)
- Agricultural Science (1)
- Approximate likelihood (1)
- Atiyah-Singer theorem (1)
- Attractive Dynamics (1)
- Automatisches Beweisen (1)
- Averaging principle (1)
- Beltrami equation (1)
- Betriebssysteme (1)
- Bibel (1)
- Bose-Einstein condensation (1)
- Boundary value methods (1)
- Boundary value problems for first order systems (1)
- Boundary-contact problems (1)
- Brownian motion (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)
- 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)
- Chern character (1)
- Clifford algebra (1)
- Corner boundary value problems (1)
- Coupling (1)
- Crack theory (1)
- Cross-effects (1)
- DLR equation (1)
- DPLL (1)
- Data Protection (1)
- Datenschutz (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)
- Dtn. 6:18 (1)
- Duality formula (1)
- Earth Sciences (1)
- Echtzeit (1)
- Edge-degenerate operators (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)
- Extremal problem (1)
- Feynman-Kac formula (1)
- Finite difference method (1)
- Fischer-Riesz equations (1)
- Form (1)
- Forschungsdaten (1)
- Fourth order Sturm-Liouville problem (1)
- Fredholm operator (1)
- G-index (1)
- G-trace (1)
- Geowissenschaften (1)
- Gevrey classes (1)
- Gibbs measure (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)
- Infinite-dimensional SDE (1)
- Integrability (1)
- Interacting Particle Systems (1)
- Judaism (1)
- Judentum (1)
- KS model (1)
- Klausellernen (1)
- Kolmogorov-Smirnov type tests (1)
- Korn’s weighted inequality (1)
- LEGO Mindstorms EV3 (1)
- Lagrangian system (1)
- Lame system (1)
- Lamé system (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)
- Markov-field property (1)
- Martin-Dynkin boundary (1)
- Maslov and Conley–Zehnder index (1)
- Meromorphic operator functions (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)
- Peano phenomena (1)
- Perron's method (1)
- Planetary Rings (1)
- Point process (1)
- Poisson bridge (1)
- Pontrjagin duality (1)
- Proportional hazards (1)
- Pseudo-differential operators (1)
- Pseudodifferential operators (1)
- Quasiconformal mapping (1)
- Quasilinear equations (1)
- Quasilinear hyperbolic system (1)
- RT_PREEMT patch (1)
- RT_PREEMT-Patch (1)
- Ramified Cauchy problem (1)
- Reciprocal process (1)
- Renormalized integral (1)
- Research Data (1)
- Riemann-Roch theorem (1)
- Runge-Kutta methods (1)
- SAT (1)
- SPECT (1)
- Saturation model (1)
- Schrödinger problem (1)
- Second order elliptic equations (1)
- Skorokhod' s invariance principle (1)
- Sobolev problem (1)
- Sobolev spaces with double weights on singular cones (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)
- 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)
- analytic index (1)
- anisotropic spaces (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)
- 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)
- classical and quantum reduction (1)
- classical solution (1)
- clause learning (1)
- coated and absorbing aerosols (1)
- coercivity (1)
- cohomology (1)
- comparison principle (1)
- completeness (1)
- composition operator (1)
- compound Poisson processes (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)
- 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)
- deformation quantization (1)
- degenerate elliptic equations (1)
- degenerate elliptic systems (1)
- determinantal point processes (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)
- 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)
- empirical Wasserstein distance (1)
- energetic space (1)
- enlargement of filtration (1)
- equivalence (1)
- estimation of regression (1)
- evolution equation (1)
- exact simulation (1)
- exact simulation method (1)
- experience report (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)
- 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)
- geometric optics approximation (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)
- 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)
- integral representation method (1)
- integration by parts on path space (1)
- interaction matrix (1)
- interfaces with conical singularities (1)
- invariant (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)
- least squares estimator (1)
- lifespan (1)
- limit theorem for integrated squared difference (1)
- logarithmic residue (1)
- logical calculus (1)
- machine learning (1)
- manifold with boundary (1)
- manifold with edge (1)
- manifolds with cusps (1)
- mapping degree (1)
- matching of asymptotic expansions (1)
- meromorphic family (1)
- metaplectic operators (1)
- minimax convergence rates (1)
- minimax rate (1)
- mixed elliptic problems (1)
- mixed problems (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)
- multilayered coated and absorbing aerosol (1)
- multiple characteristics (1)
- multiplicative Lévy noise (1)
- multiplicative noise (1)
- multiwavelength Lidar (1)
- multiwavelength lidar (1)
- new recursive algorithm (1)
- non-coercive boundary conditions (1)
- non-linear integro-differential equations (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)
- operating systems (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)
- parallelizable spheres (1)
- parameter-dependent cone operators (1)
- parameter-dependent ellipticity (1)
- parameter-dependent pseudodifferential operators (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)
- 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)
- quasilinear Fredholm operator (1)
- quasilinear equation (1)
- random walk (1)
- random walk on Abelian group (1)
- random walks on graphs (1)
- real-time (1)
- reciprocal characteristics (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)
- residue (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)
- 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)
- 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)
- 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)
Institut
- Institut für Mathematik (374)
- Interdisziplinäres Zentrum für Dynamik komplexer Systeme (51)
- Institut für Physik und Astronomie (35)
- Institut für Anglistik und Amerikanistik (19)
- Extern (7)
- Department Psychologie (2)
- Hasso-Plattner-Institut für Digital Engineering gGmbH (1)
- Institut für Informatik und Computational Science (1)
- Institut für Religionswissenschaft (1)
- Institut für Slavistik (1)
We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The “full” calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near the conical exit to infinity.
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.
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.
An expansion for a class of functions is called stable if the partial sums are bounded uniformly in the class. Stable expansions are of key importance in numerical analysis where functions are given up to certain error. We show that expansions in homogeneous functions are always stable on a small ball around the origin, and evaluate the radius of the largest ball with this property.
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.
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.
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.
We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.
Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ für identisch verteilte Zufallsvariablen 3. SGGZ für Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einführung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzsätze 5. Doob-Zerlegung 6. Eine äquivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichmäßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5.”reversed“ (Sub-,Super-)Martingale 1. Konvergenzsätze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. Äquivalente Formulierung eines (Sub-)Martingals 2. Konvergenzsätze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzsätze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9.”reversed“ Amarts und Semiamarts 1. Konvergenzsätze 2.”Aufwärts“- gegen ”Abwärts“-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilitätsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzsätze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabhängiger Zufallsvariablen B. Konvergenz
Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point
(2012)
The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.
Many formal descriptions of DPLL-based SAT algorithms either do not include all essential proof techniques applied by modern SAT solvers or are bound to particular heuristics or data structures. This makes it difficult to analyze proof-theoretic properties or the search complexity of these algorithms. In this paper we try to improve this situation by developing a nondeterministic proof calculus that models the functioning of SAT algorithms based on the DPLL calculus with clause learning. This calculus is independent of implementation details yet precise enough to enable a formal analysis of realistic DPLL-based SAT algorithms.
We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.
The two and k-sample tests of equality of the survival distributions against the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.
We study the dynamics of four wave interactions in a nonlinear quantum chain of oscillators under the "narrow packet" approximation. We determine the set of times for which the evolution of decay processes is essentially specified by quantum effects. Moreover, we highlight the quantum increment of instability.
We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochastic process over a continuum. As a measure of type I error, we extend the concept of false discovery rate (FDR) to this setting. The FDR is defined as the average ratio of the measure of two random sets, so that its study presents some challenge and is of some intrinsic mathematical interest. Our main result shows how to use the p-value process to control the FDR at a nominal level, either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting, the latter one leading to a less conservative procedure. The interest of this approach is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables. Conceptually, an interesting feature of the setting advocated here is that it focuses directly on the intrinsic hypothesis space associated with a testing model on a random process, without referring to an arbitrary discretization.
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true
regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.