Refine
Has Fulltext
- yes (222)
Is part of the Bibliography
- yes (222)
Year of publication
Document Type
- Doctoral Thesis (128)
- Journal article (73)
- Book (5)
- Report (4)
- Master Thesis (3)
- Other (3)
- Conference Proceeding (2)
- Preprint (2)
- Book article / Book chapter (1)
- Review (1)
Keywords
- Optimale Kontrolle (11)
- Extremwertstatistik (8)
- Optimierung (8)
- optimal control (8)
- Nash-Gleichgewicht (7)
- Newton-Verfahren (7)
- Mathematik (6)
- Nichtlineare Optimierung (6)
- Mathematikunterricht (5)
- Stabilität (5)
- Differentialgleichung (4)
- Elliptische Differentialgleichung (4)
- Extremwerttheorie (4)
- Finite-Elemente-Methode (4)
- MPEC (4)
- Nichtglatte Optimierung (4)
- Partielle Differentialgleichung (4)
- Pontryagin maximum principle (4)
- SAS <Programm> (4)
- SQH method (4)
- Zeitreihenanalyse (4)
- A-priori-Wissen (3)
- Copula (3)
- Differentialgeometrie (3)
- Eigenwert (3)
- Euler equations (3)
- Galerkin-Methode (3)
- Gaussian approximation (3)
- Kombinatorik (3)
- Konfidenzintervall (3)
- Ljapunov-Funktion (3)
- Magnetoelastizität (3)
- Monodromie (3)
- Nichtkonvexe Optimierung (3)
- Pareto-Verteilung (3)
- Spieltheorie (3)
- Statistik (3)
- Variationsrechnung (3)
- Zetafunktion (3)
- count time series (3)
- extreme value theory (3)
- global convergence (3)
- multi-fluid mixture (3)
- nonsmooth optimization (3)
- proximal gradient method (3)
- Abelsche Gruppe (2)
- Analysis (2)
- Anaphylaxis (2)
- Angewandte Mathematik (2)
- Anwendungssoftware (2)
- Argumentation (2)
- Audit sampling (2)
- BGK approximation (2)
- Belyi map (2)
- Biholomorphe Abbildung (2)
- Binomialverteilung (2)
- Box-Jenkins-Verfahren (2)
- Box–Jenkins Program (2)
- Cayley graph (2)
- Code examples (2)
- Controllability (2)
- D-Norm (2)
- Darstellungsmatrix (2)
- Deformationsquantisierung (2)
- Dirichlet-Reihe (2)
- Extreme Value Theory (2)
- Finanzmathematik (2)
- Finite-Volumen-Methode (2)
- Fokker-Planck-Gleichung (2)
- Fokker–Planck equation (2)
- Frequency Domain (2)
- Funktionentheorie (2)
- Galois-Theorie (2)
- Gamma-Konvergenz (2)
- Generalized Nash Equilibrium Problem (2)
- Gleichverteilung (2)
- Grundvorstellung (2)
- HIV (2)
- Homogener Raum (2)
- Hurwitz-Raum (2)
- Innere-Punkte-Methode (2)
- Inzidenzmatrix (2)
- Kohomologie (2)
- Kompakte Lie-Gruppe (2)
- Komplementaritätsproblem (2)
- Kontrolltheorie (2)
- Konvergenz (2)
- Kopula <Mathematik> (2)
- Lie groups (2)
- Lineare Algebra (2)
- Ljapunov-Stabilitätstheorie (2)
- Loewner theory (2)
- Loewner-Theorie (2)
- Lyapunov functions (2)
- Mathematica <Programm> (2)
- Mathematische Modellierung (2)
- Mehrgitterverfahren (2)
- Mikromagnetismus (2)
- Newton Methods (2)
- Newton's method (2)
- Nichtlineare Kontrolltheorie (2)
- Nikaido-Isoda function (2)
- Numerical analysis (2)
- Numerische Mathematik (2)
- Numerisches Verfahren (2)
- Optimale Steuerung (2)
- Origami (2)
- PDE (2)
- Prediction interval (2)
- Prior information (2)
- Projektive Ebene (2)
- Regressionsanalyse (2)
- Regulator (2)
- Regulator <Mathematik> (2)
- Riemann zeta-function (2)
- Riemannsche Zetafunktion (2)
- SAS (2)
- Schlichte Funktion (2)
- Simulation (2)
- Stability (2)
- State-Space Models (2)
- Stochastischer Prozess (2)
- Systemisches Risiko (2)
- Testinstrument (2)
- Time Series Analysis (2)
- Time series analyses (2)
- Torsionsfreie Abelsche Gruppe (2)
- Verallgemeinertes Nash-Gleichgewichtsproblem (2)
- Weibull-Verteilung (2)
- Zahlentheorie (2)
- Zustandsraummodelle (2)
- augmented Lagrangian method (2)
- basic mental models (2)
- cardinality constraints (2)
- conservation laws (2)
- deformation quantization (2)
- estimation error (2)
- extreme value distribution (2)
- fast vollständig zerlegbare Gruppe (2)
- finite elements (2)
- generalized Pareto distribution (2)
- globale Konvergenz (2)
- incidence matrix (2)
- jump-diffusion processes (2)
- kinetic model (2)
- mathematical modelling (2)
- mathematics (2)
- mean curvature (2)
- multigrid (2)
- nonlinear systems (2)
- numerical analysis (2)
- optimization (2)
- ordinary differential equations (2)
- prime number (2)
- regulator (2)
- representing matrix (2)
- semismooth Newton method (2)
- stability (2)
- stability analysis (2)
- state constraints (2)
- stochastic processes (2)
- trabeculectomy (2)
- viral load (2)
- Überlagerung <Mathematik> (2)
- (0 (1)
- (approximate) functional equation (1)
- *-algebra (1)
- 1)-Matrix (1)
- 1)-matrix (1)
- 1-fach-Origami (1)
- 1655-1705> (1)
- 5-fluorouracil (1)
- ADMM (1)
- AIDS (1)
- Abbildungseigenschaften (1)
- Abelsche p-Gruppe (1)
- Abhängigkeitsmaß (1)
- Ableitung (1)
- Abstiegsverfahren (1)
- Abstoßungsphänomen (1)
- Acoustic equations (1)
- Adolf Hurwitz (1)
- Affine Skalierungsverfahren (1)
- Affinminimalfläche (1)
- Affinnormal (1)
- Aggregation (1)
- Algebraic Curves (1)
- Algebraic signal processing (1)
- Algebraische Kurve (1)
- Algebraische Signalverarbeitung (1)
- Algebraische Zahlentheorie (1)
- Algebraischer Funktionenkörper (1)
- Analogie (1)
- Analogiebildung (1)
- Analytische Funktion (1)
- Analytische Zahlentheorie (1)
- Angewandte Geowissenschaften (1)
- Angular Density (1)
- Anpassungstest (1)
- Approximation (1)
- Approximationstheorie (1)
- Arbitrary Lagrangian-Eulerian (1)
- Archimedean copula (1)
- Aspekte professioneller Kompetenz (1)
- Asymptotic Preserving (1)
- Asymptotic independence (1)
- Atmosphäre (1)
- Augmented Lagrangian (1)
- Augmented Lagrangian methods (1)
- Automorphismengruppe (1)
- Axiom (1)
- Axiomatisieren (1)
- B-Spline (1)
- Babuska Brezzi Bedingung (1)
- Babuska Brezzi condition (1)
- Banach-Raum (1)
- Bayesian approach (1)
- Bayesian inverse problems (1)
- Beatty sequence (1)
- Bedingte Unabhängigkeit (1)
- Belyi-Funktionen (1)
- Beobachter (1)
- Berechnung (1)
- Bernoulli (1)
- Bernoulli Raum (1)
- Bernoulli Space (1)
- Bernstein (1)
- Bernstein-type inequality (1)
- Berstein (1)
- Beweistheorie (1)
- Bi-Fidelity method (1)
- Bildrekonstruktion (1)
- Bilinear differential games (1)
- Black Scholes equation (1)
- Blinear Quantum Control Systems (1)
- Bloch's Principle (1)
- Blochsches Prinzip (1)
- Blockplan (1)
- Bloom setting (1)
- Box-Restriktionen (1)
- Bregman distance (1)
- Brittle fracture (1)
- Brockett (1)
- Brüder Hurwitz (1)
- Burgers-Gleichung (1)
- Butler group (1)
- Butlergruppe (1)
- CSF (1)
- CSIDH (1)
- Calculus of Variations (1)
- Calculus of variations (1)
- Caputo fractional derivative (1)
- Carbon dioxide capture (1)
- Cardinality Constraints (1)
- Carleson embedding theorem (1)
- Cartan's Theorem (1)
- Cauchy-Born rule (1)
- Charakteranalyse (1)
- Code Examples (1)
- Coisotropic reduction (1)
- Complex Continued Fractions (1)
- Complex Fluids (1)
- Composite optimization problems (1)
- Compressed Sensing (1)
- Computerunterstützter Unterricht (1)
- Confidence interval (1)
- Confidence intervals (1)
- Conformal Metrics (1)
- Conjugate function (1)
- Conjugate gradient method (1)
- Conservation Laws (1)
- Constrained optimization (1)
- Constraint-Programmierung (1)
- Continuous Sample Path (1)
- Convergence (1)
- Copula <Mathematik> (1)
- Counterparty Risk (1)
- Credibility interval (1)
- Curvature Equation (1)
- D-Norms (1)
- D-norm (1)
- DAT (1)
- DC optimization (1)
- DNA replication (1)
- Darstellung vonPseudo-Metriken (1)
- Data Exploration (1)
- Deformation (1)
- Deformationsgradient (1)
- Derivation (1)
- Deskriptive Statistik (1)
- Dichtefunktionalformalismus (1)
- Differential Games (1)
- Differentialgleichungssystem (1)
- Digitale Signalverarbeitung (1)
- Dimension reduction (1)
- Diophantine approximation (1)
- Dirichlet-Problem (1)
- Discontinuous Galerkin method (1)
- Discrete to continuum (1)
- Discrete-to-continuum limits (1)
- Diskrepanz (1)
- Double sensitization (1)
- Drug allergy (1)
- Drug reaction (1)
- Dual gap function (1)
- Dualität (1)
- Dualitätstheorie (1)
- Dynamic Geometry Environment (1)
- Dynamic representations (1)
- Dynamical Systems (1)
- Dynamical system (1)
- Dynamische Geometriesysteme (1)
- Dynamische Optimierung (1)
- Dynamische Repräsentation (1)
- Dynamisches System (1)
- E-Learning (1)
- EJMA-D-19-00287 (1)
- Eigenmode (1)
- Elastizität (1)
- Elliptic equations (1)
- Elliptische Kurve (1)
- Endliche Geometrie (1)
- Ensemble optimal control (1)
- Entropiebedingung (1)
- Entropielösung (1)
- Entropy admissibility condition (1)
- Epidemiologie (1)
- Epstein zeta-function (1)
- Epstein, Paul (1)
- Erhaltungsgleichungen (1)
- Estimation (1)
- Euler system (1)
- Eulersche Differentialgleichung (1)
- Euler–Bernoulli damped beam (1)
- Exact-controllability (1)
- Exceedance Stability (1)
- Existenz schwacher Lösungen (1)
- Existenz und Eindeutigkeit (1)
- Explicit Computation (1)
- Explizite Berechnung (1)
- Exponential smoothing (1)
- Exponential smoothing with covariates (1)
- Extremal–I–Verteilung (1)
- Extreme value copula (1)
- Extremwert (1)
- Extremwertregelung (1)
- Extremwertverteilung (1)
- Falten (1)
- Faltung (1)
- Faltungscode (1)
- Fast vollständig zerlegbare Gruppe (1)
- Fermentation (1)
- Festkörper (1)
- Field sting (1)
- Filter-SQPEC Verfahren (1)
- Financial Networks (1)
- Finanzielle Netzwerke (1)
- Finite Elemente (1)
- Finite Elemente Methode (1)
- Finite support distributions (1)
- Firmwert (1)
- Fixpunktsatz (1)
- Flachfaltbarkeit (1)
- Flat-foldability (1)
- Fluid (1)
- Fluid-Partikel-Strömung (1)
- Fluid-Struktur-Wechselwirkung (1)
- Fluid-structure interaction (1)
- Fluidnetzwerk (1)
- Flüssigkeit (1)
- Flüssigkristall (1)
- Fokalmannigfaltigkeit (1)
- Fokker-Planck (1)
- Fokker-Planck optimality systems (1)
- Formoptimierung (1)
- Fragility Index (1)
- Fragilitätsindex (1)
- Freies Randwertproblem (1)
- Fréchet spaces (1)
- Fréchet-Raum (1)
- Frécheträume (1)
- Function Fields (1)
- Functional differential equations (1)
- Functions with Primitive (1)
- Funktion von beschränkter Variation (1)
- Funktionen mit Stammfunktion (1)
- Funktionenkörper (1)
- GPD (1)
- GPD-Flow (1)
- Galois theory (1)
- Galois-Erweiterung (1)
- Galois-Feld (1)
- Galoistheorie (1)
- Gamma-convergence (1)
- Gasgemisch (1)
- Gebäude (1)
- Generalized Nash Equilibrium (1)
- Generalized Nash equilibrium (1)
- Generalized Pareto Distribution (1)
- Generalized Pareto copula (1)
- GeoGebra (1)
- Geometric constraints (1)
- Geometrie (1)
- Geschaltete Systeme (1)
- Gesetz der kleinen Zahlen (1)
- Gestaltoptimierung (1)
- Gewöhnliche Differentialgleichung (1)
- Gewöhnliche Differentialgleichungen (1)
- Gleichmäßige Konvergenz (1)
- Gleichungssysteme (1)
- Globale Analysis (1)
- Glättungsverfahren (1)
- Goodness-of-Fit Test (1)
- Gram points (1)
- Gram’s law (1)
- Graph (1)
- Graph eigenvalues (1)
- Graph products (1)
- Graph spectrum (1)
- Graphnullity (1)
- Grassmann Manifold (1)
- Grassmann-Mannigfaltigkeit (1)
- Gravitationsfeld (1)
- Guignard CQ (1)
- Gumbel-Verteilung (1)
- HAND (1)
- HDL (1)
- HIV infections (1)
- Hamilton Systeme (1)
- Hamilton Sytstems (1)
- Hamilton-Jacobi-Differentialgleichung (1)
- Hautus test (1)
- Hecke L-functions (1)
- Hecke eigenforms (1)
- Hierarchische Matrix (1)
- Hilbert-Raum (1)
- Hilfe-System (1)
- Hochschuldidaktik (1)
- Hochschule+Lehre (1)
- Homicidal Chauffeur game (1)
- Homogenisierung <Mathematik> (1)
- Homologische Algebra (1)
- Honey bee (1)
- Hurwitz spaces (1)
- Hurwitz zeta function (1)
- Hybrid Dynamical Systems (1)
- Hybridsystem (1)
- Hydrodynamische Grenzwerte (1)
- Hymenoptera venom (1)
- Hyperbolic Partial Differential Equations (1)
- Hyperbolische Differentialgleichung (1)
- Hypertranscendence (1)
- Hüllenbildung (1)
- Ignorance (1)
- Ignoranz (1)
- Image Registration (1)
- Immunotherapy (1)
- Incompressibility (1)
- Infinite Optimierung (1)
- Inkompressibilität (1)
- Innere-Punkte-Verfahren (1)
- Integral graph (1)
- Integralgleichung (1)
- Integrodifferentialgleichung (1)
- Interactive Help System (1)
- Interconnection (1)
- Invarianter Unterraum (1)
- Inverse Iteration (1)
- Isomorphie (1)
- Isomorphieklasse (1)
- Isoparametrische Hyperfläche (1)
- Jacobi-Eigenwert-Verfahren (1)
- Jacobi-type eigenvalue methods (1)
- Jacobi-ähnliches Verfahren (1)
- Jacobsthal function (1)
- Jakob <Mathematiker (1)
- Julia line (1)
- Julius Hurwitz (1)
- Kanzow, C. Y. Cui, J.-S. Pang: “Modern Nonconvex Nondifferentiable Optimization” (1)
- Kapitalverflechtung (1)
- Kapitalverflechtungen (1)
- Karush-Kuhn-Tucker-Bedingungen (1)
- Kegelgebiet (1)
- Keller–Segel model (1)
- Kettenbruch (1)
- Klassifikation (1)
- Kloosterman sum (1)
- Koenigs function (1)
- Kollinearität (1)
- Kombinatorische Optimierung (1)
- Kombinatorische Zahlentheorie (1)
- Komplexe Flüssigkeiten (1)
- Komprimierte Abtastung (1)
- Kondition <Mathematik> (1)
- Konforme Abbildungen (1)
- Konforme Metrik (1)
- Konjugierte-Gradienten-Methode (1)
- Konstruktionsmethoden (1)
- Kontinuitätsgleichung (1)
- Kontinuumsmechanik (1)
- Kontrollsystem (1)
- Konvergenz bei quadratischem Eigenwertproblem (1)
- Konvexe Analysis (1)
- Korrekt gestelltes Problem (1)
- Korrelation (1)
- Krylow matrix (1)
- Kryptologie (1)
- Kurdyka--{\L}ojasiewicz property (1)
- LPEC (1)
- Ladyzhenskaya Konstante (1)
- Ladyzhenskaya constant (1)
- Landau type theorem (1)
- Langschrittmethoden (1)
- Laplace approximation (1)
- Laser (1)
- Lasersimulation (1)
- Least Action Principle (1)
- Lehrerbildung (1)
- Lennard-Jones-Potenzial (1)
- Lerch zeta function (1)
- Lie n-algebroids (1)
- Lie-Gruppe (1)
- Liegruppen (1)
- Lindblad-Kossakowski Master Equation (1)
- Lineare Funktionalanalysis (1)
- Lineare Regression (1)
- Linearer Operator (1)
- Lineares System (1)
- Liouville and transport equations (1)
- Local Lipschitz continuity (1)
- Local rings (1)
- Lyapunov Funktion (1)
- Lyapunov Stability (1)
- Lückenreihe (1)
- Lückenreihen (1)
- M-Stationär (1)
- M-stationarity (1)
- MHD (1)
- MIND estimator (1)
- MPCC (1)
- MPVC (1)
- MSC 11M35 (1)
- Machzahl (1)
- Magnetic Resonance Imaging (1)
- Magnetoelasticity (1)
- Magnetohydrodynamics (1)
- Magnetohydrodynamik (1)
- Magnetoviscoelastic Fluids (1)
- Magnetoviskoelastische Flüsse (1)
- Mapping Properties (1)
- Martensit (1)
- Master-Gleichung (1)
- Mastocytosis (1)
- Mathematical modeling (1)
- Mathematikdidaktik (1)
- Mathematiklernen (1)
- Mathematisches Modell (1)
- Matrix (1)
- Matrixpolynom (1)
- Matrizenpolynom (1)
- Matrizenzerlegung (1)
- Maximal (1)
- Maximale (1)
- Maximum Dissipation Principle (1)
- Maße für Quantenverschränkung (1)
- Medical image reconstruction (1)
- Mehragentensystem (1)
- Mehrdimensionale Signalverarbeitung (1)
- Mehrgitter (1)
- Mehrskalenmodell (1)
- Metakognition (1)
- Metrologie (1)
- Minimal surfaces (1)
- Minimalfläche (1)
- Minimalflächen (1)
- Minimalkurven (1)
- Minimizing movements (1)
- Minimum Information Probability Distribution (1)
- Minimum Information Wahrscheinlichkeitsverteilung (1)
- Mittlere Krümmung (1)
- Mobiler Roboter (1)
- Modeling (1)
- Modellierung (1)
- Moment <Stochastik> (1)
- Monodromy (1)
- Monte Carlo Simulation (1)
- Moving mesh method (1)
- Multi-agent systems (1)
- Multiple Repräsentationen (1)
- Multiple representations (1)
- Multivariate Generalized Pareto Distributions (1)
- Multivariate order statistics (1)
- Multivariate statistics (1)
- Multivariate verallgemeine Pareto-Verteilungen (1)
- NCP-Funktionen (1)
- NCP-functions (1)
- Nash Equilibrium Problem (1)
- Nash equilibrium (1)
- Navier-Stokes equations (1)
- Navier-Stokes-Gleichung (1)
- Near-Isomorphie (1)
- Nematic Liquid Crystals (1)
- Nematische Flüssigkristalle (1)
- Neue Medien (1)
- Newton method (1)
- Newton-Raphson Method (1)
- Newton-Raphson Verfahren (1)
- Newtonsches Kräftegleichgewicht (1)
- Newtonverfahren (1)
- Nichtglatte Analysis (1)
- Nichtlineare Funktionalgleichung (1)
- Nichtlinearer Operator (1)
- Nichtlineares System (1)
- Nichtparametrische Statistik (1)
- Nikaido-Isoda Funktion (1)
- Niveaustufen des Beweises (1)
- Non-smooth optimal control (1)
- Non-steroidal anti-inflammatory drug (1)
- Nonlinear systems (1)
- Nonparametric Inference (1)
- Nonsmooth optimization (1)
- Nullstelle (1)
- Numerical Asset Valuation (1)
- Numerical Methods (1)
- Numerik (1)
- Numerische Strömungssimulation (1)
- Operatortheorie (1)
- Optimal Control (1)
- Optimal control problem (1)
- Optimierung / Nebenbedingung (1)
- Optimierung auf Mannigfaltigkeiten (1)
- Optimierungsproblem (1)
- Optimization on Lie Groups (1)
- Order Statistics (1)
- Overstatement models (1)
- PDEs (1)
- Paper-folding (1)
- Papierfalten (1)
- Parabolic equations (1)
- Parametric inference (1)
- Parametric optimization (1)
- Parametrische Optimierung (1)
- Parametrisierung (1)
- Partielle Differentialgleichungen (1)
- Peaks over Threshold (1)
- Penalized Least Squares Method (1)
- Penalized Least Squares Methode (1)
- Periodic homogenization (1)
- Phasenumwandlung (1)
- Piecewise Polynomial Function (1)
- Plasma (1)
- Poisson Gleichung (1)
- Poisson algebras (1)
- Poisson equation (1)
- Poisson-Gleichung (1)
- Poisson-Prozess (1)
- Polyatomare Verbindungen (1)
- Polynomial matrices (1)
- Pontrjagin-Maximumprinzip (1)
- Pontryagin Maximum Principle (1)
- Pontryagin Maximum Prinzip (1)
- Pontryagins's maximum principle (1)
- Post-Quantum-Kryptografie (1)
- Prediction Procedure (1)
- Primzahl (1)
- Probability theory (1)
- Problemlösen (1)
- Prognose (1)
- Projection Theorem (1)
- Projektionssatz (1)
- Proof (1)
- Proving Level (1)
- Proximal Method (1)
- Proximal-Punkt-Verfahren (1)
- Präkonditionierung (1)
- Pseudo-allergy (1)
- Pseudogeodätische (1)
- Pseudometrik (1)
- Quadratischer Zahlkörper (1)
- Quantenmechanik (1)
- Quantenmechanisches System (1)
- Quantum control (1)
- Quasi-Variational Inequality (1)
- Quasi-Variationsungleichung (1)
- Quasi-variational inequalities (1)
- Quasibases (1)
- Quasibasis (1)
- Quasiconformal automorphism (1)
- Quasikonforme Abbildung (1)
- Randomness (1)
- Rangstatistik (1)
- Razumikhin method (1)
- Reachability matrix (1)
- Reelle Funktion (1)
- Registrierung <Bildverarbeitung> (1)
- Regularisation Methods (1)
- Regularisierung (1)
- Regularisierungsverfahren (1)
- Regularized gap function (1)
- Reine Untergruppen (1)
- Rekord (1)
- Relapse (1)
- Relativnormale (1)
- Relaxation method (1)
- Restklasse (1)
- Rezension (1)
- Ridge-Regression (1)
- Riemann Hypothesis (1)
- Riemann hypothesis (1)
- Riemannian manifolds (1)
- Riemannian optimization (1)
- Riemannsche Geometrie (1)
- Riemannsche Mannigfaltigkeiten (1)
- Riemannsche Optimierung (1)
- Risikomanagement (1)
- Risk factor (1)
- Rothe method (1)
- Runge-type Theorems (1)
- STEM classroom (1)
- STEM education (1)
- STEM integration (1)
- Satz von Cartan (1)
- Scheme for solving optimal control problems (1)
- Schnelle Fourier-Transformation (1)
- Schur ring (1)
- Schwache Kompaktheit (1)
- Schwache Lösungen (1)
- Sekundarstufe (1)
- Selberg Class (1)
- Selberg Klasse (1)
- Selbergsche L-Reihe (1)
- Semidefinite Optimierung (1)
- Semidefinite Programme (1)
- Semidualität (1)
- Semidualtität (1)
- Semismooth Newton Method (1)
- Sequential Quadratic Hamiltonian scheme (1)
- Sequential quadratic Hamiltonian scheme (1)
- Set-valued mapping (1)
- Shape Optimization (1)
- Simulieren (1)
- Singulärfunktionen (1)
- Skalierungsfunktion (1)
- Small-Gain Theorem (1)
- Softwareentwicklung (1)
- Sparsity (1)
- Spektraltheorie (1)
- Sphäre (1)
- Spin systems (1)
- Spinsystem (1)
- Spiralflächen (1)
- Spiraltypfläche (1)
- Spiraltypflächen (1)
- Spline (1)
- Stabilitätsanalyse (1)
- Starke Kopplung (1)
- Steuerbarkeit (1)
- Stochastic Algorithms (1)
- Stochastic Process (1)
- Stochastic homogenization (1)
- Stochastik (1)
- Stochastische Optimierung (1)
- Stochastisches System (1)
- Stokes Gleichung (1)
- Stokes equation (1)
- Stokes-Gleichung (1)
- Structrual Model (1)
- Struktur (1)
- Strömung (1)
- Stückweise Polynomiale Funktion (1)
- Symmetrie (1)
- Symmetrien (1)
- Symmetrische Konfiguration (1)
- Symplektische Geometrie (1)
- System von partiellen Differentialgleichungen (1)
- Systemhalbgruppen (1)
- Systemic Risk (1)
- Systemsemigroups (1)
- Sätze (1)
- T3s (1)
- TD Kohn-Sham equations (1)
- TDDFT (1)
- Tail-behavior (1)
- Teaching (1)
- Testen (1)
- Theorems (1)
- Topologieoptimierung (1)
- Torsion-free abelian groups (1)
- Torsionsfreie abelsche Gruppe (1)
- Total Variation (1)
- Totale Variation (1)
- Toulmin Modell (1)
- Transitive Lie Groups (1)
- Transportkoeffizient (1)
- Treatment failure (1)
- Ulm-Kaplansky Invarianten (1)
- Ulm-Kaplansky invariants (1)
- Uncertainty (1)
- Uniform distribution modulo one (1)
- Uniform topology (1)
- Universal Functions (1)
- Universality (1)
- Universalität (1)
- Unsicherheit (1)
- Untergruppe (1)
- Unternehmensbewertung (1)
- Unterraumsuche (1)
- Unterräume (1)
- Uzawa Verfahren (1)
- Uzawa iteration (1)
- Value at Risk (1)
- Value ranges (1)
- Vandermonde matrix (1)
- Variationsungleichung (1)
- Verfahren der konjugierten Gradienten (1)
- Vespula (1)
- Volumen (1)
- Von Mises conditions (1)
- Vorhersagbarkeit (1)
- Vorhersagetheorie (1)
- Vorhersageverfahren (1)
- Vorkonditionierer (1)
- Wahrscheinlichkeitsrechnung (1)
- Wahrscheinlichkeitstheorie (1)
- Wahrscheinlichkeitsverteilung (1)
- Walsh (1)
- Warteschlangennetz (1)
- Weak Solutions (1)
- Weibull distribution (1)
- Weibull type density (1)
- Wein (1)
- Well-Balanced (1)
- Well-posedness (1)
- Wettbewerbsdesign (1)
- ZRP (1)
- Zeitdiskrete Approximation (1)
- Zeitoptimale Regelung (1)
- Zero Range Prozess (1)
- Zero-divisor graph (1)
- Zero-divisor graphs (1)
- Zero-inflation (1)
- Zeta-Functions (1)
- Zeta-function (1)
- Zufall (1)
- Zwei-Ebenen-Optimierung (1)
- a-point distribution (1)
- a-posteriori error estimates (1)
- abelian groups (1)
- adaptive intervention competence (1)
- adaptive refinement (1)
- adjoint and coadjoint representations (1)
- affine minimal surface (1)
- affine normal (1)
- affine scaling methods (1)
- algebraic aggregation (1)
- algebraic degree (1)
- algebraic function field (1)
- algebraische Aggregation (1)
- almost completely decomosable group (1)
- almost completely decomposable group (1)
- almost completely decomposable groups (1)
- analytical continuation (1)
- analytische Fortsetzung (1)
- approaches in textbooks (1)
- asthma (1)
- asymptotic analysis (1)
- asymptotic sufficiency (1)
- asymptotically flat ends (1)
- atomistic models (1)
- augmented Lagrange method (1)
- augmented Lagrangian (1)
- avoidance (1)
- backward orbit (1)
- basic mental model (1)
- beispielsbasiertes Lernen (1)
- bevacizumab (1)
- bi-steerable robot (1)
- bias (1)
- bicommutators (1)
- black box (1)
- bleb failure (1)
- bleb scarring (1)
- block design (1)
- blood (1)
- body weight (1)
- bound constraints (1)
- bounded input bounded output stability (1)
- branch- and-bound Verfahren (1)
- branch-and-bound algorithm (1)
- buildings (1)
- canal surgery (1)
- canaloplasty (1)
- cancer (1)
- cataract surgery (1)
- centroaffine normal (1)
- chlamydia (1)
- chlamydia infection (1)
- chlamydia trachomatis (1)
- chordal Loewner equation (1)
- circular arc polygon domain (1)
- circumferential viscodilation (1)
- co-extremality coefficient (1)
- coherent forecasting (1)
- cohomology (1)
- collinearity (1)
- combinatorial theory (1)
- companion matrix (1)
- complementary problems (1)
- complex polynomials (1)
- composite optimization (1)
- composition of functions (1)
- compressible fluid (1)
- computational biology and bioinformatics (1)
- condenser capacity (1)
- conecontinuity type constraint qualification (1)
- conewise linear systems (1)
- confidence interval (1)
- conformal mapping (1)
- conformal pseudo-metrics (1)
- conical domain (1)
- conservation law (1)
- continuum limit (1)
- convergence (1)
- convergence for quadratic eigenvalue problems (1)
- convergent star product (1)
- converse Lyapunov theorems (1)
- convolution (1)
- convolutional code (1)
- copula (1)
- coverings (1)
- critical line (1)
- cross-ownership (1)
- cubic-monoclinic martensites (1)
- cyclic matrix (1)
- degrees of freedom in internal energy (1)
- derivation (1)
- derivative (1)
- design (1)
- diagnosis (1)
- differential games (1)
- differential graded modules (1)
- differential nash games (1)
- diffuse interface models (1)
- digital technologies (1)
- digital tools (1)
- digitale Werkzeuge (1)
- discontinuous coefficient functions (1)
- discrete systems (1)
- discrete-time systems (1)
- discrete-to-continuum (1)
- distribution modulo one (1)
- dopamine (1)
- drug adherence (1)
- duality (1)
- dyadic product BMO (1)
- echocardiography (1)
- eigenmode (1)
- elliptic PDE (1)
- elliptic curves (1)
- elliptic problems (1)
- empirical evidence (1)
- empirical investigation (1)
- enatnglement measure (1)
- ensemble optimal control problems (1)
- ensemble reachability (1)
- entropy inequality (1)
- entropy minimization (1)
- epidemiology (1)
- equivariant cohomology (1)
- ergodic transformation (1)
- error estimate (1)
- erstes Randwertproblem in PDE (1)
- euclidean normal (1)
- euklidische Normale (1)
- example based learning (1)
- examples and counterexamples (1)
- exceedance counts (1)
- exchangeable D-norms (1)
- existence of solutions (1)
- expected shortfall (1)
- expectiles (1)
- explicit discontinuous Galerkin (1)
- exponent pairs (1)
- exponential growth (1)
- extremal coefficient (1)
- extremal exchangeable D-norms (1)
- extreme order statistics (1)
- extremum seeking control (1)
- filter-SQPEC algorithm (1)
- financial network (1)
- finanzielles Netzwerk (1)
- finite differences (1)
- finite element method (1)
- finite fields (1)
- finite groups (1)
- finite projective plane (1)
- finite volume method (1)
- finite volume methods (1)
- firm valuation (1)
- first boundary value problem in PDE (1)
- flexible microcatheter (1)
- fluid networks (1)
- fluid–structure interaction model (1)
- foliation (1)
- fracture (1)
- fredholm operator (1)
- freies Randwertproblem (1)
- function identification (1)
- functional D-norm (1)
- functional thinking (1)
- galois extensions (1)
- gamma-convergence (1)
- gap power series (1)
- generalized quadrangles (1)
- generator of D-norm (1)
- geometric control (1)
- geometrically linear elasticity (1)
- geometrisch lineare Elastizitätstheorie (1)
- geometrische Kontrolltheorie (1)
- geometry (1)
- gewichtete Gleichverteilung modulo eins (1)
- gewichtete Sobolevräume (1)
- gewöhnliche Differentialgleichungen (1)
- glaucoma (1)
- glaucoma surgery (1)
- global attractor (1)
- gradient-like systems (1)
- gradientenähnliche Systeme (1)
- green energy (1)
- growth models (1)
- halbeinfache Lie Algebren (1)
- harmonic measure (1)
- hierarchical matrix (1)
- higher order methods (1)
- highly-active antiretroviral therapy (1)
- homogene Raüme (1)
- homogeneous spaces (1)
- homogenization (1)
- homogenous parameter-depedent systems (1)
- hydrodynamic limits (1)
- hyperbolic area (1)
- hyperbolic systems (1)
- image denoising (1)
- imaginary quadratic field (1)
- immune activation (1)
- impulsive systems (1)
- infeasible interior point paths (1)
- infinite dimensional optimization (1)
- infinite-dimensional systems (1)
- input-to-state stability (1)
- integral (1)
- integral graph (1)
- interior point methods (1)
- intermediate order statistics (1)
- inverse Iteration (1)
- inverse problems (1)
- isogeny-based cryptography (1)
- isomorph (1)
- isomorphic (1)
- isomorpism (1)
- kinetic chemotaxis equation (1)
- kinetic description of gases (1)
- konforme Pseudo-Metriken (1)
- kubisch-monokliner Phasenübergang (1)
- large-scale (1)
- large-time behaviour (1)
- laser simulation (1)
- linear system (1)
- literature review (1)
- local asymptotic normality (1)
- local classes (1)
- local existence (1)
- local input-to-state stability (1)
- long step methods (1)
- lonlinear reaction-diffusion equations (1)
- low Mach number (1)
- lyapunov methods (1)
- macrophages (1)
- magnetic fluids (1)
- mathematical biology (1)
- mathematical paperfolding (1)
- mathematics classrooms (1)
- mathematisches Modellieren (1)
- mathematisches Papierfalten (1)
- matrix decomposition (1)
- max-linear model (1)
- max-stable process (1)
- mid quantiles (1)
- minimal curves (1)
- minimal surface (1)
- mitomycin C (1)
- mittlere Krümmung (1)
- monodromy groups (1)
- months follow-up (1)
- morbid obesity (1)
- multigrid schemes (1)
- multiply connected domain (1)
- multiscale methods (1)
- multiscale modeling (1)
- multivariate Extreme Value Distribution (1)
- multivariate Gaussian distribution (1)
- multivariate exceedance (1)
- multivariate extreme value theory (1)
- multivariate generalized Pareto distribution (1)
- multivariate max-domain of attraction (1)
- multivariate statistical process control (SPC) (1)
- mutually permutable (1)
- near-isomorph (1)
- near-isomorphic (1)
- near-isomorphism (1)
- new media (1)
- nichtglatt (1)
- nichtglatte Newton-artige Verfahren (1)
- nichtholonomes System (1)
- nichtlineare & gemischte Komplementaritätsprobleme (1)
- nichtlineare Optimierung (1)
- non-Lipschitz optimization (1)
- non-convex optimal control problems (1)
- non-smooth and non-convex optimization (1)
- non-smooth large-scale optimisation (1)
- non-smooth optimal control problems (1)
- non-smooth optimization (1)
- nonconvex optimization (1)
- nonderogatory matrix (1)
- nonholonomic system (1)
- nonlinear and mixed complementarity problems (1)
- nonlinear inverse problems (1)
- nonlinear least squares reformulation (1)
- nonlinear optimization (1)
- normal families (1)
- normale Familien (1)
- numerical approximations (1)
- numerical finance (1)
- numerical methods (1)
- obesity (1)
- observer (1)
- one-fold-origami (1)
- open-angle glaucoma (1)
- operative principle (1)
- optimal control problem (1)
- optimal control problems (1)
- optimal control theory (1)
- optimal solution mapping (1)
- optimization on manifolds (1)
- order of growth (1)
- over-determined problem (1)
- p-Gruppen (1)
- p-groups (1)
- p-soluble groups (1)
- p-supersolubility (1)
- parametrization (1)
- partial differential equation (1)
- partial differential equations (1)
- partial differetial equations (1)
- partial integro-differential Fokker-Planck Equation (1)
- partial integro-differential equations (1)
- partielle Differentialgleichungen (1)
- pedagogical content knowledge (1)
- pedestrian motion (1)
- petal (1)
- phacocanaloplasty (1)
- phacotrabeculectomy (1)
- phase I (1)
- phase II (1)
- plasma modelling (1)
- plasma physics (1)
- polyatomic molecules (1)
- polymerase chain reaction (1)
- polymorphism (1)
- polynomial chaos (1)
- pontryagin maximum principle (1)
- preconditioning (1)
- prediction interval (1)
- predictive performance (1)
- projective plane (1)
- projektive Ebene (1)
- proximal Newton method (1)
- proximal method (1)
- proximal methods (1)
- pseudo geodesics (1)
- pulmonary function (1)
- pulmonary hypertension (1)
- pure subgroups (1)
- quadratic convergence (1)
- quadratic number field (1)
- quadratische Konvergenz (1)
- quantile forecasts (1)
- quasi-continuum (1)
- quasinormality constraint qualification (1)
- queueing networks (1)
- radial Loewner equation (1)
- random walk (1)
- reaction-diffusion (1)
- reduced residues (1)
- regression (1)
- regularization (1)
- regulating (1)
- regulating subgroup (1)
- regulierend (1)
- regulierende Untergruppen (1)
- relative normal (1)
- relaxation method (1)
- repelling phenomenon (1)
- representation of pseudo-metrics (1)
- representations up to homotopy (1)
- ridge regression (1)
- robustness (1)
- role of mathematics in STEM (1)
- secondary education (1)
- semi-convex hulls (1)
- semi-konvexe Hüllen (1)
- semidefinite Komplementaritätsprobleme (1)
- semidefinite complementarity problems (1)
- semidefinite programming (1)
- semiduality (1)
- semigroup of holomorphic functions (1)
- semilinear elliptic operators (1)
- semisimple Lie algebras (1)
- semismooth (1)
- semismooth Newton-type methods (1)
- sequential optimality condition (1)
- sequential quadratic hamiltonian method (1)
- series (1)
- simulation (1)
- singular functions (1)
- singularly perturbed problem (1)
- singulär gestörtes Problem (1)
- smoothing-type methods (1)
- sparse control problems (1)
- special sweeps (1)
- spectral theory (1)
- spezielle Sweep-Methoden (1)
- spiral surfaces (1)
- spiral type surfaces (1)
- star products (1)
- stationarity (1)
- stochastischer Prozess (1)
- structural model (1)
- structure (1)
- structured normal form problem (1)
- strukturierte Normalformprobleme (1)
- subspace clustering (1)
- subspaces (1)
- successive approximations strategy (1)
- sufficient optimality conditions (1)
- surgical outcomes (1)
- switched systems (1)
- symmetric configuration (1)
- symmetries (1)
- symplectic geometry (1)
- systemic risk (1)
- systems biology (1)
- tail conditional expectation (1)
- tail dependence (1)
- task design (1)
- teacher education (1)
- technology (1)
- tensor rank (1)
- test instrument (1)
- therapy (1)
- tight (1)
- time-optimal control (1)
- time-varying (1)
- time‐varying delay (1)
- torsionfree abelian groups (1)
- torsionsfreie abelsche Gruppen (1)
- total variation (1)
- transport coefficients (1)
- typically real functions (1)
- uncertain volatility (1)
- uncertainty quantification (1)
- univalent functions (1)
- universality (1)
- unstetige Koeffizientenfunktionen (1)
- unzulässige Innere-Punkte-Pfade (1)
- value at risk (1)
- value-distribution (1)
- variational estimation (1)
- variational fracture (1)
- velocity jump process (1)
- velocity-dependent collision frequency (1)
- verallgemeinerte Vierecke (1)
- viral replication (1)
- volume (1)
- vorticity preserving (1)
- weight loss (1)
- weighted Sobolev spaces (1)
- weighted uniform distribution modulo one (1)
- well posedness (1)
- well-balancing (1)
- wine fermentation (1)
- zeitoptimale Steuerung (1)
- zentroaffine Normale (1)
- zero-finding (1)
- zeta-functions (1)
- zweiachsgelenkter Roboter (1)
- Überschreitungen (1)
- Überschreitungsanzahl (1)
- Čebyšev-Polynome (1)
Institute
- Institut für Mathematik (222) (remove)
Sonstige beteiligte Institutionen
ResearcherID
- C-2593-2016 (1)
EU-Project number / Contract (GA) number
- 304617 (2)
In Janssen and Reiss (1988) it was shown that in a location model of a Weibull type sample with shape parameter -1 < a < 1 the k(n) lower extremes are asymptotically local sufficient. In the present paper we show that even global sufficiency holds. Moreover, it turns out that convergence of the given statistical experiments in the deficiency metric does not only hold for compact parameter sets but for the whole real line.
It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an lid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.
In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.
In this paper, convex approximation methods, suclt as CONLIN, the method of moving asymptotes (MMA) and a stabilized version of MMA (Sequential Convex Programming), are discussed with respect to their convergence behaviour. In an extensive numerical study they are :finally compared with other well-known optimization methods at 72 examples of sizing problems.
The aim of the present paper is to clarify the role of extreme order statistics in general statistical models. This is done within the general setup of statistical experiments in LeCam's sense. Under the assumption of monotone likelihood ratios, we prove that a sequence of experiments is asymptotically Gaussian if, and only if, a fixed number of extremes asymptotically does not contain any information. In other words: A fixed number of extremes asymptotically contains information iff the Poisson part of the limit experiment is non-trivial. Suggested by this result, we propose a new extreme value model given by local alternatives. The local structure is described by introducing the space of extreme value tangents. It turns out that under local alternatives a new class of extreme value distributions appears as limit distributions. Moreover, explicit representations of the Poisson limit experiments via Poisson point processes are found. As a concrete example nonparametric tests for Frechet type distributions against stochastically larger alternatives are treated. We find asymptotically optimal tests within certain threshold models.
In dieser Arbeit beschäftigen wir uns mit Themen aus der affinen Hyperflächentheorie. Nachdem wir die euklidische Normale, die Blaschkesche Affinnormale, eine gewisse Einparameterfamilie von Relativnormalen und die zentroaffine Normale besprochen und eine neue Einparameterfamilie von Relativnormalen definiert haben, behandeln wir die folgenden drei Schwerpunkte: Zuerst befassen wir uns mit Minimalflächen bezüglich verschiedener Volumina und der Rolle der jeweiligen Mittleren Krümmung. Wir berechnen die erste und zweite Variation der Volumina, die von den Normalen der erwähnten Familien induziert werden. Hierbei stellen wir fest, daß die Mittlere Krümmung nicht immer das Verschwinden der ersten Variation des Volumens anzeigt. Anschließend übertragen wir die Begriffe Adjungierte und Assoziierte bei euklidischen Minimalflächen auf Affinminimalflächen: Analog zum euklidischen Fall kann man die Konormale einer Affinminimalfläche durch bestimmte ,,harmonische'' Abbildungen darstellen. Wir geben eine Methode an, wie man aus einer gegebenen Affinminimalfläche weitere gewinnt, indem man diese Abbildungen entsprechend modifiziert. Schließlich lösen wir eine Verallgemeinerung des Björlingschen Problems für Normalen der oben erwähnten Familien: Bei Vorgabe einer Kurve mit zwei Vektorfeldern und der Art der Normalisierung existiert - mit Ausnahmen - je genau eine elliptische und eine hyperbolische Fläche in (pseudo-)isothermen Parametern mit folgenden Eigenschaften: Die Kurve ist eine Parameterlinie, die Normale längs der Kurve stimmt mit dem einen Vektorfeld überein, die Konormale mit dem anderen und die Mittlere und Gaußsche Krümmung erfüllen eine vorgegebene Bedingung.
Charakteristisch für die Lösbarkeit von elliptischen partiellen Differentialgleichungssystemen mit Nebenbedingungen ist das Auftreten einer inf-sup-Bedingung. Im prototypischen Fall der Stokes-Gleichungen ist diese auch als Ladyzhenskaya-Bedingung bekannt. Die Gültigkeit dieser Bedingung, bzw. die Existenz der zugehörigen Konstante ist eine Eigenschaft des Gebietes, innerhalb dessen die Differentialgleichung gelöst werden soll. Während die Existenz schon die Lösbarkeit garantiert, ist beispielsweise für Fehleraussagen bei der numerischen Approximation auch die Größe der Konstanten sehr wichtig. Insbesondere auch deshalb, weil eine ähnliche inf-sup-Bedingung auch bei der Diskretisierung mittel Finiter-Elemente-Methoden auftaucht, die hier Babuska-Brezzi-Bedingung heißt. Die Arbeit befaßt sich auf der einen Seite mit einer analytischen Abschätzung der Ladyzhenskaya-Konstante für verschiedene Gebiete, wobei Äquivalenzen mit verwandten Problemen aus der komplexen Analysis (Friedrichs-Ungleichung) und der Strukturmechanik (Kornsche Ungleichung) benutzt werden. Ein weiterer Teil befaßt sich mit dem Zusammenhang zwischen kontinuierlicher Ladyzhenskaya- Konstante und diskreter Babuska-Brezzi-Konstante. Die dabei gefundenen Ergebnisse werden mit Hilfe eines dazu entwickelten leistungsfähigen Finite-Elemente-Programmsystems numerisch verifiziert. Damit können erstmals genaue Abschätzungen der Konstanten in zwei und drei Dimensionen gefunden werden. Aufbauend auf diesen Resultaten wird ein schneller Lösungsalgorithmus für die Stokes-Gleichungen vorgeschlagen und anhand von problematischen Gebieten dessen Überlegenheit gegenüber klassischen Verfahren wie beispielsweise der Uzawa-Iteration demonstriert. Während selbst bei einfachen Geometrien eine Konvergenzbeschleunigung um einen Faktor 5 erwartet werden kann, sind in kritischen Fällen Faktoren bis zu 1000 möglich.
Teil 1 der Arbeit beinhaltet eine Zusammenfassung grundlegender funktionalanalytischer Ergebnisse sowie eine Einführung in die Integral- und Differentialrechnung in Frécheträumen. Insbesondere wird in Kapitel 2 eine ausführliche Darstellung des Lebesgue-Bochner-Integrals auf Frécheträumen geliefert. Teil 2 behandelt die Theorie der linearen Differentialgleichungen auf Frécheträumen. Dazu werden in Kapitel 3 stark differenzierbare Halbgruppen und deren infinitesimale Generatoren charakterisiert. In Kapitel 4 werden diese Ergebnisse benutzt, um lineare Evolutionsgleichungen (von hyperbolischem oder parabolischem Typ) zu untersuchen. Teil 3 enthält die zentralen Resultate der Arbeit. In Kapitel 5 werden zwei Existenz- und Eindeutigkeitssätze für nichtlineare gewöhnliche Differentialgleichungen in zahmen Frécheträumen bewiesen. Kapitel 6 liefert eine Anwendung der Ergebnisse aus Kapitel 5 auf nichtlineare partielle Differentialgleichungen erster Ordnung.
A completely decomposable group is a direct sum of subgroups of the rationals. An almost completely decomposable group is a torsion free abelian group that contains a completely decomposable group as subgroup of finite index. Tight subgroups are maximal subgroups (with respect to set inclusion) among the completely decomposable subgroups of an almost completely decomposable group. In this dissertation we show an extended version of the theorem of Bezout, give a new criterion for the tightness of a completely decomposable subgroup, derive some conditions under which a tight subgroup is regulating and generalize a theorem of Campagna. We give an example of an almost completely decomposable group, all of whose regulating subgroups do not have a quotient with minimal exponent. We show that among the types of elements of a coset modulo a completely decomposable group there exists a unique maximal type and define this type to be -the- coset type. We give criteria for tightness and regulating in term of coset types as well as a representation of the type subgroups using coset types. We introduce the notion of reducible cosets and show their key role for transitions from one completely decomposable subgroup up to another one containing the first one as a proper subgroup. We give an example of a tight, but not regulating subgroup which contains the regulator. We develop the notion of a fully single covered subset of a lattice, show that V-free implies fully single covered, but not necessarily vice versa, and we define an equivalence relation on the set of all finite subsets of a given lattice. We develop some extension of ordinary Hasse diagrams, and apply the lattice theoretic results on the lattice of types and almost completely decomposable groups.
In this thesis we investigate near-isomorphism classes and isomorphism classes of almost completely decomposable groups. In Chapter 2 we introduce the concept of almost completely decomposable groups and sum up their most important facts. A local group is an almost completely decomposable group with a primary regulator quotient. A uniform group is a rigid local group with a homocyclic regulator quotient. In Chapter 3 a weakening of isomorphism, called type-isomorphism, appears. It is shown that type-isomorphism agrees with Lady's near-isomorphism. By the Main Decomposition Theorem and the Primary Reduction Theorem we are allowed to restrict ourselves on clipped local groups, namely groups without a direct rank-one summand. In Chapter 4 we collect facts of matrices over commutative rings with an identity element. Matrices over the local ring (Z / p^e Z) of residue classes of the rational integers modulo a prime power play an important role. In Chapter 5 we introduce representing matrices of finite essential extensions. Here a normal form for local groups is found by the Gauß algorithm. Uniform groups have representing matrices in Hermite normal form. The classification problems for almost completely decomposable groups up to isomorphism and up to near-isomorphism can be rephrased as equivalence problems for the representing matrices. In Chapter 6 we derive a criterion for the representing matrices of local groups in Gauß normal form. In Chapter 7 we formulate the matrix criterion for uniform groups. Two representing matrices in Hermite normal form describe isomorphic groups if and only if the rest blocks of the representing matrices are T-diagonally equivalent. Starting from a fixed near-isomorphism class in Chapter 8 we investigate isomorphism classes of uniform groups. We count groups and isomorphism classes. In Chapter 9 we specialize on uniform groups of rank 2r with a regulator quotient of rank r such that the rest block of the representing matrix is invertible and normed.
In my Ph.D. thesis "On the geometry and parametrization of almost invariant subspaces and observer theory" I consider the set of almost conditioned invariant subspaces of fixed dimension for a given fixed linear finite-dimensional time-invariant observable control system in state space form. Almost conditioned invariant subspaces were introduced by Willems. They generalize the concept of a conditioned invariant subspace requiring the invariance condition to hold only up to an arbitrarily small deviation in the metric of the state space. One of the goals of the theory of almost conditioned invariant subspaces was to identify the subspaces appearing as limits of sequences of conditioned invariant subspaces. An example due to {\"O}zveren, Verghese and Willsky, however, shows that the set of almost conditioned invariant subspaces is not big enough. I address this question in a joint paper with Helmke and Fuhrmann (Towards a compactification of the set of conditioned invariant subspaces, Systems and Control Letters, 48(2):101-111, 2003). Antoulas derived a description of conditioned invariant subspaces as kernels of permuted and truncated reachability matrices of controllable pairs of the appropriate size. This description was used by Helmke and Fuhrmann to construct a diffeomorphism from the set of similarity classes of certain controllable pairs onto the set of tight conditioned invariant subspaces. In my thesis I generalize this result to almost conditioned invariant subspaces describing them in terms of restricted system equivalence classes of controllable triples. Furthermore, I identify the controllable pairs appearing in the kernel representations of conditioned invariant subspaces as being induced by corestrictions of the original system to the subspace. Conditioned invariant subspaces are known to be closely related to partial observers. In fact, a tracking observer for a linear function of the state of the observed system exists if and only if the kernel of that function is conditioned invariant. In my thesis I show that the system matrices of the observers are in fact the corestrictions of the observed system to the kernels of the observed functions. They in turn are closely related to partial realizations. Exploring this connection further, I prove that the set of tracking observer parameters of fixed size, i.e. tracking observers of fixed order together with the functions they are tracking, is a smooth manifold. Furthermore, I construct a vector bundle structure for the set of conditioned invariant subspaces of fixed dimension together with their friends, i.e. the output injections making the subspaces invariant, over that manifold. Willems and Trentelman generalized the concept of a tracking observer by including derivatives of the output of the observed system in the observer equations (PID-observers). They showed that a PID-observer for a linear function of the state of the observed system exists if and only if the kernel of that function is almost conditioned invariant. In my thesis I replace PID-observers by singular systems, which has the advantage that the system matrices of the observers coincide with the matrices appearing in the kernel representations of the subspaces. In a second approach to the parametrization of conditioned invariant subspaces Hinrichsen, M{\"u}nzner and Pr{\"a}tzel-Wolters, Fuhrmann and Helmke and Ferrer, F. Puerta, X. Puerta and Zaballa derived a description of conditioned invariant subspaces in terms of images of block Toeplitz type matrices. They used this description to construct a stratification of the set of conditioned invariant subspaces of fixed dimension into smooth manifolds. These so called Brunovsky strata consist of all the subspaces with fixed restriction indices. They constructed a cell decomposition of the Brunovsky strata into so called Kronecker cells. In my thesis I show that in the tight case this cell decomposition is induced by a Bruhat decomposition of a generalized flag manifold. I identify the adherence order of the cell decomposition as being induced by the reverse Bruhat order.
Spiraltypflächen sind Minimalflächen des dreidimensionalen euklidischen Raums, die sich durch hohe Symmetrie gegenüber komplexen Ähnlichkeitsabbildungen der Minimalkurve auszeichnen. Ihren Namen verdanken Sie folgender Eigenschaft: Sie und ihre komplex Homothetischen sind die einzigen auf Spiralflächen abwickelbaren Minimalflächen. Bekannte Spiraltypflächen sind die Spiralminimalflächen (zugleich Minimal- und Spiralflächen) und die Bourflächen (auf Rotationsflächen abwickelbare Minimalflächen). Das Katenoid und die Enneperfläche sind spezielle Bourflächen. In dieser Arbeit werden die Spiraltypflächen auf ihre geometrischen Eigenschaften untersucht. Wir stellen ihre Periodizitäten und Symmetrien fest und versuchen, ausgezeichnete Flächenkurven auf ihnen zu finden. Wir verwenden eine globale Weierstraß-Darstellung der Spiraltypflächen. In dieser Darstellung ergeben die Flächen eine Schar mit einem komplexen Scharparameter. Anhand dieser Darstellung leiten wir sämtliche Symmetrien der Spiraltypflächen zu linearen Ähnlichkeitsabbildungen der Minimalkurve her. Als Spezialfälle erhalten wir die Symmetrien unter Assoziationen und Derivationen (Drehung der Minimalkurve um einen imaginären Drehwinkel), sowie die reellen Symmetrien (Dreh-, Spiegel- und Strecksymmetrien). Unter den Spiraltypflächen gibt es nur zwei translationssymmetrische Flächen. Die Umorientierung einer Spiraltypfläche entspricht (bis auf komplexe Homothetie) dem Vorzeichenwechsel des Flächenparameters. Im Übrigen kann durch einfache Spiegelungen an den Koordinatenebenen beziehungsweise Drehungen um die Koordinatenachsen das Vorzeichen von Real- beziehungsweise Imaginärteil des Flächenparameters umgekehrt werden. Schließlich stellen wir noch ausgezeichnete Flächenkurven auf den Spiraltypflächen vor: Krümmungslinien, Asymptotenlinien und Geodätische, sowie als deren Verallgemeinerungen die Pseudokrümmungslinien und Pseudogeodätischen.
Die vorliegende Arbeit untersucht die Analytizitätseigenschaften unzulässiger Innerer-Punkte Pfade bei monotonen Komplementaritätsproblemen und diskutiert mögliche algorithmische Anwendungen. In Kapitel 2 werden einige matrixanalytische Konzepte und Resultate zusammengestellt, die für die Beweisführung in den folgenden Kapiteln benötigt werden. Kapitel 3 gibt eine genaue Definition der Begriffe "monotones lineares Komplementaritätsproblem" (LCP) bzw. "semidefinites monotones lineares Komplementaritätsproblem" (SDLCP) und zeigt die Grundidee hinter den Innere-Punkte-Verfahren zur Lösung solcher Probleme. Kapitel 4 beinhaltet die analytischen Hauptresultate für monotone Komplementaritätsprobleme. In Abschnitt 4.1 werden einige wohlbekannte Resultate über die Analytizitätseigenschaften unzulässiger Innerer-Punkte-Pfade für LCP's wiedergegeben. Diese werden in Abschnitt 4.2 auf den semidefiniten Fall übertragen. Unter der Annahme, dass das zugrundeliegende SDLCP eine strikt komplementäre Lösung besitzt, wird gezeigt, dass die Inneren-Punkte-Pfade sogar noch im Randpunkt analytisch sind. Kapitel 5 benutzt die Resultate aus Kapitel 4, um die lokal hohe Konvergenzordnung einer Langschrittmethode zur Lösung von SDLCP's zu zeigen. Kapitel 6 führt eine neue Methode zur Lösung von LCP's und SDLCP's mit Hilfe von Inneren-Punkte-Techniken ein. Dabei werden die Pfadfunktionen derart gewählt, dass alle Iterierten auf unzulässigen zentralen Pfaden liegen. Es wird globale und lokale Konvergenz des Verfahrens bewiesen.
We consider homogeneous spaces G/H with the same rational homotopy as a product of a 1-sphere and a (m+1)-sphere. We show that these spaces have also the rational cohomology of such a sphere product if H is connected and if the quotient has dimension m+2. Furthermore, we prove that if additionally the fundamental group of G/H is cyclic, then G/H is locally a product of a 1-torus and ofA/H, where A/H is a simply connected rational cohomology (m+1)-sphere (and hence classified). If H fails to be connected, then with U as the connected component of H the G-action on the covering space G/U of G/H has connected stabilizers, and the results apply to G/U. To show that under the assumptions above every natural number may be realized as the order of the group of connected components of H we calculate the cohomology of certain homogeneous spaces. We also determine the rational cohomology of the fibre bundle U-->G-->G/U if G/H meets the assumptions above. This is done by considering the respective Leray-Serre spectral sequence. The structure of the cohomology of U-->G-->G/U then gives a second proof for the structure of compact connected Lie groups acting transitively on spaces with the rational homotopy of a product of a 1-sphere and a (m+1)-sphere. Since a quotient of a homogeneous space with the same rational homotopy or cohomology as a product of a 1-sphere and a (m+1)-sphere is not simply connected, there often arises the question whether or not a considered fibre bundle or fibration is orientable. A large amount of space will therefore be given to the problem of showing that certain fibrations are orientable. For compact connected (m+2)-manifolds with cyclic fundamental groups and with the rational homotopy of a product of a 1-sphere and a (m+1)-sphere we show the following: if a connected Lie group acts transitively on the manifold, then the maximal compact subgroups are either transitive, or their orbits are simply connected rational cohomology spheres of codimension 1. Homogeneous spaces with the same rational cohomology or homotopy as a a product of a 1-sphere and a (m+1)-sphere play a role in the study of different types of geometrical objects. They appear for example as focal manifolds of isoparametric hypersurfaces with four distinct principal curvatures. Further examples of such spaces are the point spaces and the line spaces of compact connected generalized quadrangles. We determine the isometry groups of isoparametric hypersurfaces with 4 principal curvatures of multiplicities 1 and m which are transitive on the focal manifold with non-trivial fundamental group. Buildings were introduced by Jacques Tits to give interpretations of simple groups of Lie type. They are a far-reaching generalization of projective spaces, in particular a generalization of projective planes. There is another generalization of projective planes called generalized polygons. A projective plane is the same as a generalized triangle. The generalized polygons are also contained in the class of buildings: they are the buildings of rank 2. To compact quadrangles one can assign a pair of natural numbers called the topological parameters of the quadrangles. We treat the case k=1. It turns out that there are no other point-transitive compact connected Lie groups for (1,m)-quadrangles than the ones for the real orthogonal quadrangles. Furthermore, we solve the problem of three infinite series of group actions which Kramer left as open problems; there are no quadrangles with the homogeneous spaces in question as point spaces (up to maybe a finite number of small parameters in one of the three series).