Mathematik
Refine
Year of publication
Document Type
- Article (112)
- Doctoral Thesis (76)
- Preprint (46)
- diplomthesis (39)
- Book (25)
- Report (22)
- Conference Proceeding (18)
- Bachelor Thesis (8)
- Contribution to a Periodical (8)
- Diploma Thesis (8)
Has Fulltext
- yes (374) (remove)
Is part of the Bibliography
- no (374)
Keywords
- Kongress (6)
- Kryptologie (5)
- Mathematik (5)
- Stochastik (5)
- Doku Mittelstufe (4)
- Doku Oberstufe (4)
- Online-Publikation (4)
- Statistik (4)
- Finanzmathematik (3)
- LLL-reduction (3)
- Moran model (3)
- coalescent (3)
- computational complexity (3)
- contraction method (3)
- point process (3)
- spike train (3)
- Algebraische Geometrie (2)
- Arithmetische Gruppe (2)
- Biographie (2)
- Brownian motion (2)
- Commitment Scheme (2)
- Frankfurt <Main> / Universität (2)
- Fuchsian groups (2)
- Fächerübergreifender Unterricht (2)
- Geometrie (2)
- Heat kernel (2)
- Hinterlegungsverfahren <Kryptologie> (2)
- Integral Geometry (2)
- Knapsack problem (2)
- Kombinatorische Optimierung (2)
- Krein space (2)
- Laplace operator on graphs (2)
- Lattice basis reduction (2)
- Martingal (2)
- Mathematiker (2)
- Musik (2)
- Oblivious Transfer (2)
- Perception (2)
- Quantum Zeno dynamics (2)
- San Jose (2)
- Semidefinite Programming (2)
- Shortest lattice vector problem (2)
- Stochastischer Prozess (2)
- Subset sum problem (2)
- Tropical geometry (2)
- Tropische Geometrie (2)
- Valuation Theory (2)
- Verzweigungsprozess (2)
- Vision (2)
- W*-dynamical system (2)
- X-Y model (2)
- Yule-Prozess (2)
- ancestral selection graph (2)
- binary search tree (2)
- collective intelligence (2)
- combinatorial optimization (2)
- complexity (2)
- duality (2)
- firing patterns (2)
- fixation probability (2)
- genealogy (2)
- level of difficulty (2)
- quantum spin systems (2)
- return to equilibrium (2)
- segments (2)
- task space (2)
- thought structure (2)
- Λ−coalescent (2)
- A-Discriminant (1)
- ADM1 (1)
- Abelian (1)
- Action potential (1)
- Actions in mathematical learning (1)
- Activity (1)
- Adaptive dynamics (1)
- Algebra (1)
- Algorithmus (1)
- Amoeba (1)
- Anaerobe Fermentation (1)
- Analyse von Algorithmen (1)
- Ancestral selection graph (1)
- Anisotropic Norm (1)
- Approximation (1)
- Approximation algorithm (1)
- Approximationsalgorithmus (1)
- Arbitrage (1)
- Assignment Problem (1)
- Asymptotically Even Nonlinearity (1)
- Ausreißer <Statistik> (1)
- Automorphismengruppe (1)
- Axon (1)
- Banach spaces (1)
- Bayesian Inference (1)
- Berkovich spaces (1)
- Binomialmodell (1)
- Binärsuchbaum (1)
- Black and Scholes Option Price theory (1)
- Black-Scholes (1)
- Blind Signature (1)
- Block Korkin—Zolotarev reduction (1)
- Blockplay (1)
- Bolthausen-Sznitman (1)
- Boolean Lattice (1)
- Bootstrap-Statistik (1)
- Boundary (1)
- Boundary Value Problems (1)
- Branch and Bound (1)
- Branching particle systems (1)
- Branching process approximation (1)
- Breaking knapsack cryptosystems (1)
- Bruhat-Tits-Gebäude (1)
- Burst (1)
- CAT(0)-Räume (1)
- CAT(0)-spaces (1)
- CIR-1 (1)
- Calderón problem (1)
- Cannings model (1)
- Catalan number (1)
- Cauchy-Anfangswertproblem (1)
- Cayley-Graph (1)
- China-Restaurant-Prozess (1)
- Chinese Remainder Theorem (1)
- Chinese restaurant process (1)
- Chinese-restaurant-process (1)
- Circuit (1)
- Closest Vector Problem (1)
- Coamoeba (1)
- Cognitive psychology (1)
- Commitment (1)
- Commitment schemes (1)
- Computational complexity (1)
- Concentration Inequality (1)
- Condensing (1)
- Containment (1)
- Contraction method (1)
- Datenbank (1)
- Datenstruktur (1)
- Degenerate Linear Part (1)
- Dehn (1)
- Derivate (1)
- Dessins d'enfants (1)
- Diagrams and mathematical learning (1)
- Dichte <Stochastik> (1)
- Digital and analogue materials (1)
- Digital trees (1)
- Dimension 2 (1)
- Directional selection (1)
- Dirichlet bound (1)
- Dirichlet random measure (1)
- Dirichletsche L-Reihe; Nullstelle (1)
- Discrete Logarithm (1)
- Diskrete Geometrie (1)
- Diskrete Mathematik (1)
- Diskreter Markov-Prozess (1)
- Diversity in trait space (1)
- Donkers theorem (1)
- Dopamine (1)
- Doplicher-Haag-Roberts Axiomatik; Algebraische Quantenfeldtheorie; Superauswahlregeln und -sektoren; Quantenstatistik; Zopfgruppenstatistik (1)
- Dormancy (1)
- Dosis-Wirkungs-Modellierung (1)
- Dreiecksgruppe (1)
- Dreiecksgruppen (1)
- Duality (1)
- Early Childhood (1)
- Einbettung <Mathematik> (1)
- Elektronische Unterschrift (1)
- Elementar- und Primarbereich (1)
- Endliche Präsentation (1)
- Endlichkeitseigenschaften (1)
- Energie-Modell (1)
- Error Bound (1)
- Erwartungswert (1)
- Evolutionary branching (1)
- Evolving Yield Curves in the Real-World Measures (1)
- Ewens sampling formula (1)
- Examples (1)
- Extended RMJBN Modell (1)
- FEM-BEM-coupling (1)
- FID model (1)
- FIND algorithm (1)
- Face (1)
- Face recognition (1)
- Factoring (1)
- Familie (1)
- Family (1)
- Feller branching with logistic growth (1)
- Finite element methods (1)
- Finitely many measurements (1)
- Fixation probability (1)
- Fixpunkt (1)
- Fractional Brownian Motion (1)
- Fractional Laplacian (1)
- Frühe Bildung (1)
- Fuchs-Gruppe (1)
- Fuchssche Gruppe ; Modulare Einbettung (1)
- Fuchssche Gruppen (1)
- Functions (1)
- Funktionenkegel (1)
- Funktionenkörper ; Arithmetische Gruppe ; Auflösbare Gruppe ; Endlichkeit (1)
- Galerkin Approximation (1)
- Galois group (1)
- Galois-Gruppe (1)
- Game Tree (1)
- Gaussian Random Field (1)
- Gaussian process (1)
- Gelfand-Shilov space (1)
- Gemischte Volumen (1)
- Genealogical construction (1)
- Genealogische Konstruktion (1)
- Genetischer Fingerabdruck (1)
- Genus One (1)
- Geometrische Gruppentheorie (1)
- Geometry (1)
- Gespräch (1)
- Gestaenge (1)
- Girsanov transform (1)
- Gitter <Mathematik> ; Basis <Mathematik> ; Reduktion ; Algorithmus ; Laufzeit ; L-unendlich-Norm ; Rucksackproblem ; Kryptosystem (1)
- Gitter <Mathematik> ; Basis <Mathematik> ; Reduktion ; Gauß-Algorithmus (1)
- Gram-Hadamard inequalities (1)
- Graphen (1)
- Grenzwertsatz (1)
- Griffiths–Engen–McCloskey distribution (1)
- Group dynamics (1)
- Große Abweichung (1)
- Großinvestor (1)
- Gruppendynamiken (1)
- Gruppentheorie (1)
- Hadamard's Three-Lines Theorem (1)
- Halbeinfache algebraische Gruppe (1)
- Handelman (1)
- Handlung (1)
- Harmoniebox (1)
- Heisenberg algebra (1)
- Hidden Markov models (1)
- Hintertür <Informatik> (1)
- Hodge bundle (1)
- Holzklötzchen (1)
- Hopf algebroids (1)
- Householder reflection (1)
- Hyperfunktion ; Asymptotische Entwicklung (1)
- Hypotrochoid (1)
- Identification (1)
- Immigration (1)
- Index at Infinity (1)
- Infrared singularity (1)
- Integer relations (1)
- Integraldarstellung (1)
- Interaction (1)
- Internet (1)
- Invariante (1)
- Inverse problems (1)
- Iteration (1)
- Jahr der Mathematik (1)
- Kettenbruchentwicklung ; Dimension n ; Diophantische Approximation (1)
- Kieferorthopädie (1)
- Klassifizierender Raum (1)
- Klebsiella pneumoniae (1)
- Knotenabstand (1)
- Knotentiefe (1)
- Koaleszent (1)
- Kochen-Specker theorem (1)
- Kollektivintelligenz (1)
- Kombinatorische Gruppen (1)
- Konforme Feldtheorie (1)
- Konstruktiver Beweis (1)
- Kontaktprozess (1)
- Kontraktionsmethode (1)
- Konzentrationsungleichung (1)
- Korkin—Zolotarev reduction (1)
- Kreuzkorrelation (1)
- Kryptosystem (1)
- Kullback-Leibler Informational Divergence (1)
- L^p bounds (1)
- L^p means (1)
- Label cover (1)
- Lanzeitverhalten (1)
- Laplace-Differentialgleichung (1)
- Large Deviation (1)
- Lattice Reduction (1)
- Leerverkauf (1)
- Lernen (1)
- Linear Filtering (1)
- Linear Preferential Attachment Trees (1)
- Linear-Implicit Scheme (1)
- Linkages (1)
- Loewner monotonicity and convexity (1)
- Logarithmic Laplacian (1)
- Long- Range Dependence (1)
- Long-Range Dependence (1)
- Long-time behaviour (1)
- Longitudinal Study (1)
- Lotka-Volterra system (1)
- Lovász Local Lemma (1)
- Low density subset sum algorithm (1)
- MINT-Bildung (1)
- Machine Learning (1)
- Malliavin calculus (1)
- Mallows model (1)
- Markov chain Monte Carlo Method (1)
- Markov chain imbedding technique (1)
- Markov model (1)
- Markov-Kette (1)
- Mathematical Giftedness (1)
- Mathematical Reasoning (1)
- Mathematical modelling (1)
- Mathematics Learning (1)
- Mathematische Bildung (1)
- Mathematische Modellierung (1)
- Max (1)
- McEliece (1)
- Mean Anisotropy (1)
- Message authentication (1)
- Methanogenese (1)
- Mixed Volumes (1)
- Modellierung (1)
- Modular Multiplication (1)
- Mooney faces (1)
- Morava K-theory (1)
- Mouse (1)
- Multi-Harmonie-Ansatz (1)
- Multiple lineare Regression (1)
- Multityp-Verzweigungsprozess mit Immigration (1)
- Multitype Branching with Immigration (1)
- NP-complete problems (1)
- NP-hard (1)
- NP-hardness (1)
- Nash-Gleichgewicht (1)
- Nelson-Siegel (1)
- Neural encoding (1)
- Neurophysiology (1)
- Neuroscience (1)
- Neurowissenschaft (1)
- Newton–Okounkov bodies (1)
- Non-Malleability (1)
- Noticeable Probability (1)
- Optimal Mean-Square Filter (1)
- Oracle Query (1)
- Parabolic SPDE (1)
- Parisi conjecture (1)
- Participation (1)
- Partizipation (1)
- Patientenbewertung (1)
- Pause (1)
- Permutation (1)
- Permutationsgruppen (1)
- Pfadeigenschaften (1)
- Phragmén-Lindelöf principle (1)
- Piecewise-constant coefficient (1)
- Poisson Process (1)
- Poisson boundary (1)
- Poisson-Prozess (1)
- Polyedrische Kombinatorik (1)
- Polymorphic evolution sequence (1)
- Polynomial Optimization (1)
- Pontrjagin space (1)
- Populationsdynamiken (1)
- Portfolios (1)
- Positivstellensatz (1)
- Potenzialtheorie (1)
- Prag <1999> (1)
- Preferential Attachment-Modelle (1)
- Private Information Retrieval (1)
- Probabilistic analysis of algorithms (1)
- Probabilistically checkable proofs (1)
- Probabilistische Analyse von Algorithmen (1)
- Probability distribution (1)
- Probability of fixation (1)
- Professionalisierung (1)
- Profil Likelihood (1)
- Projektionen (1)
- Public Key Cryptosystem (1)
- Public Parameter (1)
- Punktprozess (1)
- Pólya urn (1)
- Quadratic Residue (1)
- Quantenfeldtheorie ; Konforme Feldtheorie ; Algebraische Methode (1)
- Quantum Zeno Effect (1)
- Quantum Zeno effect (1)
- Quasi-Automorphismen (1)
- Quaternionenalgebra (1)
- Quickselect (1)
- RSA-Verschlüsselung (1)
- Radix sort (1)
- Random Oracle (1)
- Random Split Trees (1)
- Random String (1)
- Random environment (1)
- Random variables (1)
- Randomisieren (1)
- Ray-Knight representation (1)
- Reaction time (1)
- Reale vs. risikoneutrale Welt in der Finanzmathematik (1)
- Rechenzentrum (1)
- Rekursiver Algorithmus (1)
- Relaxation (1)
- Representation Problem (1)
- Research article (1)
- Riemann surfaces (1)
- Riemannsche Fläche (1)
- Riemannsche Flächen (1)
- Ringtheorie (1)
- Risikobewertung (1)
- Risikomanagement (1)
- Robustheit (1)
- Rückkopplungseffekt (1)
- S-arithmetic groups (1)
- SLLL-reduction (1)
- Sackgassen (1)
- San Francisco (1)
- Santa Barbara (1)
- Schizophrenia (1)
- Schwarz triangel functions (1)
- Schwinger model (1)
- Security (1)
- Security Parameter (1)
- Semidefinite Optimierung (1)
- Semidefinite Optimization (1)
- Semiotics according to C. S. Peirce (1)
- Sensory perception (1)
- Sensory processing (1)
- Sigma-Invariante (1)
- Sigma-invariant (1)
- Signalverarbeitung (1)
- Signature (1)
- Small Worlds (1)
- Small order expansion (1)
- Spectrahedra (1)
- Spiel (1)
- Spielbaum (1)
- Spielbaum-Suchverfahren (1)
- Stable reduction algorithm (1)
- State dependent branching rate (1)
- Stationarity (1)
- Stochastic Analysis of Square Zero Variation Processes (1)
- Stonesches Spektrum (1)
- Striatum (1)
- Strong Taylor Scheme (1)
- Stummel, Friedrich (1)
- Suchbaum (1)
- Suchoperation (1)
- Sudoku (1)
- Sum of Squares (1)
- Support (1)
- Symmetrie (1)
- Symmetrischer Raum (1)
- Symmetry (1)
- Sympatric speciation (1)
- Tail Bound (1)
- Tailschranke (1)
- Talk (1)
- Thorne Kishino Felsenstein model (1)
- Topic Model (1)
- Trapdoor (1)
- Trinomial (1)
- Tropical Geometry (1)
- Tropical Grassmannians (1)
- Tropical bases (1)
- Tropical varieties (1)
- Tropische Basen (1)
- Trotter's product formula (1)
- Turkish immigrants (1)
- Typ-In-Algebra (1)
- Typology (1)
- Türkisch (1)
- Uniform regularity (1)
- Uniform resource locators (1)
- Unterstützung (1)
- Valuation on functions (1)
- Varianz (1)
- Vertexoperator (1)
- Verzweigende Teilchensysteme (1)
- Virasoro-Algebra (1)
- Wahrscheinlichkeit (1)
- Wahrscheinlichkeitsverteilung (1)
- Wiener Index (1)
- Wiener index (1)
- Wiener-Index (1)
- Yule process (1)
- Yule-process (1)
- Zinsstrukturmodelle (1)
- Zinsänderungsrisiko (1)
- Zolotarev metric (1)
- Zolotarev-Metrik (1)
- Zopfgruppe ; Lineare Darstellung ; Kettengruppe ; Homologiegruppe ; Automorphismengruppe ; Kettenkomplex (1)
- Zufall (1)
- Zufallsgraph (1)
- Zufällige Umgebung (1)
- Zustandsabhängige Verzweigungsrate (1)
- Zweiphasen-Biogasreaktor (1)
- Zweistufen-Biogasreaktor (1)
- abelian differentials (1)
- abstract potential theory (1)
- algebraic curves (1)
- algebraic values (1)
- alpha-stable branching (1)
- ampleness (1)
- analysis of algorithms (1)
- anti-Zeno effect (1)
- argumentation (1)
- arithmetic ball quotients (1)
- arithmetic group (1)
- assignment problem (1)
- augmented and restricted base loci (1)
- autocorrelograms (1)
- bid-ask spread (1)
- bordism theory (1)
- branching processes (1)
- branching random walk in random medium (1)
- buildings (1)
- cancer cell dormancy (1)
- canonical divisors (1)
- catastrophe modeling (1)
- central limit theorem (1)
- chosen ciphertext attack (1)
- clique problem (1)
- colorabdity (1)
- colored graphs (1)
- compact Riemann surfaces (1)
- complex multiplication (1)
- composition (1)
- computational geometry (1)
- concurrent composition (1)
- condensing (1)
- confirmatory factory analysis (1)
- consensus (1)
- contact process (1)
- continued fraction algorithm (1)
- controlled homotopy (1)
- convexity (1)
- convolution quadrature (1)
- cooperative systems (1)
- cross correlation (1)
- cryptography (1)
- cycle structure of permutations (1)
- dead ends (1)
- degenerate semigroup (1)
- delay equation (1)
- depth of a nod (1)
- dessins d’enfants (1)
- difference sets (1)
- digital search tree (1)
- digital tools (1)
- discrete dynamical system (1)
- discrete logarithm (1)
- discrete logarithm (DL) (1)
- diskrete Mathematik (1)
- dose-resoponse modelling (1)
- doubly stochastic point process (1)
- eigenvalue (1)
- elastodynamic wave equation (1)
- emergence (1)
- endliche metrische Räume (1)
- error bounds (1)
- exponentiation (1)
- external branch (1)
- face inversion (1)
- face perception (1)
- fake projective planes (1)
- families of hash functions (1)
- feedback effect (1)
- finite resolution (1)
- finiteness-properties (1)
- flat surfaces (1)
- floating norms (1)
- floating point arithmetic (1)
- floating point errors (1)
- foliated Schwarz symmetry (1)
- forming a group (1)
- fractional Brownian motion (1)
- fractions of exponentiation (1)
- frühkindliche Erziehung (1)
- fuchsian group (1)
- functional limit theorem (1)
- functional limit theorems (1)
- fächerübergreifendes Lernen (1)
- generic algorithm (1)
- generic algorithms (1)
- generic complexity (1)
- generic group model (1)
- geometry (1)
- graph coloring (1)
- graph isomorphism (1)
- h-transform (1)
- hard bit (1)
- hardcore subsets (1)
- harmonic function (1)
- heavy tails (1)
- hidden Markov model (1)
- hierarchical mean-field limit (1)
- highly regular nearby points (1)
- hyperbolische Geometrie (1)
- hypergeometric functions (1)
- hypervariable region (1)
- höhere Momente (1)
- incremental schemes (1)
- indefinite inner product space (1)
- individual-based models (1)
- inner product (1)
- integer relation (1)
- integer vector (1)
- interacting particle Systems (1)
- interdisziplinäre Lehre (1)
- internal diffusion limited aggregation (1)
- internal path length (1)
- inverse coefficient problem, (1)
- iterated subsegments (1)
- key comparisons (1)
- kinetic fingerprint (1)
- knapsack cryptosystems (1)
- kontrollierte Homotopie (1)
- large deviations (1)
- large trader (1)
- latent variance (1)
- lattice basis reduction (1)
- lattices (1)
- leapfrog (1)
- length defect (1)
- limit order markets (1)
- local LLL-reduction (1)
- local LLLreduction (1)
- local coordinates (1)
- local randomness (1)
- local time (1)
- local time drift (1)
- logarithmic geometry (1)
- logical networks (1)
- lookdown construction (1)
- lower bounds (1)
- manifold and geodesic (1)
- market making (1)
- mathematical modeling (1)
- mathematical modelling (1)
- mathematics (1)
- measurement (1)
- mehrdimensionale Ausreißererkennung (1)
- message-passing algorithm (1)
- modelling (1)
- modular automorphism group (1)
- modular group (1)
- moduli spaces (1)
- multi-agents system (1)
- multi-drug treatment (1)
- multiharmony (1)
- multilevel branching (1)
- music (1)
- mutation parameter estimation (1)
- neuronal code (1)
- neuronaler Kode (1)
- nichtlineare stochastische Integration (1)
- non-archimedean geometry (1)
- non-autonomous dynamical systems (1)
- non-malleability (1)
- noncommutative ring spectra (1)
- nondetermmistlc Turing machines (1)
- nonlinear stochastic integration (1)
- numerical experiments (1)
- observable Funktion (1)
- one-more decryption attack (1)
- one-way function (1)
- one-way functions (1)
- operator algebra (1)
- optimal transport (1)
- pair HMM (1)
- parameter dependent semimartingales (1)
- parameterabhängige Semimartingale (1)
- partial match queries (1)
- path properties (1)
- perceptual closure (1)
- permutation groups (1)
- phage (1)
- phage therapy (1)
- phase coding (1)
- phase transitions (1)
- platonischer Körper (1)
- poisson process (1)
- polynomial random number generator (1)
- population dynamics (1)
- portfolio optimization (1)
- positivity of line bundles (1)
- preferential attachment (1)
- preferential attachment models (1)
- probabilistic analysis of algorithms (1)
- probability (1)
- probability metric (1)
- professional development (1)
- profile likelihood (1)
- projections (1)
- projective planes (1)
- q-binomial theorem (1)
- quantum field theory (1)
- quasi-automorphisms (1)
- quaternion algebra (1)
- quincunx (1)
- random assignment problem (1)
- random environment (1)
- random function generator (1)
- random graphs (1)
- random measures (1)
- random media (1)
- random metric (1)
- random move (1)
- random number generator (1)
- random oracle model (1)
- random partition (1)
- random recursive tree (1)
- random rekursiv tree (1)
- random trees (1)
- random walks (1)
- raum-zeitliche Muster (1)
- reactant-catalyst systems (1)
- recursive distributional equation (1)
- reguläre Parkettierung (1)
- resistance (1)
- resistance mutation (1)
- reversibility (1)
- riemann surfaces (1)
- risk assessment (1)
- risk theory (1)
- rotating plane method (1)
- rough paths theory (1)
- satlsfiablhty (1)
- scaling (1)
- search operation (1)
- searchtrees (1)
- secure bit (1)
- security analysis of protocols (1)
- security of data (1)
- self-organizing groups (1)
- self-organizing groups; population dynamics; collective intelligence; forming groups; metric on finite sets (1)
- semidefinite optimization (1)
- sequence alignment (1)
- set-valued pullback attractors (1)
- shadow price (1)
- short integer relation (1)
- shortest lattice vector (1)
- signature size (1)
- signed ElGamal encryption (1)
- simultaneous diophantine approximations (1)
- simultaneous security of bits (1)
- single block replacement (1)
- small worlds (1)
- spatio-temporal patterns (1)
- split tree (1)
- statistic analysis (1)
- statistical alignment (1)
- statistische Analyse (1)
- statistischer Test (1)
- stoch. Analyse von Algorithmen (1)
- stochastic filtering (1)
- stochastic modeling (1)
- stochastic population dynamics (1)
- stochastische Prozesse (1)
- strong transience (1)
- subgroup growth (1)
- subset sum problems (1)
- substitution attacks (1)
- sum of squared factor loadings (1)
- switching systems (1)
- synergistic interaction (1)
- therapy evasion (1)
- topological entropy (1)
- trading strategies (1)
- transcendence (1)
- transversal learning (1)
- treatment protocol design (1)
- treatment success (1)
- triangle group (1)
- triangle groups (1)
- tropical geometry (1)
- tropical universal Jacobian (1)
- tropicalization (1)
- universal compactified Jacobian (1)
- urn model (1)
- von Neumann algebra (1)
- von Neumann algebras (1)
- von Neumann-Algebra (1)
- weak convergence (1)
- zufälliger Algorithmus (1)
- zufälliger rekursiver Baum (1)
- zufälliges Assignment Problem (1)
- Λ-coalescent (1)
- σ-field (1)
Institute
- Mathematik (374) (remove)
Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1) and the noise in the observation process includes a fractional Brownian motion as well as a Wiener process. AMS subject classifications: 93E11, 60G20, 60G35.
Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an gamma strong linear-implicit Taylor scheme with time-step delta applied to the N dimensional Itô-Galerkin SDE for a class of parabolic stochastic partial differential equation (SPDE) with a strongly monotone linear operator with eigenvalues lambda 1 <= lambda 2 <= ... in its drift term is then estimated by K(lambda N -½ + 1 + delta gamma) where the constant K depends on the initial value, bounds on the other coefficients in the SPDE and the length of the time interval under consideration.
AMS subject classifications: 35R60, 60H15, 65M15, 65U05.
We call a distribution on n bit strings (", e) locally random, if for every choice of e · n positions the induced distribution on e bit strings is in the L1 norm at most " away from the uniform distribution on e bit strings. We establish local randomness in polynomial random number generators (RNG) that are candidate one way functions. Let N be a squarefree integer and let f1, . . . , f be polynomials with coe±- cients in ZZN = ZZ/NZZ. We study the RNG that stretches a random x 2 ZZN into the sequence of least significant bits of f1(x), . . . , f(x). We show that this RNG provides local randomness if for every prime divisor p of N the polynomials f1, . . . , f are linearly independent modulo the subspace of polynomials of degree · 1 in ZZp[x]. We also establish local randomness in polynomial random function generators. This yields candidates for cryptographic hash functions. The concept of local randomness in families of functions extends the concept of universal families of hash functions by Carter and Wegman (1979). The proofs of our results rely on upper bounds for exponential sums.
We show lower bounds for the signature size of incremental schemes which are secure against substitution attacks and support single block replacement. We prove that for documents of n blocks such schemes produce signatures of \Omega(n^(1/(2+c))) bits for any constant c>0. For schemes accessing only a single block resp. a constant number of blocks for each replacement this bound can be raised to \Omega(n) resp. \Omega(sqrt(n)). Additionally, we show that our technique yields a new lower bound for memory checkers.
Die Arbeiten von Alexander Michailowitsch Lyapunov (1857-1918) waren der Anfangspunkt intensiver Erforschung des Stabilitätsverhaltens von Differentialgleichungen. In der vorliegenden Arbeit sollen Lyapunovfunktionen auf Zeitskalen in Bezug auf das Stabilitätsverhalten des homogenen linearen Systems x-delta = A(t)x untersucht werden.
We present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of symmetries using the workflow management system GPI-Space and the computer algebra system Singular. We determine the tropical Grassmannian TGr0(3,8). Our implementation works efficiently on up to 840 cores, computing the 14763 orbits of maximal cones under the canonical S8-action in about 20 minutes. Relying on our result, we show that the Gröbner structure of TGr0(3,8) refines the 16-dimensional skeleton of the coarsest fan structure of the Dressian Dr(3,8), except for 23 orbits of special cones, for which we construct explicit obstructions to the realizability of their tropical linear spaces. Moreover, we propose algorithms for identifying maximal-dimensional cones which belong to positive tropicalizations of algebraic varieties. We compute the positive Grassmannian TGr+(3,8) and compare it to the cluster complex of the classical Grassmannian Gr(3,8).
In this thesis, the focus is on the actions of primary school children using digital and analogue materials in comparable mathematical situations. To emphasise actions on different materials in the mathematical learning process, a semiotic perspective according to C. S. Peirce (CP 1931-35) on mathematics learning is adopted. This theoretical research perspective highlights the activity itself on diagrams as a mathematical activity and brings actions to the forefront of interest. The actions on comparable digital and analogue diagrams are the basis for the reconstruction of mathematical interpretations of learners in 3rd and 4th grade.
The research questions investigate to what extent possible differences between the reconstructed interpretations of the learners can be attributed to the different materials and what influence the material has on the mathematical relationships that the learners take into account in their actions to manipulate the diagram.
For the reconstruction of the diagram interpretations based on the learners' actions on the material, a semiotic specification of Vogel's (2017) adaptation of Mayring's (2014) context analysis is used. This specification is based on Peirce's triadic theory of signs (Billion, 2023). The reconstructed interpretations of the analogue and digital diagrams are compared in a second step to identify possible differences and similarities.
The results of the qualitative analyses show, among other things, that despite the different actions of the learners on the digital and analogue diagrams, it is possible to reconstruct the same diagram interpretations if the learners establish the same mathematical relationships between the parts of the diagrams in their actions. There are also passages in the analyses where the same diagram interpretations cannot be reconstructed based on the actions on the digital and analogue materials. If the digital material acts as a tool and automatically creates several relationships between the parts of the diagram triggered by an action, then the reconstruction of the learners' diagram interpretations based on the analysis of their actions is partially possible. If the tool automatically establishes relationships, these must then be interpreted by the learners using gestures and phonetic utterances to understand the newly created diagram. Thus, a tool changes how mathematical relationships are expressed, because learners no longer have to interpret the relationships before their actions to manipulate the diagram itself, but afterwards through gestures and phonetic utterances. Regarding diagrammatic reasoning according to Peirce (NEM IV), this means that with analogue material the focus is on the construction and manipulation of diagrams through rule-guided actions, whereas with digital material, which functions as a tool, there is more emphasis on observing the results of the manipulations on the diagram.
At the end of the thesis, a recommendation for teachers on how to design mathematics lessons for primary school children using digital and analogue materials will be derived from the results.
The literature cited in this summary can be found in the references of the presented thesis.