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- asymptotische Entwicklung (1)
- asymptotische Normalverteilung (1)
- attenuated Radon transform (1)
- aurora (1)
- autonomic nervous system (1)
- backtrajectories; (1)
- balanced dynamics (1)
- bar with variable cross-section (1)
- basic ideas ('Grundvorstellungen') (1)
- bayessche Inferenz (1)
- bedingter Erwartungswert (1)
- bending of an orthotropic cusped plate (1)
- beta-functions (1)
- bioinformatics (1)
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- black hole (1)
- black holes (1)
- body mass index procedure (1)
- body surface area (1)
- boun- dedness (1)
- boundary conditions (1)
- boundary element method (1)
- boundary values problems (1)
- bounds (1)
- branching processes (1)
- bridges of random walks (1)
- bundles (1)
- calculation (1)
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- canonical Marcus integration (1)
- canonical discretization schemes (1)
- category equivalence of clones (1)
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- characterization of point processes (1)
- chemical master equation (1)
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- classification with partial labels (1)
- clathrin (1)
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- clustering (1)
- coated and absorbing aerosols (1)
- coercivity (1)
- coherent set (1)
- collegial supervision (1)
- coloration of terms (1)
- colored solid varieties (1)
- compact resolvent (1)
- companies (1)
- comparison principle (1)
- completeness (1)
- completeness levels (1)
- complex systems (1)
- composition of terms (1)
- composition operator (1)
- compound Poisson processes (1)
- compound polyhedra (1)
- compressible Euler equations (1)
- computational biology (1)
- concentration (1)
- concentration inequalities (1)
- condition number (1)
- conditional Bayes factors (1)
- conditional Wiener measure (1)
- conditional expectation value (1)
- conditioned (1)
- conditioned Feller diffusion (1)
- conditions (1)
- conditions of success (1)
- confidence interval (1)
- confidence intervals (1)
- congruence (1)
- connections (1)
- conormal asymptotic expansions (1)
- conormal asymptotics (1)
- conormal symbols (1)
- conservation laws (1)
- conservative discretization (1)
- constitutive relations (1)
- constrained Hamiltonian systems (1)
- contact transformations (1)
- continuity in Sobolev spaces with double weights (1)
- continuous testing (1)
- continuous time Markov Chains (1)
- continuous time Markov chain (1)
- continuous-time data assimilation (1)
- control theory (1)
- convergence assessment (1)
- convergence rate (1)
- corner parametrices (1)
- corona virus (1)
- correlated noise (1)
- coupled solution (1)
- covering (1)
- critical and subcritical Dawson-Watanabe process (1)
- criticality theorem (1)
- crohn's disease (1)
- crossed product (1)
- curvature varifold (1)
- cusp (1)
- cusped bar (1)
- das Cauchyproblem (1)
- das Goursatproblem (1)
- das charakteristische Cauchyproblem (1)
- data-driven (1)
- dbar-Neumann problem (1)
- de Sitter model ; Fundamental solutions ; Decay estimates (1)
- decay of eigenfunctions (1)
- decomposition (1)
- deformation quantization (1)
- degenerate elliptic equations (1)
- degenerate elliptic systems (1)
- delaney-dress tiling theory (1)
- density estimation (1)
- density of a measure (1)
- design elements (1)
- design research (1)
- determinant (1)
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- determinantische Punktprozesse (1)
- dht-symmetric category (1)
- die linearisierte Einsteingleichung (1)
- differential cohomology (1)
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- differential-algebraic equations (1)
- diffusion process (1)
- dimension functional (1)
- dimension reduction (1)
- direct and indirect climate observations (1)
- direkte und indirekte Klimaobservablen (1)
- disagreement percolation (1)
- discontinuous Robin condition (1)
- discontinuous drift (1)
- discrete Schrodinger (1)
- discrete Witten complex (1)
- discrete saymptotic types (1)
- discrete spectrum (1)
- disease activity (1)
- disjunction of identities (1)
- diskontinuierliche Drift (1)
- diskreter Witten-Laplace-Operator (1)
- distorted Brownian motion (1)
- distribution (1)
- distribution with asymptotics (1)
- distributional boundary (1)
- distributions with one-sided support (1)
- division algebras (1)
- division ring of fractions (1)
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- divisors (1)
- domains with singularities (1)
- doppelsemigroup (1)
- drug monitoring (1)
- duale IT-Ausbildung (1)
- duality formulae (1)
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- e-Assessment (1)
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- early mathematical education (1)
- earthquake precursor (1)
- edge Sobolev spaces (1)
- edge algebra (1)
- edge boundary value problems (1)
- edge quantizations (1)
- edge spaces (1)
- edge symbol (1)
- edge- and corner-degenerate symbols (1)
- eigenfunction (1)
- eigenvalue asymptotics (1)
- eigenvalue decay (1)
- elastic bar (1)
- elasticity (1)
- electrodynamics (1)
- elliptic boundary (1)
- elliptic boundary conditions (1)
- elliptic complex (1)
- elliptic differential operators of firstorder (1)
- elliptic equation (1)
- elliptic functions (1)
- elliptic morphism (1)
- elliptic operators in subspaces (1)
- elliptic operators on non-compact manifolds (1)
- elliptic problem (1)
- elliptic problems (1)
- elliptic quasicomplexes (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)
- elliptische Gleichungen (1)
- elliptische Quasi-Komplexe (1)
- embedded Markov chain (1)
- embeddings (1)
- empirical Wasserstein distance (1)
- endomorphism semigroup (1)
- energetic space (1)
- enlargement of filtration (1)
- ensembles (1)
- entropy (1)
- equation of motion (1)
- equivalence (1)
- ergodic diffusion processes (1)
- ergodic rates (1)
- error diagram (1)
- erste Variation (1)
- essential position in terms (1)
- estimation of regression (1)
- eta forms (1)
- exact simulation method (1)
- exact simulation methods (1)
- exact solution (1)
- exakte Simulation (1)
- exchange algorithms (1)
- exercise collection (1)
- exit calculus (1)
- exponential decay (1)
- exponential function (1)
- exponential stability (1)
- exterior tensor product (1)
- extinction probability (1)
- eye movements (1)
- false discovery rate (1)
- fat-free mass (1)
- feedback (1)
- feedback particle filter (1)
- fence-preserving transformations (1)
- fibration (1)
- fibre coordinates (1)
- fibroblasts (1)
- field-aligned currents (1)
- filtering (1)
- finite transformation semigroup (1)
- finiteness theorem (1)
- finsler distance (1)
- first exit location (1)
- first exit times (1)
- first passage times (1)
- first variation (1)
- fixational eye movements (1)
- fixed point formula (1)
- flocking (1)
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- foliated diffusion (1)
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- fore-casting (1)
- formal (1)
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- formulas (1)
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- fundamental solution (1)
- game (1)
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- gauge group (1)
- generalized Abelian gauge theory (1)
- generalized Bruck-Reilly *-extension (1)
- generalized Laplace operator (1)
- generalized eigenfunction (1)
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- generating sets (1)
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- geordnete Gruppen von Conrad-Typ (1)
- global exact boundary controllability (1)
- global solution (1)
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- global-hyperbolisch (1)
- globally hyperbolic (1)
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- good-inner function (1)
- goodness of fit (1)
- goodness-of-fit (1)
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- graph (1)
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- group (1)
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- groups (1)
- guiding idea “Daten und Zufall” (1)
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- heavy-tailed distributions (1)
- helicates (1)
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- high-dimensional inference (1)
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- higher singularities (1)
- highly (1)
- history of branching processes (1)
- hitting times (1)
- holomorphic function (1)
- holonomic constraints (1)
- host-parasite stochastic particle system (1)
- hybrid model (1)
- hybrids (1)
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- idealised turbulence (1)
- idleness (1)
- ill-posed (1)
- ill-posed problems (1)
- illposed problem (1)
- indecomposable varifold (1)
- independent splittings (1)
- index formula (1)
- index of elliptic operator (1)
- index of stability (1)
- inegral formulas (1)
- infinitesimal generator (1)
- infliximab dosing (1)
- initial boundary value problem (1)
- instability of the process (1)
- integral Fourier operators (1)
- integral equation (1)
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- integration by parts on path space (1)
- interacting particles (1)
- interassociativity (1)
- interfaces with conical singularities (1)
- interindividual differences (1)
- intrinsic diameter (1)
- intrinsischer Diameter (1)
- invariance (1)
- invariant (1)
- inverse Probleme (1)
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- inverse problem (1)
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- isoperimetric estimates (1)
- isoperimetric inequality (1)
- isoperimetrische Ungleichung (1)
- iterated asymptotics (1)
- jump processes (1)
- k-means clustering (1)
- kanten- und ecken-entartete Symbole (1)
- kernel estimator of the hazard rate (1)
- kernel method (1)
- kernel operator (1)
- kernel-based Bayesian inference (1)
- kernel-basierte Bayes'sche Inferenz (1)
- kleine Parameter (1)
- kollegiale Supervision (1)
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- large-scale mechanistic systems (1)
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- learning (1)
- learning rates (1)
- least favorable configuration (1)
- least squares estimator (1)
- left ordered groups (1)
- left-right asymmetry (1)
- lifespan (1)
- likelihood function (1)
- limit theorem (1)
- limit theorem for integrated squared difference (1)
- limiting distribution (1)
- linear fractional case (1)
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- locality principle (1)
- locally indicable (1)
- locally indicable group (1)
- log-concavity (1)
- logarithmic convergence rate (1)
- logarithmic residue (1)
- logic (1)
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- logistische Regression (1)
- lokal indizierbar (1)
- long-time corrections (1)
- low rank matrix recovery (1)
- low rank recovery (1)
- low-lying eignvalues (1)
- low-rank approximations (1)
- lumping (1)
- macromolecular decay (1)
- magnetic (1)
- magnetic field modeling (1)
- magnetic field variations through (1)
- magnetisch (1)
- magnitude errors (1)
- makromolekularer Zerfall (1)
- manifold (1)
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- manifolds with boundary (1)
- manifolds with corners (1)
- manifolds with cusps (1)
- manifolds with edge (1)
- manifolds with edge and boundary (1)
- many-electron systems (1)
- mapping class (1)
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- mapping class groups (1)
- marked Gibbs point processes (1)
- matching of asymptotic expansions (1)
- mathematical modeling (1)
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- method (1)
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- minor planets, asteroids: individual: (162173) Ryugu (1)
- mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung (1)
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- multiple testing; (1)
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- negative numbers (1)
- new recursive algorithm (1)
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- operators on manifolds with singularities (1)
- operators with corner symbols (1)
- oracle inequalities (1)
- oracle inequality (1)
- oral anticancer drugs (1)
- order continuous norm (1)
- order filtration (1)
- order reduction (1)
- order-preserving (1)
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- ordered group (1)
- orientation-preserving (1)
- orientation-preserving and orientation-reversing transformations (1)
- orientation-preserving transformations (1)
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- parameter-dependent cone operators (1)
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- parameter-dependent pseudodifferential operators (1)
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- parity condition (1)
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- permanental and determinantal point processes (MSC 2010) 35K55 (1)
- permanental- (1)
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Institute
- Institut für Mathematik (2132) (remove)
The knowledge of the largest expected earthquake magnitude in a region is one of the key issues in probabilistic seismic hazard calculations and the estimation of worst-case scenarios. Earthquake catalogues are the most informative source of information for the inference of earthquake magnitudes. We analysed the earthquake catalogue for Central Asia with respect to the largest expected magnitudes m(T) in a pre-defined time horizon T-f using a recently developed statistical methodology, extended by the explicit probabilistic consideration of magnitude errors. For this aim, we assumed broad error distributions for historical events, whereas the magnitudes of recently recorded instrumental earthquakes had smaller errors. The results indicate high probabilities for the occurrence of large events (M >= 8), even in short time intervals of a few decades. The expected magnitudes relative to the assumed maximum possible magnitude are generally higher for intermediate-depth earthquakes (51-300 km) than for shallow events (0-50 km). For long future time horizons, for example, a few hundred years, earthquakes with M >= 8.5 have to be taken into account, although, apart from the 1889 Chilik earthquake, it is probable that no such event occurred during the observation period of the catalogue.
We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference.
The injection of fluids is a well-known origin for the triggering of earthquake sequences. The growing number of projects related to enhanced geothermal systems, fracking, and others has led to the question, which maximum earthquake magnitude can be expected as a consequence of fluid injection? This question is addressed from the perspective of statistical analysis. Using basic empirical laws of earthquake statistics, we estimate the magnitude M-T of the maximum expected earthquake in a predefined future time window T-f. A case study of the fluid injection site at Paradox Valley, Colorado, demonstrates that the magnitude m 4.3 of the largest observed earthquake on 27 May 2000 lies very well within the expectation from past seismicity without adjusting any parameters. Vice versa, for a given maximum tolerable earthquake at an injection site, we can constrain the corresponding amount of injected fluids that must not be exceeded within predefined confidence bounds.
The Groningen gas field serves as a natural laboratory for production-induced earthquakes, because no earthquakes were observed before the beginning of gas production. Increasing gas production rates resulted in growing earthquake activity and eventually in the occurrence of the 2012M(w) 3.6 Huizinge earthquake. At least since this event, a detailed seismic hazard and risk assessment including estimation of the maximum earthquake magnitude is considered to be necessary to decide on the future gas production. In this short note, we first apply state-of-the-art methods of mathematical statistics to derive confidence intervals for the maximum possible earthquake magnitude m(max). Second, we calculate the maximum expected magnitude M-T in the time between 2016 and 2024 for three assumed gas-production scenarios. Using broadly accepted physical assumptions and 90% confidence level, we suggest a value of m(max) 4.4, whereas M-T varies between 3.9 and 4.3, depending on the production scenario.
In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed.
Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.
We investigate spatio-temporal properties of earthquake patterns in the San Jacinto fault zone (SJFZ), California, between Cajon Pass and the Superstition Hill Fault, using a long record of simulated seismicity constrained by available seismological and geological data. The model provides an effective realization of a large segmented strike-slip fault zone in a 3D elastic half-space, with heterogeneous distribution of static friction chosen to represent several clear step-overs at the surface. The simulated synthetic catalog reproduces well the basic statistical features of the instrumental seismicity recorded at the SJFZ area since 1981. The model also produces events larger than those included in the short instrumental record, consistent with paleo-earthquakes documented at sites along the SJFZ for the last 1,400 years. The general agreement between the synthetic and observed data allows us to address with the long-simulated seismicity questions related to large earthquakes and expected seismic hazard. The interaction between m a parts per thousand yen 7 events on different sections of the SJFZ is found to be close to random. The hazard associated with m a parts per thousand yen 7 events on the SJFZ increases significantly if the long record of simulated seismicity is taken into account. The model simulations indicate that the recent increased number of observed intermediate SJFZ earthquakes is a robust statistical feature heralding the occurrence of m a parts per thousand yen 7 earthquakes. The hypocenters of the m a parts per thousand yen 5 events in the simulation results move progressively towards the hypocenter of the upcoming m a parts per thousand yen 7 earthquake.
Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.
Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.
Convergence of the frequency-magnitude distribution of global earthquakes - maybe in 200 years
(2013)
I study the ability to estimate the tail of the frequency-magnitude distribution of global earthquakes. While power-law scaling for small earthquakes is accepted by support of data, the tail remains speculative. In a recent study, Bell et al. (2013) claim that the frequency-magnitude distribution of global earthquakes converges to a tapered Pareto distribution. I show that this finding results from data fitting errors, namely from the biased maximum likelihood estimation of the corner magnitude theta in strongly undersampled models. In particular, the estimation of theta depends solely on the few largest events in the catalog. Taking this into account, I compare various state-of-the-art models for the global frequency-magnitude distribution. After discarding undersampled models, the remaining ones, including the unbounded Gutenberg-Richter distribution, perform all equally well and are, therefore, indistinguishable. Convergence to a specific distribution, if it ever takes place, requires about 200 years homogeneous recording of global seismicity, at least.
The paper studies catalytic super-Brownian motion on the real line, where the branching rate is controlled by a catalyst. D. A. Dawson, K. Fleischmann and S. Roelly showed, for a broad class of catalysts, that, as for constant branching, the processes are absolutely continuous measures. This paper considers a class of catalysts, called moderate, which must satisfy a uniform boundedness condition and a condition controlling the degree of singularity---essentially that the mass of catalyst in small balls should (uniformly) be of order r^a, where a>0. The main result of this paper shows that for this class of catalysts there is a continuous density field for the process. Moreover the density is the unique solution (in law) of an appropriate SPDE.
The author considers the heat equation in dimension one with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous w.r.t. the Lebesgue measure, neither in space nor in time. Under some assumptions the author gives statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions.
The morphological features in the deviations of the total electron content (TEC) of the ionosphere from the background undisturbed state as possible precursors of the earthquake of January 12, 2010 (21:53 UT (16:53 LT), 18.46A degrees N, 72.5A degrees W, 7.0 M) in Haiti are analyzed. To identify these features, global and regional differential TEC maps based on global 2-h TEC maps provided by NASA in the IONEX format were plotted. For the considered earthquake, long-lived disturbances, presumably of seismic origin, were localized in the near-epicenter area and were accompanied by similar effects in the magnetoconjugate region. Both decreases and increases in the local TEC over the period from 22 UT of January 10 to 08 UT of January 12, 2010 were observed. The horizontal dimensions of the anomalies were similar to 40A degrees in longitude and similar to 20A degrees in latitude, with the magnitude of TEC disturbances reaching similar to 40% relative to the background near the epicenter and more than 50% in the magnetoconjugate area. No significant geomagnetic disturbances within January 1-12, 2010 were observed, i.e., the detected TEC anomalies were manifestations of interplay between processes in the lithosphere-atmosphere-ionosphere system.
Geometric electroelasticity
(2014)
In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space.
A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems
We discuss the role of gravitational excitons/radions in different cosmological scenarios. Gravitational excitons are massive moduli fields which describe conformal excitations of the internal spaces and which, due to their Planck-scale suppressed coupling to matter fields, are WIMPs. It is demonstrated that, depending on the concrete scenario, observational cosmological data set strong restrictions on the allowed masses and initial oscillation amplitudes of these particles
A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic K-theory. We consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. Doppelsemigroups are a generalization of semigroups and they have relationships with such algebraic structures as interassociative semigroups, restrictive bisemigroups, dimonoids, and trioids.
In the lecture notes numerous examples of doppelsemigroups and of strong doppelsemigroups are given. The independence of axioms of a strong doppelsemigroup is established. A free product in the variety of doppelsemigroups is presented. We also construct a free (strong) doppelsemigroup, a free commutative (strong) doppelsemigroup, a free n-nilpotent (strong) doppelsemigroup, a free n-dinilpotent (strong) doppelsemigroup, and a free left n-dinilpotent doppelsemigroup. Moreover, the least commutative congruence, the least n-nilpotent congruence, the least n-dinilpotent congruence on a free (strong) doppelsemigroup and the least left n-dinilpotent congruence on a free doppelsemigroup are characterized.
The book addresses graduate students, post-graduate students, researchers in algebra and interested readers.
The aim of these lectures is a reformulation and generalization of the fundamental investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models.