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- exterior tensor product (1)
- fibre coordinates (1)
- filter (1)
- filtering (1)
- finiteness theorem (1)
- finsler distance (1)
- first boundary value problem (1)
- first variation (1)
- fixational eye movements (1)
- fixed point formula (1)
- flocking (1)
- foliated diffusion (1)
- force unification (1)
- free algebra (1)
- fully non-linear degenerate parabolic equations (1)
- functor geometry (1)
- fundamental solution (1)
- gauge group (1)
- generalized Laplace operator (1)
- geodesic distance (1)
- geodätischer Abstand (1)
- geomagnetism (1)
- geometric optics approximation (1)
- geordnete Gruppen von Conrad-Typ (1)
- global exact boundary controllability (1)
- global solution (1)
- global solutions (1)
- globally hyperbolic spacetime (1)
- good-inner function (1)
- goodness of fit (1)
- goodness-of-fit (1)
- goodness-of-fit testing (1)
- graph theory (1)
- graphs (1)
- gravitation (1)
- gravitational wave (1)
- hard core interaction (1)
- heat asymptotics (1)
- heat kernel (1)
- heavy-tailed distributions (1)
- heterogeneity (1)
- high dimensional (1)
- higher operations (1)
- higher order rectifiability (1)
- higher singularities (1)
- higher-order Sturm–Liouville problems (1)
- hitting times (1)
- host-parasite stochastic particle system (1)
- hyperbolic dynamical system (1)
- hyperbolic operators (1)
- hyperbolic tilings (1)
- hyperequational theory (1)
- hypoelliptic estimate (1)
- höhere Operationen (1)
- höhere Singularitäten (1)
- ill-posed (1)
- ill-posed problems (1)
- illposed problem (1)
- indecomposable varifold (1)
- index formula (1)
- index of elliptic operator (1)
- index of stability (1)
- infinite-dimensional diffusion (1)
- initial boundary value problem (1)
- integral Fourier operators (1)
- integral representation method (1)
- integration by parts formula (1)
- integration by parts on path space (1)
- interacting particle systems (1)
- interaction matrix (1)
- interassociativity (1)
- interfaces with conical singularities (1)
- intrinsic diameter (1)
- intrinsischer Diameter (1)
- invariant (1)
- inverse Probleme (1)
- inverse Sturm–Liouville problems (1)
- inverse ill-posed problem (1)
- inverse problems (1)
- isoperimetric inequality (1)
- isoperimetrische Ungleichung (1)
- isotopic tiling theory (1)
- jump process (1)
- jump processes (1)
- kanten- und ecken-entartete Symbole (1)
- kernel estimator of the hazard rate (1)
- kernel method (1)
- kernel methods (1)
- kernel-based Bayesian inference (1)
- kernel-basierte Bayes'sche Inferenz (1)
- kleine Parameter (1)
- knots (1)
- komplexe Systeme (1)
- komplexe mechanistische Systeme (1)
- konstitutive Gleichungen (1)
- large-scale mechanistic systems (1)
- lattice packing and covering (1)
- lattice point (1)
- least squares estimator (1)
- left ordered groups (1)
- lidar (1)
- lifespan (1)
- limit theorem for integrated squared difference (1)
- linksgeordnete Gruppen (1)
- localisation (1)
- locality principle (1)
- locally indicable (1)
- logarithmic residue (1)
- logarithmic source condition (1)
- logistic regression analysis (1)
- logistische Regression (1)
- lokal indizierbar (1)
- low-lying eignvalues (1)
- lumping (1)
- macromolecular decay (1)
- magnetic (1)
- magnetic field modeling (1)
- magnetisch (1)
- makromolekularer Zerfall (1)
- manifold (1)
- manifold with boundary (1)
- manifold with edge (1)
- manifolds with cusps (1)
- manifolds with edge (1)
- mapping class groups (1)
- mapping degree (1)
- maps on surfaces (1)
- marked Gibbs point processes (1)
- matching of asymptotic expansions (1)
- mathematical modeling (1)
- mathematical modelling (1)
- mathematical physics (1)
- mathematics (1)
- mathematics education (1)
- mathematische Physik (1)
- mean curvature (1)
- mechanistic modeling (1)
- mechanistische Modellierung (1)
- meromorphe Fortsetzung (1)
- meromorphic continuation (1)
- meromorphic family (1)
- metaplectic operators (1)
- metastability (1)
- microdialysis (1)
- microlocal analysis (1)
- microlokale Analysis (1)
- microphysics (1)
- microsaccades (1)
- middle school (1)
- mild solution (1)
- minimax convergence rates (1)
- minimax optimality (1)
- minimax rate (1)
- mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung (1)
- mittlere Krümmung (1)
- mixed elliptic problems (1)
- mixed problems (1)
- mixture of bridges (1)
- mod k index (1)
- model order reduction (1)
- model selection (1)
- model-informed precision dosing (1)
- modeling (1)
- modellinformierte Präzisionsdosierung (1)
- modified Landweber method (1)
- moduli space of flat connections (1)
- modulo n index (1)
- molecular weaving (1)
- mollifier method (1)
- moment map (1)
- monotone method (1)
- monotonicity (1)
- multi-change point detection (1)
- multilayered coated and absorbing aerosol (1)
- multiple characteristics (1)
- multiplicative Lévy noise (1)
- multiplicative noise (1)
- multitype measure-valued branching processes (1)
- multiwavelength Lidar (1)
- multiwavelength lidar (1)
- multizeta functions (1)
- networks (1)
- new recursive algorithm (1)
- nicht-lineare gemischte Modelle (NLME) (1)
- nichtlineare partielle Differentialgleichung (1)
- non-coercive boundary conditions (1)
- non-linear integro-differential equations (1)
- non-regular drift (1)
- non-uniqueness (1)
- nondegenerate condition (1)
- nonhomogeneous boundary value problems (1)
- nonlinear (1)
- nonlinear equations (1)
- nonlinear invers problem (1)
- nonlinear optimization (1)
- nonlinear partial differential equations (1)
- nonlinear semigroup (1)
- nonlocal problem (1)
- nonparametric regression (1)
- nonparametric regression estimation (1)
- nonsmooth curves (1)
- norm estimates with respect to a parameter (1)
- normal bundle (1)
- normal reflection (1)
- numerical approximation (1)
- offene Wissenschaft (1)
- oncology (1)
- open science (1)
- operator algebras on manifolds with singularities (1)
- operators on manifolds with conical and edge singularities (1)
- operators on manifolds with edges (1)
- operators on manifolds with singularities (1)
- optimal rate (1)
- order filtration (1)
- order reduction (1)
- p-Branen (1)
- p-Laplace Operator (1)
- p-branes (1)
- parallelizable spheres (1)
- parameter-dependent cone operators (1)
- parameter-dependent ellipticity (1)
- parameter-dependent pseudodifferential operators (1)
- parametrices (1)
- parity condition (1)
- parity conditions (1)
- partial algebras (1)
- partial least squares (1)
- partielle Integration (1)
- partielle Integration auf dem Pfadraum (1)
- periodic Gaussian process (1)
- periodic Ornstein-Uhlenbeck process (1)
- periodic entanglement (1)
- permanental- (1)
- pharmacokinetics (1)
- pharmacometrics (1)
- physics (1)
- physiologie-basierte Pharmacokinetic (PBPK) (1)
- point process (1)
- polydisc (1)
- polyhedra and polytopes (1)
- polymer (1)
- popPBPK (1)
- popPK (1)
- population analysis (1)
- porous medium equation (1)
- poset (1)
- principal symbolic hierarchies (1)
- problem of classification (1)
- profile likelihood (1)
- propor-tional hazard mode (1)
- pseudo-diferential operators (1)
- pseudo-differential equation (1)
- pseudo-differential operators (1)
- pseudo-differentialboundary value problems (1)
- pseudo-differentielle Gleichungen (1)
- pseudodifferential boundary value problems (1)
- pseudodifferential subspace (1)
- pseudodifferential subspaces (1)
- pseudodifferentiale Operatoren (1)
- quantizer (1)
- quantum field theory (1)
- quasilinear Fredholm operator (1)
- quasilinear equation (1)
- random walk (1)
- random walk on Abelian group (1)
- rectifiable varifold (1)
- reflecting boundary (1)
- regular figures (1)
- regularisation (1)
- regularization methods (1)
- reinforcement learning (1)
- rejection sampling (1)
- rektifizierbare Varifaltigkeit (1)
- relative cohomology (1)
- relative index formulas (1)
- relative η-invariant (1)
- removable set (1)
- removable sets (1)
- reproducing kernel Hilbert space (1)
- rescaled lattice (1)
- residue (1)
- retrieval (1)
- reziproke Invarianten (1)
- saccade detection (1)
- sampling (1)
- scaled lattice (1)
- scattering amplitude (1)
- scattering theory (1)
- schlecht gestellt (1)
- seismic source inversion (1)
- seismische Quellinversion (1)
- self-assembly (1)
- semi-classical difference operator (1)
- semi-classical spectral estimates (1)
- semiclassical spectral asymptotics (1)
- semiclassics (1)
- semiconductors (1)
- semigroup (1)
- semipermeable barriers (1)
- semiprocess (1)
- sequences of microsaccades (1)
- series representation (1)
- shock wave (1)
- singular drifts (1)
- singular integral equations (1)
- singular manifolds (1)
- singular point (1)
- singuläre Mannigfaltigkeiten (1)
- skew diffusion (1)
- skew diffusions (1)
- skew field of fraction (1)
- small noise asymptotic (1)
- soft matter (1)
- space-time Gibbs field (1)
- spacetimes with timelike boundary (1)
- specific entropy (1)
- spectral boundary value problems (1)
- spectral independence (1)
- spectral kernel function (1)
- spectral resolution (1)
- spin Hall effect (1)
- spirallike function (1)
- stability and accuracy (1)
- stable limit cycle (1)
- stark Hughes-frei (1)
- state estimation (1)
- statistical inference (1)
- statistical inverse problem (1)
- statistical machine learning (1)
- statistical model selection (1)
- statistische Inferenz (1)
- statistisches maschinelles Lernen (1)
- step process (1)
- stochastic Burgers equations (1)
- stochastic bridges (1)
- stochastic interacting particles (1)
- stochastic mechanics (1)
- stochastische Anordnung (1)
- stochastische Differentialgleichungen (1)
- stochastische Mechanik (1)
- stochastische Zellulare Automaten (1)
- stochastisches interagierendes System (1)
- stopping rules (1)
- strongly Hughes-free (1)
- strongly pseudoconvex domains (1)
- structure formation (1)
- structured numbers (1)
- strukturierte Zahlen (1)
- subRiemannian geometry (1)
- supergeometry (1)
- survival analysis (1)
- symmetry group (1)
- symplectic (canonical) transformations (1)
- symplectic manifold (1)
- symplectic methods (1)
- symplectic reduction (1)
- system Lame (1)
- systems of partial differential equations (1)
- systems pharmacology (1)
- tangles (1)
- teaching methods (1)
- terrigener Staub (1)
- terrigenous dust (1)
- tetration (1)
- the Dirichlet problem (1)
- the Goursat problem (1)
- the characteristic Cauchy problem (1)
- the first boundary value problem (1)
- the linearised Einstein equation (1)
- time reversal (1)
- time series (1)
- time series with heavy tails (1)
- time symmetry (1)
- tomogrphy (1)
- trace (1)
- transition path theory (1)
- travel time tomography (1)
- two-level interacting processes (1)
- ultracontractivity (1)
- unendlich teilbare Punktprozesse (1)
- unendliche Teilbarkeit (1)
- uniform compact attractor (1)
- unzerlegbare Varifaltigkeit (1)
- variable projection method (1)
- variational calculus (1)
- variational principle (1)
- variational stability (1)
- varifold (1)
- vibration (1)
- video study (1)
- viral fitness (1)
- wave equation (1)
- wavelet analysis (1)
- weak boundary values (1)
- weiche Materie (1)
- weighted Hölder spaces (1)
- weighted Sobolev space (1)
- weighted Sobolev spaces with discrete saymptotics (1)
- weighted spaces with asymptotics (1)
- zero-noise limit (1)
- η-invariant (1)
- ∂-operator (1)
Institute
- Institut für Mathematik (475) (remove)
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 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.
The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018.
The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan.
A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
This thesis focuses on the study of marked Gibbs point processes, in particular presenting some results on their existence and uniqueness, with ideas and techniques drawn from different areas of statistical mechanics: the entropy method from large deviations theory, cluster expansion and the Kirkwood--Salsburg equations, the Dobrushin contraction principle and disagreement percolation.
We first present an existence result for infinite-volume marked Gibbs point processes. More precisely, we use the so-called entropy method (and large-deviation tools) to construct marked Gibbs point processes in R^d under quite general assumptions. In particular, the random marks belong to a general normed space S and are not bounded. Moreover, we allow for interaction functionals that may be unbounded and whose range is finite but random. The entropy method relies on showing that a family of finite-volume Gibbs point processes belongs to sequentially compact entropy level sets, and is therefore tight.
We then present infinite-dimensional Langevin diffusions, that we put in interaction via a Gibbsian description. In this setting, we are able to adapt the general result above to show the existence of the associated infinite-volume measure. We also study its correlation functions via cluster expansion techniques, and obtain the uniqueness of the Gibbs process for all inverse temperatures β and activities z below a certain threshold. This method relies in first showing that the correlation functions of the process satisfy a so-called Ruelle bound, and then using it to solve a fixed point problem in an appropriate Banach space. The uniqueness domain we obtain consists then of the model parameters z and β for which such a problem has exactly one solution.
Finally, we explore further the question of uniqueness of infinite-volume Gibbs point processes on R^d, in the unmarked setting. We present, in the context of repulsive interactions with a hard-core component, a novel approach to uniqueness by applying the discrete Dobrushin criterion to the continuum framework. We first fix a discretisation parameter a>0 and then study the behaviour of the uniqueness domain as a goes to 0. With this technique we are able to obtain explicit thresholds for the parameters z and β, which we then compare to existing results coming from the different methods of cluster expansion and disagreement percolation.
Throughout this thesis, we illustrate our theoretical results with various examples both from classical statistical mechanics and stochastic geometry.
In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.
In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfies certain nondegenerate condition, then from the results in [20], we know that there exists a unique blowup point at the blowup time such that the first order derivates of smooth solution blow up meanwhile the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of shock curve, moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in the neighbourhood of the blowup point.
This note is devoted to the study on the global existence of a shock wave for the supersonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle of the wedge is less than some critical value, wwe show that a shock attached at the wedge will exist globally.