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  • QA1-939  (20)
  • KIT Scientific Publishing  (20)
  • English  (20)
  • 2020-2024  (20)
  • 1955-1959
  • 1950-1954
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Keywords
Publisher
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  • 2020-2024  (20)
  • 1955-1959
  • 1950-1954
Year
  • 1
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    Palm theory, mass transports and ergodic theory for group-stationary processes (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-12-20
    Description: This work is about random measures stationary with respect to a possibly non-transitive group action. It contains chapters on Palm Theory, the Mass-Transport Principle and Ergodic Theory for such random measures. The thesis ends with discussions of several new models in Stochastic Geometry (Cox Delauney mosaics, isometry stationary random partitions on Riemannian manifolds). These make crucial use of the previously developed techniques and objects.
    Keywords: QA1-939 ; mass-transport principle ; Random measure ; ergodic theory ; Stochastic Geometry ; Palm theory ; bic Book Industry Communication::P Mathematics & science
    Language: English
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  • 2
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    Linear Estimation in Interconnected Sensor Systems with Information Constraints (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-12-20
    Description: A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed.
    Keywords: QA1-939 ; Schätztheorie ; Kalman Filter ; estimation theory ; Sensornetze ; Verteilte SystemsData fusion ; distributed systems ; Datenfusion ; sensor networks ; Kalman filtering ; bic Book Industry Communication::P Mathematics & science
    Language: English
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  • 3
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    Factorization methods for photonics and rough surfaces (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-07-05
    Description: This thesis investigates non-destructive testing problems for rough and periodic surfaces, where the task is to determine such structures from scattered waves. Such problems are non-linear and ill-posed. We are interested in the analysis of the Factorization method applied to this class of inverse scattering problems. This method does not attempt to solve a non-linear operator equation for the unknown object but computes a binary criterion characterizing points inside and outside the structure.
    Keywords: QA1-939 ; Factorization method ; inverse scattering problem ; surface scattering
    Language: English
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  • 4
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    Heat kernel estimates and L p -spectral theory of locally symmetric spaces (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-12-20
    Description: In this work we derive upper Gaussian bounds for the heat kernel on locally symmetric spaces of non-compact type. Furthermore, we determine explicitly the Lp-spectrum of locally symmetric spaces M whose universal covering is a rank one symmetric space of non-compact type if either the fundamental group of M is small (in a certain sense) or if the fundamental group is arithmetic and M is non-compact.
    Keywords: QA1-939 ; Laplace-Beltrami-Operator ; Wärmeleitungskern ; Lokal symmetrischer Raum ; Spektrum ; bic Book Industry Communication::P Mathematics & science
    Language: English
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  • 5
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    From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-12-20
    Description: Based on Sperner's lemma the fixed point theorem of Brouwer is proved. Rather than presenting also other beautiful proofs of Brouwer's fixed point theorem, many nice applications are given in some detail. Also Schauder's fixed point theorem is presented which can be viewed as a natural generalization of Brouwer's fixed point theorem to an infinite-dimensional setting. Finally, Tarski's fixed point theorem is applied to differential equations in Banach spaces.
    Keywords: QA1-939 ; Banachräume ; Brouwer ; SchauderFixed points ; Fixpunkt ; Anwendungen ; Banach spaces ; verification methods ; bic Book Industry Communication::P Mathematics & science
    Language: English
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  • 6
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    Veech Groups and Translation Coverings (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-12-20
    Description: A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
    Keywords: QA1-939 ; cyclic covering ; monodromy group ; Kongruenzgruppe ; zyklische Überlagerung ; Translationsüberlagerung ; translation coveringVeechgruppe ; congruence subgroup ; Monodromiegruppe ; Veech group ; bic Book Industry Communication::P Mathematics & science
    Language: English
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  • 7
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    Bijective point maps, point-stationarity and characterization of Palm measures (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-07-05
    Description: In the theory of stationary spatial point processes, Palm distributions are used to describe the point process seen from one of its points. Such an intrinsic frame of reference is not only interesting for theoretical considerations, but also useful in related fields such as queuing theory and stochastic geometry.
    Keywords: QA1-939 ; Stochastik ; Punktprozess ; Stationärer Punktprozess ; Maßtheorie ; Stochastische Geometrie
    Language: English
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  • 8
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    Discrete Time Analysis of Consolidated Transport Processes (2021)
    KIT Scientific Publishing
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    Publication Date: 2023-12-20
    Description: The objective of this work is to develop models for the analysis of consolidated transport processes. With the discrete time queuing models developed for inventory and vehicle consolidation, in particular milkrun systems, a detailed performance evaluation of different design scenarios can be conducted faster than with simulation. Moreover, it is demonstrated how the models can be connected with each other in form of a network analysis, in order to analyze hub-and-spoke networks.
    Keywords: QA1-939 ; Consolidation ; Milkrun Concept ; Hub-and-Spoke Network ; Queueing Theory ; Stochastic ; Discrete Time Analysis ; bic Book Industry Communication::P Mathematics & science
    Language: English
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  • 9
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    The factorization method for inverse scattering from periodic inhomogeneous media (2021)
    KIT Scientific Publishing
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    Publication Date: 2023-12-20
    Description: This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data.
    Keywords: QA1-939 ; Lippmann-Schwinger equation ; crystal ; inverse scattering problem ; factorization method ; photonics ; bic Book Industry Communication::P Mathematics & science
    Language: English
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  • 10
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    The method of densities for non-isotropic Boolean models (2021)
    KIT Scientific Publishing
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    Publication Date: 2023-07-05
    Description: This book deals with the Boolean model, a basic model of stochastic geometry for the description of porous structures like the pore space in sand stone. The main result is a formula which gives in two and three dimensions a series representation of the most important model parameter, the intensity, using densities of so-called harmonic intrinsic volumes, which are new observable geometric quantities.
    Keywords: QA1-939 ; Stochastic geometry ; Boolean model ; Intensitätsschätzung ; method of densities ; anisotropy ; Anisotropie ; intensity estimation ; Boolesches Modell ; Stochastische Geometrie
    Language: English
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  • 11
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    Some weak limit laws for the diameter of random point sets in bounded regions (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-07-05
    Description: This book establishes several weak limit laws for problems in geometric extreme value theory. We find the limit law of the maximum Euclidean distance of i.i.d. points, as the number of points tends to infinity, under certain assumptions on the underlying distribution. One of the methods is also applicable for some other functionals, such as the maximum area or the maximum perimeter of triangles formed by point triplets.
    Keywords: QA1-939 ; limit distribution ; random point set ; maximum distance ; Poisson approximation ; geometric extreme value theory
    Language: English
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  • 12
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    Path regularity for stochastic differential equations in Banach spaces (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-07-05
    Description: In this work we analzyse the Stochastic Cauchy Problem driven by a cylindrical Wiener process. Given the existence of solutions we show regularity of the paths of the solution. In dependence on properties of the operators in the equation or on geometrical properties of the underlying Banachspace we derive space time regularity results for the paths of the solution.
    Keywords: QA1-939 ; Partielle Differentialgl ; Stochastischer Prozess ; Banach-Raum ; Stark stetige Halbgruppe ; Regularität ; Stochastisches Integral
    Language: English
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  • 13
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    On Length Spectra of Lattices (2021)
    KIT Scientific Publishing
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    Publication Date: 2023-07-05
    Description: The aim of this work is to study Schmutz Schaller's conjecture that in dimensions 2 to 8 the lattices with the best sphere packings have maximal lengths. This means that the distinct norms which occur in these lattices are greater than those of any other lattice in the same dimension with the same covolume. Although the statement holds asymptotically we explicitly present a counter-example. However, it seems that there is nothing but this exception.
    Keywords: QA1-939 ; Lattices ; Geodesics ; Quadratic Forms
    Language: English
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  • 14
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    Geometric Regularization in Bioluminescence Tomography (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-12-20
    Description: Bioluminescence tomography is a recent biomedical imaging technique which allows to study molecular and cellular activities in vivo. From a mathematical point of view, it is an ill-posed inverse source problem: the location and the intensity of a photon source inside an organism have to be determined, given the photon count on the organism's surface. To face the ill-posedness of this problem, a geometric regularization approach is introduced, analyzed and numerically verified in this book.
    Keywords: QA1-939 ; bioluminescence tomography ; shape optimization ; Tikhonov like regularization ; domain derivative ; inverse source problem ; bic Book Industry Communication::P Mathematics & science
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  • 15
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    Invariants of complex and p-adic origami-curves (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-12-20
    Description: Origamis (also known as square-tiled surfaces) are Riemann surfaces which are constructed by glueing together finitely many unit squares. By varying the complex structure of these squares one obtains easily accessible examples of Teichmüller curves in the moduli space of Riemann surfaces.Different Teichmüller curves can be distinguished by several invariants, which are explicitly computed. The results are then compared to a p-adic analogue where Riemann surfaces are replaced by Mumford curves.
    Keywords: QA1-939 ; moduli space ; Teichmüller curves ; translation surfaces ; Mumford curves ; p-adic Schottky groups ; bic Book Industry Communication::P Mathematics & science
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  • 16
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    Geometry and topology of wild translation surfaces (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-07-05
    Description: A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.
    Keywords: QA1-939 ; infinite translation surfaces ; wild singularities ; Drehkomponentengeometric topology ; unendliche Translationsflächen ; wilde Singularitäten ; geometrische Topologie ; rotational components
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  • 17
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    Monodromy representations and Lyapunov exponents of origamis (2021)
    KIT Scientific Publishing
    Details
    Publication Date: 2023-07-05
    Description: Origamis are translation surfaces obtained by gluing finitely many unit squares and provide an easy access to Teichmüller curves. In particular, their monodromy represenation can be explicitely determined. A general principle for the decomposition of this represenation is exhibited and applied to examples. Closely connected to it is a dynamical cocycle on the Teichmüller curve. It is shown that its Lyapunov exponents, otherwise inaccessible, can be computed for a subrepresentation of rank two.
    Keywords: QA1-939 ; variation of Hodge structures ; Lyapunov exponent ; square-tiled surface ; Kontsevich-Zorich cocycle ; Teichmüller curve ; Veech group
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  • 18
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    Variational Integrators and Generating Functions for Stochastic Hamiltonian Systems (2021)
    KIT Scientific Publishing
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    Publication Date: 2023-07-05
    Description: In this work, the stochastic version of the variational principle is established, important for stochastic symplectic integration, and for structure-preserving algorithms of stochastic dynamical systems. Based on it, the stochastic variational integrators in formulation of stochastic Lagrangian functions are proposed, and some applications to symplectic integrations are given. Three types of generating functions in the cases of one and two noises are discussed for constructing new schemes.
    Keywords: QA1-939 ; Weißes Rauschen ; Variationsprinzip ; Hamilton-Jacobi-Differentialgleichung ; Stochastische Differentialgleichung ; Hamilton-Gleichungen ; Hamiltonsches System ; Symplektische Abbildung ; Numerische Mathematik ; Symplektische Matrix
    Language: English
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  • 19
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    Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval (2021)
    KIT Scientific Publishing
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    Publication Date: 2023-07-05
    Description: Lattice Boltzmann methods are a promising approach for the numerical solution of fluid-dynamic problems. We consider the one-dimensional Goldstein-Taylor model with the aim to answer some of the questions concerning the numerical analysis of lattice Boltzmann schemes. Discretizations for the solution of the heat equation are presented for a selection of boundary conditions. Stability and convergence of the solutions are proved by employing energy estimates and explicit Fourier representations.
    Keywords: QA1-939 ; CFD ; Konvergenz ; Lattice-Boltzmann ; Numerische Strömungssimulation ; Gitter-Boltzmann-Methode ; Wärmeleitungsgleichung ; Heat Equation ; Convergence
    Language: English
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  • 20
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    Dynamic risk management with Markov decision processes (2021)
    KIT Scientific Publishing
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    Publication Date: 2023-07-05
    Description: An important tool in risk management is the implementation of risk measures. We study dynamic models where risk measures and dynamic risk measures can be applied. In particular, we solve various portfolio optimization problems and introduce a class of dynamic risk measures via the notion of Markov decision processes. Using Bayesian control theory we furthermore derive an extension of the latter setting when we face model uncertainty.
    Keywords: QA1-939 ; Value at Risk ; Risikomanagement ; Risikomaß ; Stochastischer Prozess ; Portfoliooptimierung
    Language: English
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