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This book is devoted to the least gradient problem and its variants. The least gradient problem concerns minimization of the total variation of a function with prescribed values on the boundary of a Lipschitz domain. It is the model problem for studying minimization problems involving functionals with linear growth. Functions which solve the least gradient problem for their own boundary data, which arise naturally in the study of minimal surfaces, are called functions of least gradient.The main part of the book is dedicated to presenting the recent advances in this theory. Among others are presented an Euler-Lagrange characterization of least gradient functions, an anisotropic counterpart of the least gradient problem motivated by an inverse problem in medical imaging, and state-of-the-art results concerning existence, regularity, and structure of solutions. Moreover, the authors present a surprising connection between the least gradient problem and the Monge-Kantorovich optimal transport problem and some of its consequences, and discuss formulations of the least gradient problem in the nonlocal and metric settings. Each chapter is followed by a discussion section concerning other research directions, generalizations of presented results, and presentation of some open problems. The book is intended as an introduction to the theory of least gradient functions and a reference tool for a general audience in analysis and PDEs. The readers are assumed to have a basic understanding of functional analysis and partial differential equations. Apart from this, the text is self-contained, and the book ends with five appendices on functions of bounded variation, geometric measure theory, convex analysis, optimal transport, and analysis in metric spaces.

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.

Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances.After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety.This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an openaccess book.

This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray's problem on existence of a solution to the boundary value problem for the stationary Navier--Stokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors' work over the past few years on this under-explored topic within the study of the Navier--Stokes equations. This book will be the first major work on the Navier--Stokes equations to explore Leray's problem in detail. The results are presented with detailed proofs, as are the history of the problem and the previous approaches to finding a solution to it. In addition, for the reader's convenience and for the self-sufficiency of the text, the foundations of the mathematical theory for incompressible fluid flows described by the steady state Stokes and Navier--Stokes systems are presented. For researchers in this active area, this book will be a valuable resource.

The book gives the basic results of the theory of the spaces Ap¿ of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ¿ permitting any rate of growth of a function near the boundary of the domain. This continues and essentially improves M.M. Djrbashian's theory of spaces Ap¿ (1945) of functions holomorphic in the unit disc, the English translation of the detailed and complemented version of which (1948) is given in Addendum to the book. Besides, the book gives the ¿-extensions of M. M. Djrbashian's two factorization theories of functions meromorphic in the unit disc of 1945-1948 and 1966-1975 to classes of functions delta-subharmonic in the unit disc and in the half-plane.The book can be useful for a wide range of readers. It can be a good handbook for Master, PhD students and Postdoctoral Researchers for enlarging their knowledge and analytical methods, as well as a useful resource for scientists who want to extend their investigation fields.

Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles, spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature.

This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar. The volume has two main topics: 1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integro-differential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using micro-local and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown. 2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered.

This volume explores state-of-the-art developments in theoretical and applied fluid mechanics with a focus on stabilization and control. Chapters are based on lectures given at the summer school "Fluids under Control", held in Prague from August 23-27, 2021. With its accessible and flexible presentation, readers will be motivated to deepen their understanding of how mathematics and physics are connected. Specific topics covered include: Stabilization of the 3D Navier-Stokes systemFlutter stabilization of flow-state systemsTurbulence controlDesign through analysis Fluids Under Control will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.

John Corcoran was a very well-known logician who worked on several areas of logic. He produced decisive works giving a better understanding of two major figures in the history of logic, Aristotle and Boole. Corcoran had a close association with Alfred Tarski, a prominent 20th-century logician. This collaboration manifested in Corcoran's substantial introduction to Tarski's seminal book, Logic, Semantics, Metamathematics (1956). Additionally, Corcoran's posthumous editorial involvement in 'What are logical notions?' (1986) breathed new life into this seminal paper authored by Tarski. His scholarly pursuits extended to the intricate explication of fundamental concepts in modern logic, including variables, propositions, truth, consequences, and categoricity. Corcoran's academic curiosity extended further to the intersection of ethics and logic, reflecting his contemplation of their interrelation. Beyond these theoretical contributions, Corcoran was deeply engaged in the pedagogical dimensions of logic instruction. This volume serves as a compilation of articles contributed by Corcoran's students, colleagues, and international peers. By encompassing a diverse range of subjects, this collection aptly mirrors Corcoran's wide-ranging interests, offering insights that not only deepen our understanding of his work but also advance the theoretical frameworks he explored.

I: Genetics and conservation biology.- Introductory remarks: Genetics and conservation biology.- Global issues of genetic diversity.- II: Genetic variation and fitness.- Introductory remarks.- Genetic variation and fitness: Conservation lessons from pines.- Genetic diversity and fitness in small populations.- Mutation load depending on variance in reproductive success and mating system.- Extinction risk by mutational meltdown: Synergistic effects between population regulation and genetic drift.- III: Inbreeding, population and social structure.- Introductory remarks.- Inbreeding: One word, several meanings, much confusion.- The genetic structure of metapopulations and conservation biology.- Effects of inbreeding in small plant populations: Expectations and implications for conservation.- The interaction of inbreeding depression and environmental stochasticity in the risk of extinction of small populations.- Genetic structure of a population with social structure and migration.- Guidelines in conservation genetics and the use of the population cage experiments with butterflies to investigate the effects of genetic drift and inbreeding.- IV: Molecular approaches to conservation.- Introductory remarks.- Rare alleles, MHC and captive breeding.- Andean tapaculos of the genus Scytalopus (Aves, Rhinocryptidae): A study of speciation using DNA sequence data.- Genetic distances and the setting of conservation priorities.- Multi-species risk analysis, species evaluation and biodiversity conservation.- V: Case studies.- Introductory remarks.- On genetic erosion and population extinction in plants: A case study in Scabiosa columbaria and Salvia pratensis.- Effects of releasing hatchery-reared brown trout to wild trout populations.- Genetics and demography of rare plants and patchily distributed colonizing species.- Response to environmental change: Genetic variation and fitness in Drosophila buzzatii following temperature stress.- Alternative life histories and genetic conservation.- The principles of population monitoring for conservation genetics.- VI: Genetic resource conservation.- Introductory remarks.- Optimal sampling strategies for core collections of plant genetic resources.- Conservation genetics and the role of botanical gardens.- Animal breeding and conservation genetics.- Scenarios.- Introductory remarks.- A: The genetic monitoring of primate populations for their conservation.- B: Heavy metal tolerance, plant evolution and restoration ecology.- C: Genetic conservation and plant agriculture.- D: Fragmented plant populations and their lost interactions.- E: Host-pathogen coevolution under in situ conservation.- Concluding remarks.

Parallel Completion Techniques.- The Computation of Gröbner Bases Using an Alternative Algorithm.- Symmetrization Based Completion.- On the Reduction of G-invariant Polynomials for an Arbitrary Permutation Groups G.- The Non-Commutaive Gröbner Freaks.- Alternatives in Implementing Noncommutative Gröbner Basis Systems.- String Rewriting and Gröbner Bases - A General Approach to Monoid and Group Rings.- Gröbner Fans and Projective Schemes.- Normalized Rewriting: A Unified View of Knuth-Bendix Completion and Gröbner Bases Computation.- New Directions for Syntactic Termination Orderings.- Two-sided Gröbner Bases in Iterated Ore Extensions.- Computing the Torsion Group of Elliptic Curves by the Method of Gröbner Bases.- Finding a Finite Group presentation Using Rewriting.- Deciding Degree-Four-Identities for Alternative Rings by Rewriting.

Structural optimization - a survey.- Mathematical optimization: an introduction.- Design optimization with the finite element program ANSYSR.- B&B: a FE-program for cost minimization in concrete design.- The CAOS system.- Shape optimization with program CARAT.- DYNOPT: a program system for structural optimization weight minimum design with respect to various constraints.- MBB-Lagrange: a computer aided structural design system.- The OASIS-ALADDIN structural optimization system.- The structural optimization system OPTSYS.- SAPOP: an optimization procedure for multicriteria structural design.- SHAPE: a structural shape optimization program.- STARS: mathematical foundations.

In Krisenzeiten: Quo vadis, Architektur? Angetrieben vom Wunsch, angesichts von Krisen bessere Welten zu erschaffen, versuchen Architekt: innen, Gesellschaft, Städte und Wohnformen neu zu denken, die Architektur und ihre Materialität zu erneuern - und prägen damit eine neue Ästhetik. Denn Krisen eröffnen als "Kippmomente" neue Perspektiven: Anhand historischer wie zeitgenössischer Projekte untersucht Susanne Stacher unterschiedliche Strategien in der Architektur. Ansätze aus Wissenschaft und Philosophie (u. a. Pierre-Henri Castel, Hartmut Rosa) ermöglichen es, Vorstellungen von Fortschritt, Wachstum, Natur, Gesellschaft zu hinterfragen, die in den vorgestellten Architekturprojekten sichtbar werden. Das Buch spannt einen weiten historischen Bogen und ist ein Plädoyer, über die Rolle von Architektur und Städtebau in Zeiten ökologischer Krisen nachzudenken. Eine historische und philosophische Betrachtung von Architektur in Krisenzeiten Vom Archaismus über das Streben nach Entschleunigung, Erschaffung durch Zerstörung bis zur Wiederverzauberung der Welt Projekte/Konzepte von Hans Hollein, Ebenezer Howard, Bjarke Ingels, Le Corbusier, Adolf Loos, Paul Otlet, Bernard Rudofsky u. a.

1 The Beginning: Family, Gymnasium, Universities.- 2 Back to Petrograd.- 3 In Germany.- 4 The Years 1926-1930.- 5 In America.- 6 Prewar Years.- 7 Years of War.- 8 Years 1945-1952.- 9 A Mosaic of Reminiscences.- Frenkel's Books.

1 Grundlagen.- 1.1 Allgemeine Grundlagen.- 1.1.1 Ziele und Aufgaben.- 1.1.2 Methoden.- 1.1.3 Geschichte und Einordnung.- 1.1.3.1 Geschichte der Bauwerksvermessung.- 1.1.3.2 Geschichte des Vermessungswesens.- 1.1.3.3 Geschichte der Architekturphotogrammetrie.- 1.1.4 Rechtliche Grundlagen und Rahmenbedingungen.- 1.1.4.1 Internationale Vereinbarungen und Organisationen.- 1.1.4.2 Baugesetzbuch, Denkmalpflegegesetze, Vermessungsgesetze.- 1.2 Messgrößen und Maßeinheiten.- 1.2.1 Strecken.- 1.2.2 Winkel.- 1.3 Bezugssysteme und Koordinaten.- 1.3.1 Bezugsflächen.- 1.3.2 Koordinaten.- 1.3.3 Koordinatensysteme.- 1.3.3.1 Polarkoordinaten.- 1.3.3.2 Lokale Koordinatensysteme.- 1.3.3.3 Regionale Koordinatensysteme.- 1.3.3.4 Globale Koordinatensysteme.- 1.3.3.5 Geographische Koordinaten.- 1.3.3.6 Geozentrische Koordinaten.- 1.3.4 Koordinatentransformationen.- 1.3.4.1 Translation (2D).- 1.3.4.2 Maßstabslose Transformation (2D).- 1.3.4.3 Ähnlichkeitstransformation (2D).- 1.3.4.4 Vereinfachte Ähnlichkeitstransformation mit 2 Passpunkten (2D).- 1.3.4.5 Affintransformation (2D).- 1.3.4.6 Weitere ebene Koordinatentransformationen.- 1.3.4.7 Räumliche Koordinatentransformation (3D).- 1.3.5 Festpunktfelder.- 1.3.5.1 Netz trigonometrischer Punkte zur Lagedefinition.- 1.3.5.2 Höhennetz.- 1.3.6 Vermessungsnetze für die Bauwerksvermessung.- 1.3.6.1 Netzdesign.- 1.3.6.2 Vermarkung.- 1.3.6.3 Design und Fertigung von Punktsignalisierungen.- 1.3.6.4 Auswahl natürlicher Passpunkte.- 1.3.6.5 Schnurnetz zur temporären Vermarkung.- 1.3.6.6 Punktübersichten und Einmessskizzen.- 1.4 Fehlerlehre und Statistik.- 1.4.1 Fehlerarten und ihre Wirkung.- 1.4.1.1 Zufällige Fehler.- 1.4.1.2 Systematische Fehler.- 1.4.1.3 Grobe Fehler.- 1.4.2 Fehlerfortpflanzung und Ausgleichsrechnung.- 1.4.3 Rechenschärfe und Rundung.- 1.4.4 Toleranzen im Bauwesen.- 2 Dokumentation von Gebäuden und Ensembles.- 2.1 Amtliche Dokumentation.- 2.1.1 Katasterunterlagen.- 2.1.2 Amtliche Karten.- 2.1.3 Lageplan.- 2.1.4 Geoinformationssysteme (GIS).- 2.2 Pläne.- 2.2.1 Grundriss.- 2.2.2 Schnitt.- 2.2.3 Ansicht.- 2.2.4 Detaildarstellungen.- 2.2.5 Maßstäbe und Detaillierungsgrad.- 2.2.6 Materialien und Aufbewahrung.- 2.3 3D-Beschreibungen.- 2.3.1 CAD-Modell.- 2.3.2 Animation.- 2.3.3 Virtual Reality.- 2.3.4 Augmented Reality.- 2.4 Fotografie.- 2.4.1 Analoge Fotografie.- 2.4.1.1 Fotografisches Material.- 2.4.1.2 Kameras.- 2.4.1.3 Objektive.- 2.4.1.4 Licht.- 2.4.1.5 Belichtung.- 2.4.1.6 Archivierungen von Fotomaterialien.- 2.4.2 Digitale Bilder.- 2.4.2.1 Flächensensoren.- 2.4.2.2 Zeilenkameras.- 2.4.2.3 Spezialkameras.- 2.4.3 Scannen analoger Fotovorlagen.- 2.4.4 Digitale Bildverarbeitung.- 2.5 Textliche und hybride Beschreibungen.- 2.5.1 Raumbuch.- 2.5.2 Hypertext Dokumente.- 2.5.3 Informationssystem.- 2.6 Archivierung digitaler Daten.- 2.6.1 Datenträger.- 2.6.2 Datenformate.- 2.6.2.1 Texte.- 2.6.2.2 Datenbanken.- 2.6.2.3 Vektordaten.- 2.6.2.4 Rasterdaten.- 2.6.2.5 Hypermedia.- 3 Erfassung von Messelementen.- 3.1 Messprinzipien.- 3.1.1 Vom-Großen-ins-Kleine.- 3.1.2 Überbestimmungen.- 3.1.3 Vermeidung von systematischen Fehlern.- 3.2 Geräte und Instrumente.- 3.2.1 Bauteile, Kleingeräte und Zubehör.- 3.2.1.1 Lote und Libellen.- 3.2.1.2 Fernrohr.- 3.2.1.3 Stative.- 3.2.1.4 Fluchtstab.- 3.2.1.5 Nivellierlatten und Kleingerät.- 3.2.1.6 Aufstellen eines Instruments.- 3.2.2 Winkelmessung.- 3.2.2.1 Bestimmung rechter Winkel.- 3.2.2.2 Theodolit.- 3.2.2.3 Satzmessung.- 3.2.2.4 Berechnung von Richtungswinkeln aus Koordinaten.- 3.2.3 Streckenmessung.- 3.2.3.1 Streckenmessung mit dem Messband.- 3.2.3.2 Optische Streckenmessung.- 3.2.3.3 Elektro-optische Entfernungsmessung (EDM).- 3.2.4 Höhenmessung.- 3.2.4.1 Einfache Werkzeuge.- 3.2.4.2 Nivellement.- 3.2.4.3 Rotationslaser.- 3.3 Beschaffung einer Vermessungsausrüstung.- 4 Messverfahren.- 4.1 Schrittskizze.- 4.2 Handaufmaß.- 4.3 Punktbestimmung ohne Theodolit.- 4.3.1 Bogenschlag.- 4.3.2 Einbindeverfahren.- 4.3.3 Orthogonalverfahren.- 4.3.4

Intermediate and deep earthquakes in Spain.- Spanish national strong motion network. Recording of the Huelva earthquake of 20 December, 1989.- Regional focal mechanisms for earthquakes in the Aegean area.- Rates of crustal deformation in the North Aegean trough-North Anatolian fault deduced from seismicity.- Regional stresses along the Eurasia-Africa plate boundary derived from focal mechanisms of large earthquakes.- Focal mechanisms of intraplate earthquakes in Bolivia, South America.- Partial breaking of a mature seismic gap: The 1987 earthquakes in New Britain.- Size of earthquakes in Southern Mexico from indirect methods.- Numerical simulation of the earthquake generation process.- Intermagnitude relationships and asperity statistics.- Complete synthetic seismograms for high-frequency multimode SH-waves.- Body-wave dispersion: Measurement and interpretation.

Approximate Two Layer (Inviscid/Viscous) Methods to Model Aerothermodynamic Environments.- Second-Order Effects in Hypersonic Boundary Layers.- Unstructured-Grid Algorithms for High-Speed CFD Analysis.- Numerical Simulation of Three-Dimensional Hypersonic Viscous Flows.- Numerical Simulation of Entry Flow over Blunt Swept-Wing Planes.- Viscous Nonequilibrium Flow Calculations.- The Finite Pointset Method for Hypersonic Flows in the Rarefied Gas Regime.- Computation of Flowfields for Hypersonic Flight at High Altitudes.

Turbulence Modeling for Hypersonic Flows.- Advanced Topics in Turbulence Theory.- Different Levels of Air Dissociation Chemistry and Its Coupling with Flow Models.- Modeling of Hypersonic Reacting Flows.- Modeling of Hypersonic Non Equilibrium Flows.- Wall Catalytic Recombination and Boundary Conditions in Nonequilibrium Hypersonic Flows-With Applications.- Physical Aspects of Hypersonic Flow: Fluid Dynamics and Non-Equilibrium Phenomena.- Permissions.

Turbulence Modeling for Hypersonic Flows.- Advanced Topics in Turbulence Theory.- Different Levels of Air Dissociation Chemistry and Its Coupling with Flow Models.- Modeling of Hypersonic Reacting Flows.- Modeling of Hypersonic Non Equilibrium Flows.- Wall Catalytic Recombination and Boundary Conditions in Nonequilibrium Hypersonic Flows-With Applications.- Physical Aspects of Hypersonic Flow: Fluid Dynamics and Non-Equilibrium Phenomena.- Permissions.

The Cray Research MPP Fortran Programming Model.- Resource Optimisation via Structured Parallel Programming.- SYNAPS/3 - An Extension of C for Scientific Computations.- The Pyramid Programming System.- Intelligent Algorithm Decomposition for Parallelism with Alfer.- Symbolic Array Data Flow Analysis and Pattern Recognition in Numerical Codes.- A GUI for Parallel Code Generation.- Formal Techniques Based on Nets, Object Orientation and Reusability for Rapid Prototyping of Complex Systems.- Adaptor - A Transformation Tool for HPF Programs.- A Parallel Framework for Unstructured Grid Solvers.- A Study of Software Development for High Performance Computing.- Parallel Computational Frames: An Approach to Parallel Application Development based on Message Passing Systems.- A Knowledge-Based Scientific Parallel Programming Environment.- Parallel Distributed Algorithm Design Through Specification Transformation: The Asynchronous Vision System.- Steps Towards Reusability and Portability in Parallel Programming.- An Environment for Portable Distributed Memory Parallel Programming.- Reuse, Portability and Parallel Libraries.- Assessing the Usability of Parallel Programming Systems: The Cowichan Problems.- Experimentally Assessing the Usability of Parallel Programming Systems.- Experiences with Parallel Programming Tools.- The MPI Message Passing Interface Standard.- An Efficient Implementation of MPI.- Post: A New Postal Delivery Model.- Asynchronous Backtrackable Communications in the SLOOP Object-Oriented Language.- A Parallel I/O System for High-Performance Distributed Computing.- Language and Compiler Support for Parallel I/O.- Locality in Scheduling Models of Parallel Computation.- A Load Balancing Algorithm for Massively Parallel Systems.- Static Performance Prediction in PCASE: A Programming Environment for Parallel Supercomputers.- A Performance Tool for High-Level Parallel Programming Languages.- Implementation of a Scalable Trace Analysis Tool.- The Design of a Tool for Parallel Program Performance Analysis and Tuning.- The MPP Apprentice Performance Tool: Delivering the Performance of the Cray T3D.- Optimized Record-Replay Mechanism for RPC-based Parallel Programming.- Abstract Debugging of Distributed Applications.- Design of a Parallel Object-Oriented Linear Algebra Library.- A Library for Coarse Grain Macro-Pipelining in Distributed Memory Architectures.- An Improved Massively Parallel Implementation of Colored Petri-Net Specifications.- A Tool for Parallel System Configuration and Program Mapping based on Genetic Algorithms.- Emulating a Paragon XP/S on a Network of Workstations.- Evaluating VLIW-in-the-large.- Implementing a N-Mixed Memory Model on a Distributed Memory System.- Working Group Report: Reducing the Complexity of Parallel Software Development.- Working Group Report: Usability of Parallel Programming System.- Working Group Report: Skeletons/Templates.

1 Introductory Material.- 2 The Direct and Indirect B.I.E.M. for Bilateral Problems.- 3 Boundary Integral Formulations for Some Special Elastostatic B.V.Ps.- 4 On the Numerical Implementation of Boundary Element Equations.- 5 Extension to Dynamic Problems.- 6 Dynamic Interaction Problems.- 7 B.I. Formulations for the Signorini-Fichera Inequality Problem.- 8 Mathematical Study of the B.I. Formulations of the Signorini-Fichera B.V.P..- 9 Boundary Integral Formulation of the Frictional Unilateral Contact B.V.P..- 10 Boundary Integral Formulations for the Monotone Multivalued Boundary Conditions.- 11 Elastodynamic Unilateral Problems. A B.I.E. Approach.- 12 Nonconvex Unilateral Contact Problems.- 13 Miscellanea.- References.

1 Technische Regelwerke.- 1.1 Literatur.- 2 Beschreibung der PE-HD-Werkstoffe und Herstellung der Dichtungsbahnen.- 2.1 Werkstoff.- 2.2 Morphologie.- 2.3 Herstellung.- 2.4 Literatur.- 3 Prüfung der Eigenschaften von PE-HD-Dichtungsbahnen.- 3.1 Übersicht.- 3.2 Prüfverfahren.- 3.2.1 Äußere Beschaffenheit, Homogenität, Geradheit und Planlage.- 3.2.2 Dicke.- 3.2.3 Rußgehalt und Rußverteilung.- 3.2.4 Schmelzindex und Dichte.- 3.2.5 Maßänderung.- 3.2.6 Permeation.- 3.2.7 Thermoanalytische Messungen und Oxidationsstabilität.- 3.2.8 Zugversuch.- 3.2.9 Wölbversuch.- 3.2.10 Relaxationsversuch.- 3.2.11 Beständigkeit gegen Chemikalien.- 3.2.12 Beständigkeit gegen thermisch-oxidativen Abbau.- 3.2.13 Spannungsrissprüfung: Zeitstand-Rohrinnendruckversuch und NCTL-Test.- 3.2.14 Witterungsbeständigkeit.- 3.2.15 Beständigkeit gegen biologische Einwirkungen.- 3.2.16 Zeitstand-Zugversuch.- 3.2.17 Reibungseigenschaften.- 3.2.18 Zeitstand-Scherversuch.- 3.3 Weitere Prüfungen.- 3.4 Literatur.- 4 Verformungsverhalten.- 4.1 Spannungsrelaxation und Kriechen.- 4.2 Phänomenologisches Werkstoffmodell.- 4.3 Verformungsverhalten im Zug- und Wölbversuch.- 4.4 Bestimmung der Verformung aus der Konturlinie.- 4.5 Literatur.- 5 Langzeitverhalten.- 5.1 Alterung.- 5.2 Oxidativer Abbau.- 5.2.1 Autoxidation unstabilisierter Polyolefine.- 5.2.2 Chemische Stabilisierung.- 5.2.3 Strukturelle Stabilisierung.- 5.3 Spannungsrissbildung.- 5.3.1 Beschreibung der Risserscheinungen und Begriffe.- 5.3.2 Prüfverfahren für Spannungsrissbeständigkeit.- 5.3.3 Exkurs in die Bruchmechanik.- 5.3.4 Modelle zur Beschreibung der Spannungsrissbildung.- 5.4 Funktionsdauer von PE-HD-Dichtungsbahnen.- 5.5 Literatur.- 6 PE-HD-Dichtungsbahnen mit strukturierter Oberfläche.- 6.1 Art und Herstellung von Oberflächenstrukturen.- 6.2 Prüfungen an strukturierten Dichtungsbahnen.- 6.3 Eigenschaften strukturierter Dichtungsbahnen, Gleitsicherheit von Abdichtungssystemen.- 6.4 Literatur.- 7 Stofftransport.- 7.1 Vorbemerkung.- 7.2 Stofftransport in der Kunststoffdichtungsbahn.- 7.3 Stofftransport in Böden (Auflager der Dichtungsbahn).- 7.4 Stofftransport in der Kombinationsdichtung (Dichtungsbahn und Erdstoff).- 7.5 Auswirkungen von Fehlstellen in der Dichtungsbahn.- 7.6 Literatur.- 8 Anforderungen an Schutzschichten.- 8.1 Funktion von Schutzschichten.- 8.2 Arten von Schutzschichten.- 8.2.1 Überblick.- 8.2.2 Mineralische Schutzschichten.- 8.2.3 Schutzschichten aus Geokunststoffen.- 8.3 Dimensionierung und Prüfung von Schutzschichten.- 8.3.1 Eindellungen in der Dichtungsbahn.- 8.3.2 Schutzwirksamkeitsprüfung.- 8.3.3 Prüfung zur Perforation der Dichtungsbahn.- 8.4 Literatur.- 9 Einbau der PE-HD-Dichtungsbahn.- 9.1 Einleitung: PE-HD-Dichtungsbahnen im Deponiebau.- 9.2 Verlegeplanung.- 9.3 Einbau.- 9.3.1 Exkurs: Entstehung und Auswirkung von Wellen in der Dichtungsbahn.- 9.3.2 Die Riegelbauweise.- 9.4 Qualitätssicherung.- 9.4.1 Anforderungen an Verlegefachbetriebe.- 9.4.2 Anforderungen an fremdprüfende Stellen.- 9.5 Literatur.- 10 Schweißen von Kunststoffdichtungsbahnen.- 10.1 Schweißmaschinen, -geräte und Schweißnähte.- 10.2 Prüfung von Schweißnähten.- 10.3 Prozessmodell zur Bewertung der Qualität von Heizkeil-Überlappnähten.- 10.4 Literatur.- 11 Dichtungskontrollsysteme für Kunststoffdichtungsbahnen.- 11.1 Funktion und Arten von Dichtungskontrollsystemen.- 11.2 Anforderungen an Dichtungskontrollsysteme.- 11.3 Art und Häufigkeit von Fehlstellen.- 11.4 Literatur.- Anhang 1 Anforderungstabellen aus der Zulassungsrichtlinie der BAM.- Tabelle 1: Allgemeine physikalische Anforderungen.- Tabelle 2: Mechanische Anforderungen.- Tabelle 3: Anforderungen an die Beständigkeit und das Langzeitverhalten.- Tabelle 4: Zusätzliche Anforderungen an Dichtungsbahnen mit strukturierter Oberfläche.- Tabelle 5: Art und Umfang der Prüfungen an der Formmasse und am Rußbatch im Rahmen der Eigenüberwachung der Herstellung der Dichtungsbahnen.- Tabelle 6: Art und Umfang der Prüfu