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This book provides an introduction to propagator theory. Propagators, or evolution families, are two-parameter analogues of semigroups of operators. Propagators are encountered in analysis, mathematical physics, partial differential equations, and probability theory. They are often used as mathematical models of systems evolving in a changing environment. A unifying theme of the book is the theory of Feynman-Kac propagators associated with time-dependent measures from non-autonomous Kato classes. In applications, a Feynman-Kac propagator describes the evolution of a physical system in the pre

Linear operators. --- Banach spaces. --- Operator theory. --- Functional analysis --- Functions of complex variables --- Generalized spaces --- Topology --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Analytical spaces --- Mechanical properties of solids

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Geological structures are three dimensional, yet are typically represented by, and - terpreted from, outcrop maps and structure contour maps, both of which are curved two-dimensional surfaces. Maps plus serial sections, called 2½-D, provide a closer approach to three dimensionality. Computer technology now makes it possible for geological interpretations to be developed from the beginning in a fully three dim- sional environment. Fully 3-D geological models allow significantly better interpre- tions and interpretations that are much easier to share with other geologists and with the general public. This book provides an overview of techniques for constructing structural interpretations in 2-D, 2½-D and 3-D environments; for interpolating - tween and extrapolating beyond the control points; and for validating the final int- pretation. The underlying philosophy is that structures are three-dimensional solid bodies and that data from throughout the structure, whether in 2-D or 3-D format, should be integrated into an internally consistent 3-D interpretation. It is assumed that most users of this book will do their work on a computer. C- sequently, the book provides quantitative structural methods and techniques that are designed for use with spreadsheets, mapping software, and three-dimensional c- puter-graphics programs. The book is also intended to provide the background for understanding what interpretive software, for example, a computer contouring p- gram, does automatically. Most techniques are presented in both a traditional format appropriate for paper, pencil, and a pocket calculator, and in quantitative format for use with spreadsheets and computer-graphics or computer-aided-design programs.

Geology, Structural --- Maps --- Data processing --- Geological mapping. --- Data processing. --- Geology. --- Geology, Structural. --- Structural Geology. --- Geotechnical Engineering & Applied Earth Sciences. --- Geotectonics --- Structural geology --- Tectonics (Geology) --- Physical geology --- Geognosy --- Geoscience --- Earth sciences --- Natural history --- GG Structural geology --- cartography --- Geology --- Photointerpretation --- Structural geology. --- Geotechnical engineering. --- Engineering, Geotechnical --- Geotechnics --- Geotechnology --- Engineering geology --- Geological mapping --- Geologic mapping --- Cartography --- Maps&delete& --- Geology, Structural - Maps - Data processing

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The book gives a streamlined and systematic introduction to strongly continuous semigroups of bounded linear operators on Banach spaces. It treats the fundamental Hille-Yosida generation theorem as well as perturbation and approximation theorems for generators and semigroups. The special feature is its treatment of spectral theory leading to a detailed qualitative theory for these semigroups. This theory provides a very efficient tool for the study of linear evolution equations arising as partial differential equations, functional differential equations, stochastic differential equations, and others. Therefore, the book is intended for those wanting to learn and apply functional analytic methods to linear time dependent problems arising in theoretical and numerical analysis, stochastics, physics, biology, and other sciences. It should be of interest to graduate students and researchers in these fields.

Semigroups of operators. --- Linear operators. --- Banach spaces. --- Functions of complex variables --- Generalized spaces --- Topology --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Operators, Semigroups of --- Operator theory. --- Global analysis (Mathematics). --- Operator Theory. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Functional analysis --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis

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In March 2004, an international conference was held in Vienna, Austria, on the occasion of the retirement of Heinz Langer, one of the leading experts in operator theory of indefinite inner product spaces. This volume contains some of the papers presented at the meeting. These fifteen refereed articles report on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, e.g., to boundary value problems, the study of orthogonal functions or moment problems. The book closes with a historical survey paper. The scientific part of the book is preceeded by some biographical material and some information about the conference itself. This includes the conference program, the list of participants and an updated list of publications of Heinz Langer.

Inner product spaces. --- Linear operators. --- Differential equations, Linear. --- Mathematics. --- Matrix theory. --- Algebra. --- Functional analysis. --- Integral equations. --- Operator theory. --- Operator Theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Functional Analysis. --- Integral Equations. --- Functional analysis --- Equations, Integral --- Functional equations --- Functional calculus --- Calculus of variations --- Integral equations --- Mathematics --- Mathematical analysis --- Math --- Science --- Linear differential equations --- Linear systems --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Hermitian inner product spaces --- Scalar product spaces --- Spaces, Inner product --- Spaces, Scalar product --- Bilinear forms --- Vector spaces --- Hilbert space

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The third in a series that explores cultural and ethical values in Classical antiquity, this volume examines the dichotomy between 'city' and 'country' in ancient Greek and Roman cultures. Fourteen papers address a variety of topics on this theme, and include a variety of methodological approaches—archaeological, iconographic, literary and philosophical. The book demonstrates that, despite a common rhetoric of polarity in antiquity that tended to construct city and countryside as very distinct, oppositional categories, there was far less consistency (and far more nuance) about the ideologies felt to inhere in each.

Rural-urban relations --- Classical literature --- City and town life in literature --- Country life in literature --- Space in literature --- Relations villes-campagnes --- Littérature ancienne --- Vie urbaine dans la littérature --- Vie rurale dans la littérature --- Espace dans la littérature --- History --- Congresses. --- History and criticism --- Histoire --- Congrès --- Histoire et critique --- Landscape assessment --- Geographical perception --- Landscape in literature --- History. --- History and criticism. --- Landscapes in literature. --- Littérature ancienne --- Vie urbaine dans la littérature --- Vie rurale dans la littérature --- Espace dans la littérature --- Congrès --- Landscapes in literature --- Assessment, Landscape --- Environmental perception --- Landscape evaluation --- Landscape perception --- Perception, Landscape --- Human ecology --- Land use --- Landscape protection --- Maps, Mental --- Mental maps --- Perceptual cartography --- Perceptual maps --- Perception --- Orientation (Psychology) --- Space perception --- Rural-urban interaction --- Urban-rural interaction --- Urban-rural relations --- Sociology, Rural --- Sociology, Urban --- Landscape assessment - Greece - History. --- Landscape assessment - Rome - History. --- Geographical perception - Greece - History. --- Geographical perception - Rome - History. --- Rural-urban relations - Greece. --- Rural-urban relations - Rome. --- Landscape in literature - History and criticism. --- Classical literature - History and criticism.