This book traces the emergence and development of the deification theme in Greek patristic theology and its subsequent transformation into the theology of theosis in Pseudo-Dionysius the Areopagite. This volume dwells on the deification theme as it is situated in the complex context of its historical development and thus avoids the common tendency to treat this notion of Christian theology in an anachronistic manner. Significant attention is given to the influence of Neoplatonism on Pseudo-Dionysius. His theology is justified neither as essentially orthodox Christian nor as essentially orthodox Neoplatonic. Dionysius's sophisticated synthesis of Christian and Neoplatonic elements, especially in his exposition of theosis, does justice to this anonymous author's originality and demonstrates the importance of his influence both on the further development of Christian theology, and on the advancement of the Neoplatonic tradition. The intricate cultural background of the Pseudo-Dionysian world helps clarify the formation process of Christian imperial identity, and throws additional light on why these works were attributed to Dionysius the Areopagite, not as a conscious forgery, but as a literary device. Such attribution was a common practice of the time. Comprehensive analysis of the development of the deification theme opens possibilities for further study of Trinitarian and christological formations, of philosophical and individual moral theology, of Christian and Neoplatonic mysticism, and of cultural studies. By surveying the historical development of deification and by opening further areas of research, this book serves a valuable introductory source for both professionals and students. While primarily focusing on academic interests, the book is written keeping the general reading audience in mind as well. All quotations of the original texts are provided with existing or new English translations, while important Greek terminology is acknowledged. Readers interested in Christian spirituality, late antiquity, early Christian theology, and Neoplatonism will find this book useful.
This monograph revisits one of the most debated aspects of Dionysian scholarship: the enigma of its authorship. To establish the identity of the author remains impossible. However, the legitimacy of the attribution of the corpus to Dionysius the Areopagite should not be seen as an intended forgery but rather as a masterfully managed literary device, which better indicates the initial intention of the actual author. The affiliation with Dionysius the Areopagite has metaphorical and literary significance. Dionysius is the only character in the New Testament who is unique in his conjunction between the apostle Paul and the Platonic Athenian Academy. In this regard this attribution, to the mind of the actual author of the corpus, could be a symbolic gesture to demonstrate the essential truth of both traditions as derived essentially from the same divine source. The importance of this assumption taken in its historical context highlights the culmination of the formation of the civilized Roman-Byzantine Christian identity.
This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.
This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.
This book describes physical, mathematical and experimental methods to model flows in micro- and nanofluidic devices. It takes in consideration flows in channels with a characteristic size between several hundreds of micrometers to several nanometers. Methods based on solving kinetic equations, coupled kinetic-hydrodynamic description, and molecular dynamics method are used. Based on detailed measurements of pressure distributions along the straight and bent microchannels, the hydraulic resistance coefficients are refined. Flows of disperse fluids (including disperse nanofluids) are considered in detail. Results of hydrodynamic modeling of the simplest micromixers are reported. Mixing of fluids in a Y-type and T-type micromixers is considered. The authors present a systematic study of jet flows, jets structure and laminar-turbulent transition. The influence of sound on the microjet structure is considered. New phenomena associated with turbulization and relaminarization of the mixing layer of microjets are discussed. Based on the conducted experimental investigations, the authors propose a chart of microjet flow regimes. When addressing the modeling of microflows of nanofluids, the authors show where conventional hydrodynamic approaches can be applied and where more complicated models are needed, and they analyze the hydrodynamic stability of the nanofluid flows. The last part of the book is devoted the statistical theory of the transport processes in fluids under confined conditions. The authors present the constitutive relations and the formulas for transport coefficients. In conclusion the authors present a rigorous analysis of the viscosity and diffusion in nanochannels and in porous media.
This volume presents articles originating from invited talks at an exciting international conference held at The Fields Institute in Toronto celebrating the sixtieth birthday of the renowned mathematician, Vladimir Arnold. Experts from the world over--including several from "Arnold's school"--gave illuminating talks and lively poster sessions. The presentations focused on Arnold's main areas of interest: singularity theory, the theory of curves, symmetry groups, dynamical systems, mechanics, and related areas of mathematics. The book begins with notes of three lectures by V. Arnold given in the framework of the Institute's Distinguished Lecturer program. The topics of the lectures are: (1) From Hilbert's Superposition Problem to Dynamical Systems (2) Symplectization, Complexification, and Mathematical Trinities (3) Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Arnold's three articles include insightful comments on Russian and Western mathematics and science. Complementing the first is Jurgen Moser's "Recollections", concerning some of the history of KAM theory.
The topic of this book is Cold Spray technology. Cold Spray is a process of applying coatings by exposing a metallic or dielectric substrate to a high velocity (300 to 1200 m/s) jet of small (1 to 50 μm) particles accelerated by a supersonic jet of compressed gas. This process is based on the selection of the combination of particle temperature, velocity, and size that allows spraying at the lowest temperature possible. In the Cold Spray process, powder particles are accelerated by the supersonic gas jet at a temperature that is always lower than the melting point of the material, resulting in coating formation from particles in the solid state. As a consequence, the deleterious effects of high-temperature oxidation, evaporation, melting, crystallization, residual stresses, gas release, and other common problems for traditional thermal spray methods are minimized or eliminated. This book is the first of its kind on the Cold Spray process. Cold Spray Technology covers a wide spectrum of various aspects of the Cold Spray technology, including gas-dynamics, physics of interaction of high-speed solid particles with a substrate as well as equipment, technologies, and applications. Cold Spray Technology includes the results of more than 20 years of original studies (1984-2005) conducted at the Institute of Theoretical and Applied Mechanics of the Siberian Division of the Russian Academy of Science, as well as the results of studies conducted at most of the research centres around the world. The authors' goal is threefold. The first goal is to explain basic principles and advantages of the Cold Spray process. The second goal is, to give practical information on technologies and equipment. The third goal is to present the current state of research and development in this field over the world. The book provides coverage and data that will be of interest for users of Cold Spray technology as well as for other coating experts. At the present time the Cold Spray method is recognized by world leading scientists and specialists. A wide spectrum of research is being conducted at many research centres and companies in many countries. New approach to spray coatings Results are exceptionally pure coatings Low spray temperature without degradation of powder and substrate materials High productivity, high deposition efficiency High operational safety because of absence of high temperature gas jets, radiation and explosive gases Excellent thermal and electrical conductivity Wide spectrum of applications because of important advantages of the process
The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincare normal forms and the inverse scattering method.
The book presents an integrated approach to studying the geomechanical processes occurring in oil and gas-bearing formations during their development. It discusses the choice of a model that takes into account the basic properties of rocks; experiments to find model parameters; numerical modeling; and direct physical modeling of deformation and filtration processes in reservoir and host rocks. Taking into account features of rock behavior, such as anisotropy of the mechanical properties of rocks during elastoplastic deformation; dependence of permeability on the total stress tensor; the contribution of the filtration flow to the formation stress state; and the influence of tangential as well as normal stresses on the transition to inelastic deformation, it demonstrates how the presented approach allows the practical problems of increasing the productivity of wells, oil recovery, and ensuring the stability of wellbores to be solved. The book is intended for specialists, including geoengineers working in the oil and gas sector, teachers, graduate students and students, as well as all those interested in scientific and technological developments to meet the enormous demand for raw materials and energy.
This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory.
This book traces the emergence and development of the deification theme in Greek patristic theology and its subsequent transformation into the theology of theosis in Pseudo-Dionysius the Areopagite. This volume dwells on the deification theme as it is situated in the complex context of its historical development and thus avoids the common tendency to treat this notion of Christian theology in an anachronistic manner. Significant attention is given to the influence of Neoplatonism on Pseudo-Dionysius. His theology is justified neither as essentially "orthodox" Christian nor as essentially "orthodox" Neoplatonic. Dionysius's sophisticated synthesis of Christian and Neoplatonic elements, especially in his exposition of theosis, does justice to this anonymous author's originality and demonstrates the importance of his influence both on the further development of Christian theology, and on the advancement of the Neoplatonic tradition. The intricate cultural background of the Pseudo-Dionysian world helps clarify the formation process of Christian imperial identity, and throws additional light on why these works were attributed to Dionysius the Areopagite, not as a conscious forgery, but as a literary device. Such attribution was a common practice of the time. Comprehensive analysis of the development of the deification theme opens possibilities for further study of Trinitarian and christological formations, of philosophical and individual moral theology, of Christian and Neoplatonic mysticism, and of cultural studies. By surveying the historical development of deification and by opening further areas of research, this book serves a valuable introductory source for both professionals and students. While primarily focusing on academic interests, the book is written keeping the general reading audience in mind as well. All quotations of the original texts are provided with existing or new English translations, while important Greek terminology is acknowledged. Readers interested in Christian spirituality, late antiquity, early Christian theology, and Neoplatonism will find this book useful.
This monograph revisits one of the most debated aspects of Dionysian scholarship: the enigma of its authorship. To establish the identity of the author remains impossible. However, the legitimacy of the attribution of the corpus to Dionysius the Areopagite should not be seen as an intended forgery but rather as a masterfully managed literary device, which better indicates the initial intention of the actual author. The affiliation with Dionysius the Areopagite has metaphorical and literary significance. Dionysius is the only character in the New Testament who is unique in his conjunction between the apostle Paul and the Platonic Athenian Academy. In this regard this attribution, to the mind of the actual author of the corpus, could be a symbolic gesture to demonstrate the essential truth of both traditions as derived essentially from the same divine source. The importance of this assumption taken in its historical context highlights the culmination of the formation of the civilized Roman-Byzantine Christian identity.
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