الصفحة 1
الصفحة 1
Non-Euclidean Geometries : János Bolyai Memorial Volume
Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics. This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information.
Nearrings and Nearfields ; Proceedings of the Conference on Nearrings and Nearfields, Hamburg, Germany July 27 - August 3, 2003
This present volume is the Proceedings of the 18th International Conference on Nearrings and Nearfields held at the Helmut-Schmidt-Universitat, Universitat der Bundeswehr Hamburg, from July 27-August 3, 2003. It contains the written versions of the lectures by the five invited speakers. These concern recent developments of planar nearrings, nearrings of mappings, group nearrings and loop-nearrings. One of them is a long and very substantial research paper "The Z-Constrained Conjecture". These are followed by 13 contributions reflecting the diversity of the subject of nearrings and related structures. Besides the purely algebriac structure theory, these papers show many connections of nearring theory with group theory, combinatorics, geometries, and topology, and all contain original research.
Modeling Solid Oxide Fuel Cells : Methods, Procedures and Techniques
The volume is structured in two parts. Part one presents the basic theory, and the general equations describing SOFC operation phenomena. Part two deals with the application of the theory to practical examples, where different SOFC geometries, configurations (from single cells to hybrid systems), operating conditions (steady-state and dynamic), and different phenomena (e.g. performance, temperature and chemical species, and mechanical stress distribution) are analyzed in detail.
Introduction to Classical Geometries
This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions.
Handbook of molecular force spectroscopy
Modern materials science and biophysics are increasingly focused on studying and controlling intermolecular interactions on the single-molecule level. Molecular force spectroscopy was developed in the past decade as the result of several unprecedented advances in the capabilities of modern scientific instrumentation, and defines a number of techniques that use mechanical force measurements to study interactions between single molecules and molecular assemblies in chemical and biological systems. Examples of these techniques, which typically target a specific range of experimental systems and geometries, include atomic force microscopy, optical tweezers, surface forces apparatus, and magnetic tweezers.
Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key Features The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts, and discusses several open problems and extensions.
Flow and transport processes with complex obstructions : Applications to cities, vegetative canopies and industry
The NATO Advanced Study Institute “Flow and Transport Processes in Complex - structed Geometries: from cities and vegetative canopies to engineering problems” was held in Kyiv, Ukraine in the period of May 4 - 15, 2004. This book based on the papers presented there provides an overview of this new area in ?uid mechanics and its app- cations that have developed over the past three decades. The subject, whose origins lie both in theory and in practice, is now rapidly developing in many directions. The focus of applied ?uid mechanics research has steadily been shifting from - gineering to environmental applications.
Fibonacci’s de practica geometrie = Fibonacci’s practice geometry
Practical Geometry is the name of the craft for medieval landmeasurers, otherwise known as surveyors in modern times. Fibonacci wrote De practica geometrie for these artisans, a fitting complement to Liber abbaci. He had been at work on the geometry project for some time when a friend encouraged him to complete the task, which he did, going beyond the merely practical, as he remarked, "Some parts are presented according to geometric demonstrations, other parts in dimensions after a lay fashion, with which they wish to engage according to the more common practice."
Computational Materials Chemistry : Methods and Applications
As a result of the advancements in algorithms and the huge increase in speed of computers over the past decade, electronic structure calculations have evolved into a valuable tool for characterizing surface species and for elucidating the pathways for their formation and reactivity. It is also now possible to calculate, including electric field effects, STM images for surface structures. To date the calculation of such images has been dominated by density functional methods, primarily because the computational cost of - curate wave-function based calculations using either realistic cluster or slab models would be prohibitive. DFT calculations have proven especially valuable for elucidating chemical processes on silicon and other semiconductor surfaces. However, it is also clear that some of the systems to which DFT methods have been applied have large non-dynamical correlation effects, which may not be properly handled by the current generation of Kohn-Sham-based density functionals. For example, our CASSCF calculations on the Si(001)/acetylene system reveal that at some geometries there is extensive 86 configuration mixing. This, in turn, could signal problems for DFT cal- lations on these systems.
Computational Contact Mechanics
This is the second edition of the valuable reference source for numerical simulations of contact mechanics suitable for many fields like civil engineering, car design, aeronautics, metal forming, or biomechanics. Boundary value problems involving contact are of great importance in industrial applications in engineering such as bearings, metal forming processes, rubber seals, drilling problems, crash analysis of cars, rolling contact between car tires and the road, cooling of electronic devices... Other applications are related to biomechanical engineering design where human joints, implants or teeth are of consideration. Due to this variety, contact problems are today combined either with large elastic or inelastic deformations including time dependent responses. Thermal coupling also might have to be considered. Even stability behaviour has to be linked to contact.
Lectures on Algebraic Geometry I : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Complex Effects in Large Eddy Simulations
This volume contains a collection of expert views on the state of the art in Large Eddy Simulation (LES) and its application to complex ?ows. Much of the material in this volume was inspired by contributions that were originally presented at the symposium on Complex E?ects in Large Eddy Simulation held in Lemesos (Limassol), Cyprus, between September 21st and 24th, 2005.
Classical geometries in modern contexts : Geometry of real inner product spaces
This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts.
Classical geometries in modern contexts : Geometry of real inner product spaces
This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized.
Charged Particle Traps : Physics and Techniques of Charged Particle Field Confinement
This book provides an introduction and guide to modern advances in charged particle (and antiparticle) confinement by electromagnetic fields. Confinement in different trap geometries, the influence of trap imperfections, classical and quantum mechanical description of the trapped particle motion, different methods of ion cooling to low temperatures, and non-neutral plasma properties (including Coulomb crystals) are the main subjects. They form the basis of such applications of charged particle traps as high-resolution optical and microwave spectroscopy, mass spectrometry, atomic clocks, and, potentially, quantum computing.
