2007, Hardcover
ISBN: 978-3-540-72184-0
Due: June 2007
About this book
The two fields of Geometric Modeling and Algebraic Geometry, though
closely related, are traditionally represented by two almost disjoint
scientific communities. Both fields deal with objects defined by
algebraic equations, but the objects are studied in different ways.
This contributed book presents, in 12 chapters written by
leading experts, recent results which rely on the
interaction of both fields. Some of these results have been obtained
in the frame of the European GAIA II project (IST 2001-35512) entitled
`Intersection algorithms for geometry-based IT applications using
approximate algebraic methods'.
Series: Fundamental Theories of Physics , Vol. 153
2007, Approx. 310 p., Hardcover
ISBN: 978-1-4020-6317-6
Due: June 2007
About this book
All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirety and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space.
But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the forth dimension, then such a world is drastically different from its image based on our perceptions. Minkowski four-dimensional world is a block Universe, a frozen world in which nothing happens since all moments of time are given ‘at once', which means that physical bodies are four-dimensional worldtubes containing the whole histories in time of the three-dimensional bodies of our everyday experience. The implications of a real Minkowski world for physics itself and especially for our world view are enormous.
The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? It contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues
Table of contents
Preface
1. The Meaning of Dimensions; Paul Wesson.
2. Some Remarks on the Space-Times of Newton and Einstein; Graham Hall.
3. The adventures of Spacetime; Orfeu Bertolami.
4. Physics in the Real Universe: Time and Spacetime; George F. R. Ellis.
5. The Real World and Spacetime; Hans C. Ohanian.
6. Four-dimensional Reality and Determinism: an Answer to Stein; Wim Rietdijk.
7. Relativity, Dimensionality, and Existence; Vesselin Petkov.
8. Canonical Relativity and the Dimensionality of the World; Martin Bojowald.
9. Relativity theory does not imply that the future already exists: a counterexample; Rafael D. Sorkin.
10. Absolute Being versus Relative Becoming; Joy Christian.
11. An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics; Michael Silberstein, W.M. Stuckey, and Michael Cifone.
12. Spacetime: Arena or Reality? H. I. Arcos and J. G. Pereira.
13. Dynamical emergence of instantaneous 3-spaces in a class of models of general relativity; Luca Lusanna and Massimo Pauri.
14. Lorentzian spacetimes from Parabolic and Elliptic systems of PDEs; Carlos Barcelo.
Series: Fundamental Theories of Physics , Vol. 156
2007, XVI, 784 p., Hardcover
ISBN: 978-1-4020-5873-8
Due: June 2007
About this book
This book ushers in a new era of experimental and theoretical investigations into collective processes, structure formation, and self-organization of nuclear matter. It reports the results of experiments wherein for the first time the nuclei constituting our world (those displayed in Mendeleev's table as well as the super-heavy ones) have been artificially created. Pioneering breakthroughs are described, achieved at the "Proton-21" Laboratory, Kiev, Ukraine, in a variety of new physical and technological directions.
A detailed description of the main experiments, their analyses, and the interpretation of copious experimental data are given, along with the methodology governing key measurements and the processing algorithms of the data that empirically confirm the occurrence of macroscopic self-organizing processes leading to the nuclear transformations of various materials. The basic concepts underlying the initiation of self-sustaining collective processes that result in the formation of nuclear structures are also examined.
How to realize nucleosynthesis of stable nuclei in the laboratory? Why are metallic meteorites of iron or nickel-iron? Could the iron be nuclear fuel and could an iron star blow up as a supernova? And what could be the energy source of such an explosion? Is it possible to obtain nuclear energy from any terrestrial substance without producing radioactivity? Do super-heavy (Migdal's) nuclei exist, and is it possible to synthesize them in the laboratory? What physical mechanisms could one use to control nuclear transformations and particularly the sign of the overall energy balance involved?
Answers to these and other intriguing questions are to be found in this book.
Table of contents
Introduction. 1. Novel experimental approach to initiation of collective processes in nuclear systems. Initiated collapse and anomalous nucleosynthesis in condensed matter. 2. Experimental research of artificial nucleothynsesis products and processes. Methods, results and speculations. 3. Theory of matter evolution under the influence of concentrated energy fluxes. 4. Theoretical grounds of initiated collapse mechanism. 5. Conception of plasma-beam and nuclear processes interrelation. 6. Energy balance in collective nuclear processes. Conclusion: The energy power of the “new nuclear physics”: new nuclear paradigm and its technology.
Geometrizing Interactions in Four and Five Dimensions
Series: Fundamental Theories of Physics , Vol. 157
2007, XVIII, 528 p., Hardcover
ISBN: 978-1-4020-6282-7
Due: June 2007
About this book
This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy.
Such a formalism (Deformed Special Relativity, DSR) allows one
to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense)
to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational)
Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.
The mathematical properties of such a generalized KK scheme are illustrated. They include the solutions of the five-dimensional Einstein equations in vacuum in most cases of physical relevance, the infinitesimal symmetries of the theory for the phenomenological metrics of the four interactions, and the study of the five-dimensional geodesics.
The mathematical results concerning the geometry of the deformed five-dimensional spacetime (like its Killing symmetries) can be applied also to other multidimensional theories with infinite extra dimensions.
Some experiments providing preliminary evidence for the hypothesized deformation of space-time for all the four fundamental interactions are discussed.
Table of contents
Part I: Physics of Deformed Space-Time.- Part II: Mathematics of Deformed Space-Time.- Part III: Experimental Arguments for Deformed Space-Time.- Part IV: Deformed Space-Time in Five Dimensions: Geometry.- Part V: Deformed Space-Time in Five Dimensions: Dynamics.- Appendix A: Reductivity of the Y-Hypothesis for the 12 Classes of the vacuum Einstein Equations in the Power Ansatz. Appendix B: Gravitational Killing Symmetries for Special Forms of b12(x5) and b22(x5). Appendix C: Explicit and Implicit Forms of geodesics for the 12 Classes of Solutions of Einstein's Equations in Vacuum in the Power Ansatz.
Series: Lecture Notes in Mathematics , Vol. 1914
2007, XII, 142 p., Softcover
ISBN: 978-3-540-72916-7
Due: July 10, 2007
About this book
In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems.
This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
Table of contents