the geometry of special relativity a concise course springerbriefs in physics

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The Geometry Of Special Relativity A Concise Course

Author : Norbert Dragon
ISBN : 9783642283291
Genre : Science
File Size : 57. 8 MB
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In this concise primer it is shown that, with simple diagrams, the phenomena of time dilatation, length contraction and Lorentz transformations can be deduced from the fact that in a vacuum one cannot distinguish physically straight and uniform motion from rest, and that the speed of light does not depend on the speed of either the source or the observer. The text proceeds to derive the important results of relativistic physics and to resolve its apparent paradoxes. A short introduction into the covariant formulation of electrodynamics is also given. This publication addresses, in particular, students of physics and mathematics in their final undergraduate year.

Kp Solitons And The Grassmannians

Author : Yuji Kodama
ISBN : 9789811040948
Genre : Science
File Size : 33. 49 MB
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This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of the combinatorial aspect of the TNN Grassmannians and their parameterizations, which will be useful for solving the classification problem. This work appeals to readers interested in real algebraic geometry, combinatorics, and soliton theory of integrable systems. It can serve as a valuable reference for an expert, a textbook for a special topics graduate course, or a source for independent study projects for advanced upper-level undergraduates specializing in physics and mathematics.

From Stars To States

Author : Thierry J.-L. Courvoisier
ISBN : 9783319592329
Genre : Science
File Size : 78. 56 MB
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The aim of this essay is to understand the relationship between knowledge and society and to reflect on the links between science and political decision making. The text evolved from a number of reflections the author made while president of the European Astronomical Society, president of the Swiss Academy of Sciences and vice-president of the European Academies Science Advisory Council (EASAC). The book starts by using astronomy as a showcase for what science brings to society in terms of intellectual enrichment, of practical tools and of societal inputs. It then turns to looking generally at science as a human endeavour for which pleasure is a prime motivation and it describes the efforts made by researchers to rationalise their findings, thus making them universally acceptable. The author also describes the role of science in shaping our environment and discusses resulting responsibility of the scientists with respect to the evolution of the world. As part of an analysis of the relationship between science and policy the author describes the way in which scientists can (and must) bring knowledge in the political decision making process. The argument is closed with considerations on global governance, while the conclusion puts evidence based decision making processes in relation with the more emotional aspects of our behaviour. The readership of the book is intended to be all scientists involved in “science for policy” activities, as well as those who should become more active in this domain. This includes, but is not limited to, all members of science academies. Astronomers will find specific elements to help them think about their science. The intended readers of the book also include civil servants and policy makers who develop legislation and societal action in domains in which a solid knowledge base is important. The book should furthermore be of interest to citizens following public life and all those worried by the “post evidence” trends in policy.

Geometry Of Minkowski Space Time

Author : Francesco Catoni
ISBN : 3642179770
Genre : Science
File Size : 21. 24 MB
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This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions. The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.

Fundamentals Of Plasma Physics

Author : J. A. Bittencourt
ISBN : 9781483293196
Genre : Science
File Size : 28. 85 MB
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A general introduction designed to present a comprehensive, logical and unified treatment of the fundamentals of plasma physics based on statistical kinetic theory. Its clarity and completeness make it suitable for self-learning and self-paced courses. Problems are included.

Medical Imaging Technology

Author : Mark A Haidekker
ISBN : 9781461470731
Genre : Science
File Size : 88. 1 MB
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Biomedical imaging is a relatively young discipline that started with Conrad Wilhelm Roentgen’s discovery of the x-ray in 1895. X-ray imaging was rapidly adopted in hospitals around the world. However, it was the advent of computerized data and image processing that made revolutionary new imaging modalities possible. Today, cross-sections and three-dimensional reconstructions of the organs inside the human body is possible with unprecedented speed, detail and quality. This book provides an introduction into the principles of image formation of key medical imaging modalities: X-ray projection imaging, x-ray computed tomography, magnetic resonance imaging, ultrasound imaging, and radionuclide imaging. Recent developments in optical imaging are also covered. For each imaging modality, the introduction into the physical principles and sources of contrast is provided, followed by the methods of image formation, engineering aspects of the imaging devices, and a discussion of strengths and limitations of the modality. With this book, the reader gains a broad foundation of understanding and knowledge how today’s medical imaging devices operate. In addition, the chapters in this book can serve as an entry point for the in-depth study of individual modalities by providing the essential basics of each modality in a comprehensive and easy-to-understand manner. As such, this book is equally attractive as a textbook for undergraduate or graduate biomedical imaging classes and as a reference and self-study guide for more specialized in-depth studies.

Quantum Potential Physics Geometry And Algebra

Author : Ignazio Licata
ISBN : 9783319003337
Genre : Science
File Size : 48. 36 MB
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Recently the interest in Bohm realist interpretation of quantum mechanics has grown. The important advantage of this approach lies in the possibility to introduce non-locality ab initio, and not as an “unexpected host”. In this book the authors give a detailed analysis of quantum potential, the non-locality term and its role in quantum cosmology and information. The different approaches to the quantum potential are analysed, starting from the original attempt to introduce a realism of particles trajectories (influenced by de Broglie’s pilot wave) to the recent dynamic interpretation provided by Goldstein, Durr, Tumulka and Zanghì, and the geometrodynamic picture, with suggestion about quantum gravity. Finally we focus on the algebraic reading of Hiley and Birkbeck school, that analyse the meaning of the non-local structure of the world, bringing important consequences for the space, time and information concepts.

The Chemical History Of Color

Author : Mary Virginia Orna
ISBN : 9783642326424
Genre : Science
File Size : 73. 60 MB
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In this brief, Mary Virginia Orna details the history of color from the chemical point of view. Beginning with the first recorded uses of color and ending in the development of our modern chemical industry, this rich, yet concise exposition shows us how color pervades every aspect of our lives. Our consciousness, our perceptions, our useful appliances and tools, our playthings, our entertainment, our health, and our diagnostic apparatus – all involve color and are based in no small part on chemistry.

Bulk And Boundary Invariants For Complex Topological Insulators

Author : Emil Prodan
ISBN : 9783319293516
Genre : Science
File Size : 48. 98 MB
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This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.

Sparse And Redundant Representations

Author : Michael Elad
ISBN : 9781441970114
Genre : Mathematics
File Size : 30. 57 MB
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A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

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