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Author: Pijush K. Ghosh Publisher: John Wiley & Sons ISBN: 0470823089 Category : Technology & Engineering Languages : en Pages : 272
Book Description
Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book. Key Features Explains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approach Promotes interaction of image processing geochronology and mathematics in the field of algebraic geometry Provides a shape description scheme that is a notational system for the shape of objects Offers a thorough and detailed discussion on the mathematical characteristics and significance of the Minkowski operators
Author: Pijush K. Ghosh Publisher: John Wiley & Sons ISBN: 0470823089 Category : Technology & Engineering Languages : en Pages : 272
Book Description
Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book. Key Features Explains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approach Promotes interaction of image processing geochronology and mathematics in the field of algebraic geometry Provides a shape description scheme that is a notational system for the shape of objects Offers a thorough and detailed discussion on the mathematical characteristics and significance of the Minkowski operators
Author: Vialar Thierry Publisher: BoD - Books on Demand ISBN: 2955199052 Category : Mathematics Languages : en Pages : 1134
Book Description
The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.
Author: Paul Roman Publisher: Elsevier ISBN: 1483187373 Category : Mathematics Languages : en Pages : 427
Book Description
Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis, Volume 1 focuses on the operations, principles, methodologies, and approaches employed in algebra, topology, and functional analysis. The publication first offers information on sets, maps, and algebraic composition laws and systems. Discussions focus on morphisms of algebraic systems, sequences and families, cardinal numbers, ordered sets and maps, equivalence relations and maps, composite functions and inverses, operations with sets, and relations in sets. The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions. The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.
Author: Petre P. Teodorescu Publisher: Springer Science & Business Media ISBN: 9781402020469 Category : Mathematics Languages : en Pages : 466
Book Description
The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non contradictory formulations for the investigated phenomena.
Author: Gérard Favier Publisher: John Wiley & Sons ISBN: 1786301547 Category : Technology & Engineering Languages : en Pages : 324
Book Description
Nowadays, tensors play a central role for the representation, mining, analysis, and fusion of multidimensional, multimodal, and heterogeneous big data in numerous fields. This set on Matrices and Tensors in Signal Processing aims at giving a self-contained and comprehensive presentation of various concepts and methods, starting from fundamental algebraic structures to advanced tensor-based applications, including recently developed tensor models and efficient algorithms for dimensionality reduction and parameter estimation. Although its title suggests an orientation towards signal processing, the results presented in this set will also be of use to readers interested in other disciplines. This first book provides an introduction to matrices and tensors of higher-order based on the structures of vector space and tensor space. Some standard algebraic structures are first described, with a focus on the hilbertian approach for signal representation, and function approximation based on Fourier series and orthogonal polynomial series. Matrices and hypermatrices associated with linear, bilinear and multilinear maps are more particularly studied. Some basic results are presented for block matrices. The notions of decomposition, rank, eigenvalue, singular value, and unfolding of a tensor are introduced, by emphasizing similarities and differences between matrices and tensors of higher-order.
Author: Nils Jansen Publisher: Oxford University Press ISBN: 0191015105 Category : Law Languages : en Pages : 577
Book Description
This English translation makes available to anglophone readers a modern classic of German tort theory. It argues that modern German tort law is faced with doctrinal tensions based on problematic theoretical assumptions which stem from historical conceptions of tortious liability, inappropriate to modern times. From a theoretical perspective, it argues against the prevalent doctrinal view in Germany that conceives of tortious liability as split between two tracks - a fault-based track and a strict liability track - each with different normative foundations. Instead, Jansen asserts that there is no rigid distinction between the normative foundations of each form of liability. Rather, both fault liability and strict liability in German law, and indeed other European systems, are best considered as resting upon the unifying theoretical structure of outcome responsibility. The book thus places responsibility rather than wrongdoing at the centre of the normative foundations of tort law. Historically, the book traces in detail how conceptions of tort liability have changed from Roman law to contemporary legal doctrine. It shows how particular historical understandings of the normative basis of tort law have led to continuing normative tensions in contemporary doctrine. Finally, the book examines how a reconstruction of modern German - and, indeed, European - law as based upon outcome responsibility should affect its doctrinal structure. This book makes contributions to the study of the theory, history, and doctrinal structure of tort law. While drawing on and explaining German tort law, its comparative, theoretical, and historical analysis will be of interest to scholars in all legal systems.
Author: Luc B. Tremblay Publisher: McGill-Queen's Press - MQUP ISBN: 0773566910 Category : Law Languages : en Pages : 360
Book Description
Tremblay's theory of the rule of law involves a set of practical principles that constitute the ideal type of a conception of law that is both constitutive and regulative of legal discourse and practice. Tremblay examines two competing ideal types, the "rule of law as certainty" and the "rule of law as justice." The former, a standard doctrine within contemporary legal, social, and political theory, is shown to be incoherent. Thus the "rule of law as justice," he shows, provides the best basis for understanding legal discourse in general and Canadian constitutional law in particular. Tremblay offers a coherent reconstruction of Canadian law from fundamental principles of the rule of law as justice and tests the theory through applications to key judicial decisions that have proven resistant to positivist interpretation. The Rule of Law, Justice, and Interpretation is both a stimulating work of contemporary legal theory and an innovative challenge to the traditions of Canadian constitutional law. Tremblay examines fundamental issues of legal epistemology and ontology and brings rigorous analytical jurisprudence to bear on interpretations and applications specific to Canadian constitutional law. Given the important implications of his theory for statutory and constitutional interpretation, especially with respect to the Canadian Charter of Rights and Freedoms and the potential crisis involving provincial rights of secession and partition, this book will be central to the practice of law in Canada.
Author: J. M. Arnaiz Publisher: Ediciones Go Beyond ISBN: Category : Science Languages : en Pages : 638
Book Description
In this book we develop step by step the FIRST ALGEBRA OF MAGNITUDES, the specific dyadic algebra for physical quantities, in order to rectify the sloppy hypothesis of «arithmetization» of Physics, normalized by the International System of Units in sections 2.1, 5.2 , 5.4.1 and 5.4.6 of his brochure SI, which is tolerated by a clueless scientific community. With dyadic algebra, full meaning is given to the meanings of the laws, equations and compound units of Physics, a sense that we all neglect today . As a culmination, the «DYSMETRIC» FORECAST is reached, with innumerable and far-reaching implications for the enrichment of physical models and the development of infinite innovations. In this way, the trap of «arithmetizing» Physics in which we all easily fall, even the most reputable and award-winning scientists, is ended. Except for one in the entire history of Physics, which was Newton, the only one who operated with magnitudes through the affinity of physical quantities with the elements of geometry, teaching us that, although Physics is not «arithmetizable», on the other hand it is it can be «geometrized». It seems incredible, but it is a grotesque fact that nowadays no one cares about what is really done when operating with physical magnitudes or what is the full meaning of the composite magnitudes or of the analytical formulations, which underlie all of Physics, for what no one should take a step without first having clarified this knowledge. On the contrary, it turns out that operations apparently as elementary as the multiplication of a meter by a kilogram have no arithmetic explanation, because no one identifies what the multiplier of that product is, which does not multiply numbers, but rather dyads or quantities of length and mass. Despite which, it seems that no one is bothered by such a ridiculous embarrassment. Can one call himself a physicist who cannot rigorously define this simple operation and does not care? Can a science be called Physics that lacks a coherent algebra to operate with its fundamental elements, the quantities of physical phenomena? The truth is that the defect is too gross not to take it into account. All this as a consequence of the fact that the current arithmetic hypothesis that postulates the abelian multiplicative group structure for the magnitudes is impossible. Such a structure is only valid for internal additive laws, it is not valid for external multiplicative laws. Obviously, this situation is shameful and pernicious for Physics, it is unsustainable and must be corrected as soon as possible. The dyadic algebra of magnitudes, in addition to giving meaning to the laws, equations, and compound magnitudes, reveals striking consequences, such as the non-existence of inverse elements of physical units, since heterogeneous multiplicative dyadic operations are not internal composition laws, but external. In turn, it naturally leads to «dysmetry», which makes it possible to represent the infinite physical realms of empty space and which radically transforms the vision of physical constants, incompatible in an absolute sense with «dysmetric» spaces, including the number pi and the speed of light.
Author: Tom Stonier Publisher: Springer Science & Business Media ISBN: 1447132653 Category : Computers Languages : en Pages : 156
Book Description
Not so if the book has been translated into Arabic. Now the reader can discern no meaning in the letters. The text conveys almost no information to the reader, yet the linguistic informa tion contained by the book is virtually the same as in the English original. The reader, familiar with books will still recognise two things, however: First, that the book is a book. Second, that the squiggles on the page represent a pattern of abstractions which probably makes sense to someone who understands the mean ing of those squiggles. Therefore, the book as such, will still have some meaning for the English reader, even if the content of the text has none. Let us go to a more extreme case. Not a book, but a stone, or a rock with engravings in an ancient language no longer under stood by anyone alive. Does such a stone not contain human information even if it is not decipherable? Suppose at some point in the future, basic knowledge about linguistics and clever computer aids allow us to decipher it? Or suppose someone discovers the equivalent of a Rosetta stone which allows us to translate it into a known language, and then into English? Can one really say that the stone contained no information prior to translation? It is possible to argue that the stone, prior to deciphering contained only latent information.
Author: Pijush K. Ghosh
Author: Pijush K. Ghosh
Author: Vialar Thierry
Author: Paul Roman
Author: Petre P. Teodorescu
Author: Gérard Favier
Author: Nils Jansen
Author: Luc B. Tremblay
Author: J. M. Arnaiz
Author: Tom Stonier
Author: L. Hart Wright