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  • Books  (5)
  • DDC 160/.9  (3)
  • Approximation theory  (2)
  • Amsterdam ; Boston : Elsevier  (5)
  • Berlin [u.a.] : Springer
  • Paris : IEA Publications
  • Wabern : Federal Office of Topography, Swiss Geological Survey
  • 2005-2009  (2)
  • 2000-2004  (3)
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  • Books  (5)
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  • 2005-2009  (2)
  • 2000-2004  (3)
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  • 1
    Unknown
    Amsterdam ; Boston : Elsevier
    Keywords: DDC 519.2/4 ; LC QA273.6 ; Approximation theory ; Distribution (Probability theory) ; Information theory
    Description / Table of Contents: Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory.〈P〉 Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC〈P〉 - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC
    Pages: Online-Ressource (xvii, 299 pages)
    Edition: 1st ed
    ISBN: 9780444527967
    Language: English
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  • 2
    Keywords: DDC 620/.001/51 ; LC TA330 ; Approximation theory ; Engineering mathematics
    Pages: Online-Ressource (ix, 248 pages)
    Edition: 1st ed
    ISBN: 9780444518606
    Language: English
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  • 3
    Unknown
    Amsterdam ; Boston : Elsevier
    Keywords: DDC 160/.9 ; LC BC15 ; Logic - History
    Description / Table of Contents: With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century. Contents: Preface (D.M. Gabbay, J. Woods). List of Contributors. Leibniz's Logic (W. Lenzen). Kant: From General to Transcendental Logic (M. Tiles). Hegel's Logic (J.W. Burbidge). Bolzano as Logician (P. Rusnock, R. George). Husserl's Logic (R. Tieszen). Algebraical Logic 1685-1900 (T. Hailperin). The Algebra of Logic (V.S. Valencia). The Mathematical Turn in Logic (I. Grattan-Guinness). Schroder's Logic (V. Peckhaus). Peirce's Logic (R. Hilpinen). Frege's Logic (P. Sullivan). Index.
    Pages: Online-Ressource (x, 770 pages)
    Edition: 1st ed
    ISBN: 9780444516114
    Language: English
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  • 4
    Unknown
    Amsterdam ; Boston : Elsevier
    Keywords: DDC 160/.9 ; LC BC15 ; Logic - History
    Description / Table of Contents: Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Godel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value. Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas. Contents: Preface (D.M. Gabbay, J. Woods). List of Contributors. Logic before Aristotle: Development or Birth? (J. Moravcsik). Aristotle's Early Logic (J. Woods, A. Irvine). Aristotle's Underlying Logic (G. Boger). Aristotle's Modal Syllogisms (F. Johnson). Indian Logic (J. Ganeri). The Megarians and the Stoics (R. R. O'Toole, R. E. Jennings). Arabic Logic (T. Street). The Translation of Arabic Works on Logic into Latin in the Middle Ages and Renaissance (C. Burnett). Index.
    Pages: Online-Ressource (ix, 618 pages)
    Edition: 1st ed
    ISBN: 9780444504661
    Language: English
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  • 5
    Unknown
    Amsterdam ; Boston : Elsevier
    Keywords: DDC 160/.9 ; LC BC15 ; Logic - History
    Description / Table of Contents: The present volume of the Handbook of the History of Logic is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic. British Logic in the Nineteenth Century is indispensable reading and a definitive research resource for anyone with an interest in the history of logic. Contents: 1. "Bentham's Logic" by Charissa Varma and Gordon McOuat 2. "Coleridge's Logic" by Timothy Milnes 3. "Whately's Logic" by James Van Evra 4. "Hamilton's Logic" by Ralph Jessop 5. "Whewell's Logic" by Laura Snyder 6. "Mill's Logic" by Fred Wilson 7. "DeMorgan's Logic" by Michael Hobards & Joan Richards 8. "Boole's Logic" by Dale Jacquette 9. "French Logique and British Logic: On the Origins of Augustus deMorgan early Logical Enquiries 1805-1835" by Maria Panteki 10. "Lewis Carroll's Logic" by Amirouche Moktefi 11. "Venn's Logic" by James Van Evra 12. "Jevons' Logic" by Bert Mosselmans and Ard Van Moer 13. "MacColl's Logic" by Shahid Rahman 14. "The Idealists" by David Sullivan
    Pages: Online-Ressource (xiv, 735 pages)
    Edition: 1st ed
    ISBN: 9780444516107
    Language: English
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