Infinite Processes

Author : A. Gardiner
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461256540

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Infinite Processes by A. Gardiner Pdf

What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways: firstly, as a genuine pro logue to analysis; secondly, as a supplementary text within an analysis course, providing a source of elementary motivation, background and ex amples; thirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them. But the contents of the book should be of interest to a much wider audience than this including teachers, teachers in training, students in their last year at school, and others interested in mathematics.

Author : Olaf Burkart
Publisher : Springer
Page : 166 pages
File Size : 41,5 Mb
Release : 2003-08-06
Category : Computers
ISBN : 9783540696780

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Automatic Verification of Sequential Infinite-State Processes by Olaf Burkart Pdf

A common approach in software engineering is to apply during the design phase a variety of structured techniques like top-down design, decomposition and abstraction, while only subsequently, in the implementation phase, is the design tested to ensure reliability. But this approach neglects that central aspects of software design and program development have a strong formal character which admits tool support for the construction of reliable and correct computer systems based on formal reasoning. This monograph provides much information both for theoreticians interested in algebraic theories, and for software engineers building practically relevant tools. The author presents the theoretical foundations needed for the verification of reactive, sequential infinite-state systems.

Author : Lloyd Leroy Smail
Publisher : Unknown
Page : 192 pages
File Size : 54,7 Mb
Release : 1925
Category : Processes, Infinite
ISBN : STANFORD:36105031175297

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History and Synopsis of the Theory of Summable Infinite Processes by Lloyd Leroy Smail Pdf

Author : Robert F. Nagaev,E. B. Kremer
Publisher : World Scientific
Page : 268 pages
File Size : 44,8 Mb
Release : 1999
Category : Technology & Engineering
ISBN : 9810235046

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Mechanical Processes with Repeated Attenuated Impacts by Robert F. Nagaev,E. B. Kremer Pdf

Mapping out a “family constellation,” explains Dr. Joy Manné, encompasses exploring previous powerful life events from accidents to adoptions and accessing the deepest dynamics in that family system. This process helps us recognize and then resolve deeply seated family patterns. For example, in order to understand a person’s inability to trust, the family history of betrayal must be uncovered and released. These insights replace resentment with respect, pain with understanding.Dr. Manné uses the knowledge gained from her own practice as well as her educational experiences with Bert Hellinger, the founder of Family Constellations therapy, to clearly describe this technique. Most family constellation sessions are carried out in a group setting, with the facilitator first seeking clarity regarding the issue or problem the client has come to work out. Representatives are then chosen from among the group and the constellation is set up and worked in until it comes to resolution. This may be followed by a closing ritual and advice about how to integrate what the constellation has revealed. Through the use of real-life examples of family constellations, Dr. Manné makes this increasingly popular practice understandable and relatable.

Author : J. H. Heinbockel
Publisher : Trafford Publishing
Page : 531 pages
File Size : 41,7 Mb
Release : 2010-12
Category : Mathematics
ISBN : 9781426949548

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Introduction to Finite and Infinite Series and Related Topics by J. H. Heinbockel Pdf

An introduction to the analysis of finite series, infinite series, finite products and infinite products and continued fractions with applications to selected subject areas. Infinite series, infinite products and continued fractions occur in many different subject areas of pure and applied mathematics and have a long history associated with their development. The mathematics contained within these pages can be used as a reference book on series and related topics. The material can be used to augment the mathematices found in traditional college level mathematics course and by itself is suitable for a one semester special course for presentation to either upper level undergraduates or beginning level graduate students majoring in science, engineering, chemistry, physics, or mathematics. Archimedes used infinite series to find the area under a parabolic curve. The method of exhaustion is where one constructs a series of triangles between the arc of a parabola and a straight line. A summation of the areas of the triangles produces an infinite series representing the total area between the parabolic curve and the x-axis.

Author : Nicholas Rescher
Publisher : Routledge
Page : 189 pages
File Size : 40,9 Mb
Release : 2017-09-08
Category : Philosophy
ISBN : 9781351512596

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Infinite Regress by Nicholas Rescher Pdf

Regression addresses what has come before; it is a matter of looking backward of retrospections? The motionless things of nature are generally forward-looking their problem is that of the question: Where do we go from here? It is primarily with intelligent beings that we ask: How did we get to where we now find ourselves? Regression and infinite regression in particular is thus a concept that has gained a greater prominence in the human sciences than in the sciences of nature. Argumentation to infinite regress has long been a favored instrument of philosophical dialectic. Philosophers have used it to disprove the positions they model to criticize. Infinite regresses, so they reason, are unrealizable: they cannot be completed so as to achieve some definitive result. And thereby anything that would engender an infinite regress is automatically made ineffective. Infinite Regress examines the theory of regression and includes information on the topics of vicious regress, innocuous regress, circularity regress, and propositional regress. Also discussed is the history of regression stemming from ancient times, to medieval times, to early modern history. Some of the other chapters in this book focus on world class philosophers including Immanuel Kant, Georg Wilhelm Friedrich Hegel, and Bertrand Russell. The book will play a significant role in theoretical philosophy as well as in social philosophy and the philosophy of mind.

Author : Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 52,9 Mb
Release : 2002
Category : Conformal invariants
ISBN : 9780821827161

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Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory by Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall Pdf

Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.

Author : Alexander Bendikov
Publisher : Walter de Gruyter
Page : 200 pages
File Size : 52,9 Mb
Release : 1995
Category : Mathematics
ISBN : 311014283X

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Potential Theory on Infinite-dimensional Abelian Groups by Alexander Bendikov Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Author : Anastasios A Tsonis
Publisher : World Scientific
Page : 204 pages
File Size : 40,9 Mb
Release : 2008-09-18
Category : Science
ISBN : 9781908978882

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Randomnicity by Anastasios A Tsonis Pdf

This unique book explores the definition, sources and role of randomness. A joyful discussion with many non-mathematical and mathematical examples leads to the identification of three sources of randomness: randomness due to irreversibility which inhibits us from extracting whatever rules may underlie a process, randomness due to our inability to have infinite power (chaos), and randomness due to many interacting systems. Here, all sources are found to have something in common: infinity. The discussion then moves to the physical system (our universe). Through the quantum mechanical character of small scales, the second law of thermodynamics and chaos, randomness is shown to be an intrinsic property of nature — this is consistent with the three sources of randomness identified above. Finally, an explanation is given as to why rules and randomness cannot exist by themselves, but instead have to coexist. Many examples are presented, ranging from pure mathematical to natural and social processes, that clearly demonstrate how the combination of rules and randomness produces the world we live in. Contents: The Three Parts of EverythingSources of RandomnessRandomness in the UniverseThe Emergence of Real WorldThe Role of Randomness Readership: Academic and general public. Keywords:Randomness;Chaos;Fractals;Determinism;Natural ProcessesKey Features:Differs from other books on this subject in that it treats randomness from a complex systems point of view rather than from a solely probabilistic oneSuitable for the general public with an interest in scienceUseful for scientists in all areasReviews:“Reading the book is like visiting a museum, and as the reader goes successively through the chapters he (or she) encounters beautiful ideas and interesting comments. Although the book is not a book on the history of mathematics, it contains interesting historical facts.”Zentralblatt MATH “I recommend reading it to those who want a quick introduction to ideas about randomness and those whose exposure to these ideas has been piecemeal, as mine was. The book may spark the imaginations of readers and advance our science through innovative application of the concepts. Someone might just find life-changing inspiration.”Vadose Zone Journal “As a contribution to popular science this book is welcome. Tsonis explains randomness as it enters into mathematics, science and everyday life.”Mathematical Reviews

Author : Anthony Gardiner
Publisher : Courier Corporation
Page : 324 pages
File Size : 42,9 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 048642538X

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Understanding Infinity by Anthony Gardiner Pdf

Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.

Author : Irina V. Melnikova
Publisher : CRC Press
Page : 232 pages
File Size : 50,7 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315360263

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Stochastic Cauchy Problems in Infinite Dimensions by Irina V. Melnikova Pdf

Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.

Author : Analysis on Infinit Ams Special Session,Hui-Hsiung Kuo,Ambar Sengupta
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 47,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832028

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Finite and Infinite Dimensional Analysis in Honor of Leonard Gross by Analysis on Infinit Ams Special Session,Hui-Hsiung Kuo,Ambar Sengupta Pdf

This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross' former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross' work and permeate diverse fields. Topics of this title include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.

Author : V. A. Malyshev Robert Adol_fovich Minlos
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 54,8 Mb
Release : 1995-02-13
Category : Mathematics
ISBN : 0821897608

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Linear infinite-particle operators by V. A. Malyshev Robert Adol_fovich Minlos Pdf

The main subject of this book can be viewed in various ways. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the viewpoint of probability theory, it is concerned with the analysis of singular Markov processes; and, from the vantage point of mathematical physics, it analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory. Malyshev and Minlos describe two new approaches to the subject which have not been previously treated in monograph form. They also present background material which makes the book accessible and useful to researchers and graduate students working in functional analysis, probability theory, and mathematical physics.

Author : Slavoj Žižek,Clayton Crockett,Creston Davis
Publisher : Columbia University Press
Page : 256 pages
File Size : 45,5 Mb
Release : 2011-03-23
Category : Philosophy
ISBN : 9780231512879

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Hegel and the Infinite by Slavoj Žižek,Clayton Crockett,Creston Davis Pdf

Catherine Malabou, Antonio Negri, John D. Caputo, Bruno Bosteels, Mark C. Taylor, and Slavoj Zizek join seven others—including William Desmond, Katrin Pahl, Adrian Johnston, Edith Wyschogrod, and Thomas A. Lewis—to apply Hegel's thought to twenty-first-century philosophy, politics, and religion. Doing away with claims that the evolution of thought and history is at an end, these thinkers safeguard Hegel's innovations against irrelevance and, importantly, reset the distinction of secular and sacred. These original contributions focus on Hegelian analysis and the transformative value of the philosopher's thought in relation to our current "turn to religion." Malabou develops Hegel's motif of confession in relation to forgiveness; Negri writes of Hegel's philosophy of right; Caputo reaffirms the radical theology made possible by Hegel; and Bosteels critiques fashionable readings of the philosopher and argues against the reducibility of his dialectic. Taylor reclaims Hegel's absolute as a process of infinite restlessness, and Zizek revisits the religious implications of Hegel's concept of letting go. Mirroring the philosopher's own trajectory, these essays progress dialectically through politics, theology, art, literature, philosophy, and science, traversing cutting-edge theoretical discourse and illuminating the ways in which Hegel inhabits them.

Author : I͡Uriĭ Anatolʹevich Rozanov
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 50,6 Mb
Release : 1971
Category : Distribution (Probability theory)
ISBN : 0821830082

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Infinite-Dimensional Gaussian Distributions by I͡Uriĭ Anatolʹevich Rozanov Pdf