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Author: M. Bunge
Publisher: Springer Science & Business Media
ISBN: 9401025169
Category : Science
Languages : en
Pages : 217
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Book Description
The papers that follow were read and discussed at the first Symposium on Exact Philosophy. This conference was held at Montreal on November 4th and 5th, 1971, to celebrate the sesquicentennial of McGill University and establish the Society for Exact Philosophy. The expression 'exact philosophy' is taken to signify mathematical phi losophy, i.e., philosophy done with the explicit help of mathematical logic and mathematics. So far the expression denotes an attitude rather than a fully blown discipline: it intends to convey the intention to try and pro ceed in as exact a manner as we can in formulating and discussing phi losophical problems and theories. The kind of philosophy we wish to practice and promote is disciplined rather than wild, systematic rather than disconnected, and capable of being argued over rather than oracular. We believe that even metaphysics, notoriously riotous, can be subjected to the control of logic and mathematics. Even the history of philosophy, notoriously unsystematic, can benefit from an exact reconstruction of some classical ideas.
Author: M. Bunge
Publisher: Springer Science & Business Media
ISBN: 9401025169
Category : Science
Languages : en
Pages : 217
Get Book Here
Book Description
The papers that follow were read and discussed at the first Symposium on Exact Philosophy. This conference was held at Montreal on November 4th and 5th, 1971, to celebrate the sesquicentennial of McGill University and establish the Society for Exact Philosophy. The expression 'exact philosophy' is taken to signify mathematical phi losophy, i.e., philosophy done with the explicit help of mathematical logic and mathematics. So far the expression denotes an attitude rather than a fully blown discipline: it intends to convey the intention to try and pro ceed in as exact a manner as we can in formulating and discussing phi losophical problems and theories. The kind of philosophy we wish to practice and promote is disciplined rather than wild, systematic rather than disconnected, and capable of being argued over rather than oracular. We believe that even metaphysics, notoriously riotous, can be subjected to the control of logic and mathematics. Even the history of philosophy, notoriously unsystematic, can benefit from an exact reconstruction of some classical ideas.
Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 100046363X
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.
Author: Tommy Wright
Publisher: Springer Science & Business Media
ISBN: 146123140X
Category : Mathematics
Languages : en
Pages : 446
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Book Description
There is a very simple and fundamental concept· to much of probability and statistics that can be conveyed using the following problem. PROBLEM. Assume a finite set (universe) of N units where A of the units have a particular attribute. The value of N is known while the value of A is unknown. If a proper subset (sample) of size n is selected randomly and a of the units in the subset are observed to have the particular attribute, what can be said about the unknown value of A? The problem is not new and almost anyone can describe several situations where a particular problem could be presented in this setting. Some recent references with different focuses include Cochran (1977); Williams (1978); Hajek (1981); Stuart (1984); Cassel, Samdal, and Wretman (1977); and Johnson and Kotz (1977). We focus on confidence interval estimation of A. Several methods for exact confidence interval estimation of A exist (Buonaccorsi, 1987, and Peskun, 1990), and this volume presents the theory and an extensive Table for one of them. One of the important contributions in Neyman (1934) is a discussion of the meaning of confidence interval estimation and its relationship with hypothesis testing which we will call the Neyman Approach. In Chapter 3 and following Neyman's Approach for simple random sampling (without replacement), we present an elementary development of exact confidence interval estimation of A as a response to the specific problem cited above.
Author: Victor A. Galaktionov
Publisher: CRC Press
ISBN: 9781584886631
Category : Mathematics
Languages : en
Pages : 538
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Book Description
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Author: Sergey Lemeshevsky
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110489724
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
Author: Jianer Chen
Publisher: Springer
ISBN: 3642112692
Category : Computers
Languages : en
Pages : 345
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Book Description
This book constitutes the refereed best selected papers of the 4th International Workshop on Parameterized and Exact Computation, IWPEC 2009, held in Copenhagen, Denmark, in September 2009. The 25 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 52 submissions. The topics addressed cover research in all aspects of parameterized and exact computation and complexity, including but not limited to new techniques for the design and analysis of parameterized and exact algorithms, parameterized complexity theory, relationship between parameterized complexity and traditional complexity classifications, applications of parameterized and exact computation, implementation issues of parameterized and exact algorithms, high-performance computing and fixed-parameter tractability.
Author: Oliver Keszocze
Publisher: Springer
ISBN: 3319909363
Category : Technology & Engineering
Languages : en
Pages : 138
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Book Description
This book presents exact, that is minimal, solutions to individual steps in the design process for Digital Microfluidic Biochips (DMFBs), as well as a one-pass approach that combines all these steps in a single process. All of the approaches discussed are based on a formal model that can easily be extended to cope with further design problems. In addition to the exact methods, heuristic approaches are provided and the complexity classes of various design problems are determined. Presents exact methods to tackle a variety of design problems for Digital Microfluidic Biochips (DMFBs); Describes an holistic, one-pass approach solving different design steps all at once; Based on a formal model of DMFBs that is easily adaptable to deal with further design tasks.
Author: Helena Petrovna Blavatsky
Publisher: Philaletheians UK
ISBN:
Category : Religion
Languages : en
Pages : 31
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Book Description
Sound and Light, hearing and sight, are always associated. But sound is seen before it is heard. It is useless to demand or expect from the learned men of our age that which they are absolutely incapable of doing for us, until the next cycle changes and transforms entirely their inner nature by “improving the texture” of their spiritual minds. Unless there is an opening, however small, for the passage of a ray from a man’s higher self to chase the darkness of purely material conceptions from the seat of his intellect, his task can never be wrought to a successful termination. For the sun needs an eye to manifest its light. And this, we think, is the case with the materialist: he can judge psychic phenomena only by their external aspect, and no modification is, or ever can be, created in him, so as to open his insight to their spiritual aspect.
Author: Kofi Kissi Dompere
Publisher: Springer
ISBN: 3642311229
Category : Technology & Engineering
Languages : en
Pages : 191
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Book Description
The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space is defective from the simple principles of acquaintances and the limitations of cognitive agents operating in the epistemological space. How then do we arrive and claim exactness in our knowledge-production system? The general conclusion of this book is that the conditions of the fuzzy paradigm with its laws of thought and mathematics present a methodological unity of exact and inexact sciences where every zone of thought has fuzzy covering.
Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 1040092934
Category : Mathematics
Languages : en
Pages : 660
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Book Description
This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.
