Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers PDF Download
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Author: W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599731797
Category : Algebra
Languages : en
Pages : 152
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Book Description
In this book we explore the possibility of extending the natural operations on reals to intervals and matrices. The extension to intervals makes us define a natural class of intervals in which we accept [a, b], a greater than b. Further, we introduce a complex modulo integer in Z_n (n, a positive integer) and denote it by iF with iF^2 = n-1.
Author: W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599731797
Category : Algebra
Languages : en
Pages : 152
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Book Description
In this book we explore the possibility of extending the natural operations on reals to intervals and matrices. The extension to intervals makes us define a natural class of intervals in which we accept [a, b], a greater than b. Further, we introduce a complex modulo integer in Z_n (n, a positive integer) and denote it by iF with iF^2 = n-1.
Author: W. B. Vasantha Kandasamy, Florentin Smarandache, Indra Venkatbabu
Publisher: Infinite Study
ISBN: 1599732084
Category :
Languages : en
Pages : 229
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Book Description
Author: Kyandoghere Kyamakya
Publisher: MDPI
ISBN: 3036508481
Category : Technology & Engineering
Languages : en
Pages : 494
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Book Description
Building around innovative services related to different modes of transport and traffic management, intelligent transport systems (ITS) are being widely adopted worldwide to improve the efficiency and safety of the transportation system. They enable users to be better informed and make safer, more coordinated, and smarter decisions on the use of transport networks. Current ITSs are complex systems, made up of several components/sub-systems characterized by time-dependent interactions among themselves. Some examples of these transportation-related complex systems include: road traffic sensors, autonomous/automated cars, smart cities, smart sensors, virtual sensors, traffic control systems, smart roads, logistics systems, smart mobility systems, and many others that are emerging from niche areas. The efficient operation of these complex systems requires: i) efficient solutions to the issues of sensors/actuators used to capture and control the physical parameters of these systems, as well as the quality of data collected from these systems; ii) tackling complexities using simulations and analytical modelling techniques; and iii) applying optimization techniques to improve the performance of these systems.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599734680
Category : Mathematics
Languages : en
Pages : 232
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Book Description
This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.
Author: Pelin Gulum
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 17
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Book Description
Earthquakes are the leading natural disasters that seriously affect human life. Furthermore, earthquakes are natural disasters that have the ability to trigger a second disaster in addition to the damages they cause. From this point of view, post-earthquake fires are defined as the one of the most dangerous secondary disasters after an earthquake and often cause even more serious dangers. For this reason, government officials and relevant decision-makers should effectively determine post-earthquake fire risks and take necessary precautions. In this study, we consider the problem of determining the fire risk after an earthquake as a multi-criteria decision problem and present a two-level framework for risk assessment. The main and sub-criteria are determined by a detailed literature review and Modified Delphi method is employed to gain and consolidate expert opinions.
Author: Robert M. Gray
Publisher: Now Publishers Inc
ISBN: 1933019239
Category : Computers
Languages : en
Pages : 105
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Book Description
The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.
Author:
Publisher:
ISBN:
Category : Ada (Computer program language)
Languages : en
Pages : 516
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Book Description
Author: Ramon E. Moore
Publisher: SIAM
ISBN: 089871771X
Category : Mathematics
Languages : en
Pages : 223
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Book Description
An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.
Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595
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Book Description
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author: Mark Levi
Publisher: Princeton University Press
ISBN: 1400830478
Category : Mathematics
Languages : en
Pages : 197
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Book Description
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.
