Exploring The Extension Of Natural Operations On Intervals Matrices And Complex Numbers

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.

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.

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.

In this book the authors introduce and study the properties of natural class of intervals built using (-, ) and (, -). The operations on these matrices with entries from natural class of intervals behave like usual reals. So working with these interval matrices takes the same time as usual matrices. Hence, when applying them to fuzzy finite element methods or finite element methods the determination of solution is simple and time saving.

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.

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.