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A Concise Introduction to the Theory of Integration

The choice of topics included in this book, as well as the presentation of those topics, has been guided by the author's experience in teaching this material to classes consisting of advanced graduate students who are not concentrating in mathematics. This book contains an introduction to the modern theory of integration with a strong emphasis on the case of LEBESGUE's measure for (RN and eye toward applications to real analysis and probability theory. Following a brief review of the classical RIEMANN theory in Chapter I, the details of LEBESGUE's construction are given in Chapter II, which also contains a derivation of the transformation properties of LEBESGUE's measure under linear maps. Chapter III is devoted to LEBESGUE's theory of integration of real-valued functions on a general measure space. Besides the basic convergence theorems, this chapter introduces product measures and FUBINI's Theorem. In Chapter IV, various topics having to do with the transformation properties of measures are derived. These include: the representation of general integrals in terms of RIEMANN integrals with respect to the distribution function, polar coordinates, JACOBI's transformation formula and finally the introduction of surface measure followed by a proof of the Divergence Theorem. A few of the basic inequalitites of measure theory are derived in Chapter V. In particular, the inequalities of JENSEN, MINKOWSKI and H™LDER are presented. Finally, Chapter VI starts with the DANIELL integral and its applications to the CARATHODORY Extension and RIESZ Representation Theorems. It closes with VON NEUMANN's derivation of the RADON-NIKODYM Theorem.

The choice of topics included in this book, as well as the presentation of those topics, has been guided by the author's experience in teaching this material to classes consisting of advanced graduate students who are not concentrating in ...

Advanced Calculus

An Introduction to Mathematical Analysis

This book is an introduction to mathematical analysis (i.e real analysis) at a fairly elementary level. A great (unusual) emphasis is given to the construction of rational and then of real numbers, using the method of equivalence classes and of Cauchy sequences. The text includes the usual presentation of: sequences of real numbers, infinite numerical series, continuous functions, derivatives and Riemann-Darboux integration. There are also two “special” sections: on convex functions and on metric spaces, as well as an elementary appendix on Logic, Set Theory and Functions. We insist on a rigorous presentation throughout in the framework of the classical, standard, analysis. Contents: NumbersSequences of Real NumbersInfinite Numerical SeriesContinuous FunctionsDerivativesConvex FunctionsMetric SpacesIntegrationIndexIndex of NotationsAppendix (Logic, Set Theory and Functions)Bibliography Readership: Undergraduate students of calculus and real analysis. keywords:Numbers;Sequences;Series;Continuous Functions;Derivatives;Convex Functions;Metric Spaces;Integration

This book is an introduction to mathematical analysis (i.e real analysis) at a fairly elementary level.

A Sequential Introduction to Real Analysis

Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time. This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course. Request Inspection Copy

This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course. Request Inspection Copy

Multiple Criteria and Multiple Constraint Levels Linear Programming

Concepts, Techniques and Applications

This book introduces multiple criteria and multiple constraint levels linear programming (MC2LP), which is an extension of linear programming (LP) and multiple criteria linear programming (MCLP). In the last decade, the author and a group of researchers from the USA, China, Korea, Germany, and Hungary have been working on the theory and applications of MC2LP problems. This volume integrates their main research results ranging from theoretical bases to broad areas of real world applications. The theoretical bases include the formulation of MC2LP; integer MC2LP and MC2 transportation model; fuzzy MC2LP and fuzzy duality of MC2LP; optimal system designs and contingency plans; MC2 decision support system; and MC2 computer software development. The application areas are accounting, management information systems, production planning, and telecommunications management.The book serves as a seminar text for both undergraduates and graduates who have a linear algebra or equivalent background. For practitioners, it will help in handling LP type problems in multiple decision making environment.

By using the techniques in multiple criteria (MC) linear programming (Zeleny
1974 and Yu 1985), they developed an algorithm to identify the set of
nondominated extreme points in the criteria space. Other formulations and
solution methods for ...

Understanding Brain and Mind

A Connectionist Perspective

How can we understand a system as complex as the brain? Does the brain use the same operational principles to control physical and mental activities? How can we incorporate in a model what we know and what we do not know about the brain?The connectionist model presented in this book provides tools for addressing such questions. Its nodes represent well-established biological facts combined with observations of the overall behaviors of the system. The model is based on comparing and contrasting brains, computers, and neural networks. It defines a framework for understanding the relationships between the brain and the mind. It can serve both as a starting point for developing Artificial Intelligence applications for all levels of mental activities and as a guide in the search for biological correlates of observed behaviors.

However, the actual withdrawal is based on additional information. If the hand
approached the hot object from above, it will be withdrawn upward. If it
approached the object from below, the withdrawal will be downwards. Other than
the cue, the system has also considered the history of the event. This information
may have been encoded as certain motor neurons being active. The reflex
caused the activation of neurons that control antagonistic movements. In all these
cases, the action ...

Methods, Models, Simulations and Approaches Towards a General Theory of Change - Proceedings of the Fifth National Conference on Systems Science

The book contains the Proceedings of the 2010 Conference of the Italian Systems Society, see also www.AIRS.it. Papers will deal with the interdisciplinary study of processes of changing related to a wide variety of specific aspects. Attempts to deal with them, based on generalising approaches used to study the movement of bodies and environmental influence, have included ineffective reductionistic simplifications. Indeed changing also relates, for instance, to processes of acquisition and varying properties such as for software; growing and aging biological systems; learning/cognitive systems; and socio-economic systems growing and developing through innovations. The aim of the book is to present very advanced studies and the generalisation of processes of changing as for processes of emergence. Papers in the book study the problem considering its transdisciplinary nature, i.e., systemic properties studied per se and not within specific disciplinary contexts. The aim of these studies is to outline a transdisciplinary theory of changes in systemic properties. Such a theory should have simultaneous, corresponding and eventually hierarchical disciplinary aspects as expected for a general theory of emergence. Within this transdisciplinary context, specific disciplinary research activities and results are assumed to be mutually represented as within a philosophical and conceptual framework based on the theoretical centrality of the observer. Models and theories will be based on the conceptual inseparability between observer and observer as in constructivism and for logically open systems. Contributions will deal such issues in interdisciplinary ways considering theoretical aspects and applications from Physics, Cognitive Science, Biology, Artificial Intelligence, Economics, Architecture, Philosophy, Music and Social Systems. Opening lecture “Criticality of Criticality in Causal Networks: Information transfer, storage and further issues” by Stuart Kauffman is found at http://www.santafe.edu/about/people/profile/Stuart%20Kauffman.

Multimodal Interface for Human-Machine Communication

With the advance of speech, image and video technology, human–computer interaction (HCI) will reach a new phase. In recent years, HCI has been extended to human–machine communication (HMC) and the perceptual user interface (PUI). The final goal in HMC is that the communication between humans and machines is similar to human-to-human communication. Moreover, the machine can support human-to-human communication (e.g. an interface for the disabled). For this reason, various aspects of human communication are to be considered in HMC. The HMC interface, called a multimodal interface, includes different types of input methods, such as natural language, gestures, face and handwriting characters. The nine papers in this book have been selected from the 92 high-quality papers constituting the proceedings of the 2nd International Conference on Multimodal Interface (ICMI '99), which was held in Hong Kong in 1999. The papers cover a wide spectrum of the multimodal interface. Contents:Introduction to Multimodal Interface for Human–Machine Communication (P C Yuen et al.)Algorithms:A Face Location and Recognition System Based on Tangent Distance (R Mariani)Recognizing Action Units for Facial Expression Analysis (Y-L Tian et al.)View Synthesis Under Perspective Projection (G C Feng et al.)Single Modality Systems:Sign Language Recognition (W Gao & C Wang)Helping Designers Create Recognition-Enabled Interfaces (A C Long et al.)Information Retrieval:Cross-Language Text Retrieval by Query Translation Using Term Re-Weighting (I Kang et al.)Direct Feature Extraction in DCT Domain and Its Applications in Online Web Image Retrieval for JPEG Compressed Images (G Feng et al.)Multimodality Systems:Advances in the Robust Processing of Multimodal Speech and Pen Systems (S Oviatt)Information-Theoretic Fusion for Multimodal Interfaces (J W Fisher III & T Darrell)Using Virtual Humans for Multimodal Communication in Virtual Reality and Augmented Reality (D Thalmann) Readership: Computer scientists and engineers. Keywords:

The HMC interface, called a multimodal interface, includes different types of input methods, such as natural language, gestures, face and handwriting characters.The nine papers in this book have been selected from the 92 high-quality papers ...

Language Prototyping: An Algebraic Specification Approach

Language prototyping provides a means to generate language implementations automatically from high-level language definitions. This volume presents an algebraic specification approach to language prototyping, and is centered around the ASF+SDF formalism and Meta-Environment. The volume is an integrated collection of articles covering a number of case studies, and includes several chapters proposing new techniques for deriving advanced language implementations. The accompanying software is freely available. Contents: PrefaceAn Overview of ASF+SDFThe Static Semantics of PascalA Kernel Object-Oriented LanguageTypechecking with Modular Error HandlingMulti-Level SpecificationsIncremental TypecheckingOrigin Tracking and Its ApplicationsSecond-Order Term Rewriting Specification of Static Semantics: An ExerciseOrigin Tracking for Higher-Order Term Rewriting Systems Readership: Software practitioners, graduate students and researchers in computer science. keywords:

This construct aids reuse of methods defined earlier and the maintenance of such
programs, since any modification to the inherited class is effective in all classes
that inherit it. However, neither the dynamic nor static semantics of KOOL are
dependent on the structure of the hierarchy itself. Rule [FO] removes the 'TV'
subclass of TV' construct by copying all instance variables and methods from the '
super class' TV to the (sub)class TV'. Methods and instance variables could get
multiply ...

A First Course in Integral Equations

Second Edition

This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods. This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering. Click here for solutions manual.

This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations.

Cities of Love

Roadmap for Sustaining Future Cities

Earth's environmental problems are far from being resolved. A large part of these are due to ever-growing cities. Despite more efforts made to improve cities, it has been difficult to change cities. One of the fundamental reasons is that people are not motivated to help change their cities. Apathy is now the number one obstacle to positive change. There is hope and Love is the antidote. What you love, you will sustain. Cities of Love aims to urge, persuade and provoke fellow residents of our earth to collectively shape the cities we live in. To achieve this, her residents must again uncover the reasons to love and therefore sustain her cities. To this end, Cities of Love tries to identify the ingredients that could possibly be the reasons for such active love. When a city is filled by the people who love their cities, then can a city have a greater chance of advancing towards a better tomorrow. Love is a mighty force to be reckoned with. Cities of Love comes alive with augmented reality! See, watch, and read beyond the contents of the book. Scan the pages for more photos and maybe selfie videos of the author in a new city exploring urban developments around the world. Immerse and discover more things to love about cities and inspire yourself to do the same with yours. An app will be available for download (from the App store and Google Play store). Watch this space for more exciting features of the book!

Earth's environmental problems are far from being resolved. A large part of these are due to ever-growing cities. Despite more efforts made to improve cities, it has been difficult to change cities.