"Principles of Duality: The Quest for Balance in the World" Discover the profound connections of duality that shape our lives and the world we live in. In "Principles of Duality: The Quest for Balance in the World," the author sheds light on the eternal opposites that seem to conflict with each other, but in truth work together to achieve balance in all things. This book offers a philosophical reflection on the universal principle of duality. It explains how opposing forces such as light and darkness, order and chaos, good and evil, love and fear are not only in conflict with each other, but also depend on each other to achieve harmony and balance. Whether in nature, human relationships, or world politics, the interplay of these forces is essential to understanding and the existence of the world. "Principles of Duality" encourages you to rethink the pursuit of balance in all areas of life and gain new perspectives on the challenges of everyday life. What you can expect: Extensive insights into the contradictions that shape our world Philosophical reflections on the interplay of forces and their significance for all of our lives Practical considerations and inspiration for more harmony and balance This book is aimed at anyone who wants to look at the world through a new, deeper lens - regardless of whether you are interested in philosophy, personal development or the realities of world events. Immerse yourself in the fascinating principles of duality and embark on a journey through the universe of balance and contradictions.

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims

This book is concerned with the development of the understanding of the relational structures of information, knowledge, decision–choice processes of problems and solutions in the theory and practice regarding diversity and unity principles of knowing, science, non-science, and information–knowledge systems through dualistic-polar conditions of variety existence and nonexistence. It is a continuation of the sequence of my epistemic works on the theories on fuzzy rationality, info-statics, info-dynamics, entropy, and their relational connectivity to information, language, knowing, knowledge, cognitive practices relative to variety identification–problem–solution dualities, variety transformation–problem–solution dualities, and variety certainty–uncertainty principle in all areas of knowing and human actions regarding general social transformations. It is also an economic–theoretic approach in understanding the diversity and unity of knowing and science through neuro-decision–choice actions over the space of problem–solution dualities and polarities. The problem–solution dualities are argued to connect all areas of knowing including science and non-science, social science, and non-social-science into unity with diversities under neuro-decision–choice actions to support human existence and nonexistence over the space of static–dynamic dualities. The concepts of diversity and unity are defined and explicated to connect to the tactics and strategies of decision–choice actions over the space of problem–solution dualities. The concepts of problem and solution are defined and explicated not in the space of absoluteness but rather in the space of relativity based on real cost–benefit conditions which are shown to be connected to the general parent–offspring infinite process, where every solution generates new problem(s) which then generates a search for new solutions within the space of minimum–maximum dualities in the decision–choice space under the principle of non-satiation over the space of preference–non-preference dualities with analytical tools drawn from the fuzzy paradigm of thought which connects the conditions of the principle of opposites to the conditions of neuro-decision–choice actions in the zone of variety identifications and transformations. The Monograph would be useful to all areas of Research, Learning and Teaching at Advanced Stages of Knowing and Knowledge Production.

The Theory of Categorial Conversion is advanced by Professor Kofi Kissi Dompere as mathematical-philosophical and game-theoretic foundations to solve the problem of socio-natural transformation as governed by some internal process in relation to Marx, Schumpeter and Nkrumah. Dompere's methodology is based on the Africentric principles of opposites made up of actual-potential polarity, negative-positive duality with relational continuum and unity under cost-benefit rationality and Asantrofi-Anoma principle supported by fuzzy paradigm of thought. Socio-natural transformations are seen in terms of game theories in a fuzzy-stochastic space admitting of defective-deceptive information structures in quality-quantity space within the subjective-objective duality. The main premise of the monograph is that there exists a set of necessary and sufficient conditions for internal self-transformation. The necessary conditions are made up of categorial moments and categorial transfer functions forming the domain of control instrumentation in creating the sufficient conditions for categorial-conversion processes. Dompere presents an important methodological framework for the study and construction of the theories of socioeconomic development and political change, as well as info-dynamics connecting knowledge, sciences, innovation and engineering to the space of knowing, under qualitative-quantitative transformational dynamics with defective-deceptive information structures in the games for power and dominance by duals and poles in conflicts. The necessary conditions of socio-natural transformation are internally derived based on the relational structure of matter-energy-information activities within the dynamics of qualitative dispositions of dualities of actual-potential polarities. The theory consists of category formation showing ontological-epistemological categories, and categorial dynamics shows elemental conversions of categorial varieties in a continuum. The logical tools and the paradigm of thought for the theoretical development of Nkrumah's framework involve self-excitement, self-correction and self-control systems induced by internal contradictions. The set of necessary conditions constitutes the natural necessity that constrains cognitive freedom in socio-natural transformations. Had this conceptual system been familiar to economists and social scientists, the construct of the theories of socioeconomic development and transformations would have been increasingly successful.

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