International Journal of Mathematical Combinatorics, Volume 3, 2012


Book Description

Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces; Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathematical theory on parallel universes; Other applications of Smarandache multi-space and combinatorics.




Ultrametric Functional Analysis


Book Description

This volume contains research articles based on lectures given at the Seventh International Conference on $p$-adic Functional Analysis. The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis (Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions, strict topologies, operator theory, automatic continuity, measure and integrations, Banach and topological algebras, summability methods, and ultrametric spaces), analytic functions (meromorphic functions, roots of rational functions, characterization of injective holomorphic functions, and Gelfand transforms in algebras of analytic functions), differential equations, Banach-Hopf algebras, Cauchy theory of Levi-Civita fields, finite differences, weighted means, $p$-adic dynamical systems, and non-Archimedean probability theory and stochastic processes. The book is written for graduate students and research mathematicians. It also would make a good reference source for those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical systems, orthomodular spaces, number theory, and representations of $p$-adic groups.




Ultrametric Banach Algebras


Book Description

In this book, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebras, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. In uniform Banach algebras, the spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. KrasnerTate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametric Banach algebras. Given a KrasnerTate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A.




Game Theory and Applications


Book Description

This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.




Guide to Information Sources in Mathematics and Statistics


Book Description

This book is a reference for librarians, mathematicians, and statisticians involved in college and research level mathematics and statistics in the 21st century. We are in a time of transition in scholarly communications in mathematics, practices which have changed little for a hundred years are giving way to new modes of accessing information. Where journals, books, indexes and catalogs were once the physical representation of a good mathematics library, shelves have given way to computers, and users are often accessing information from remote places. Part I is a historical survey of the past 15 years tracking this huge transition in scholarly communications in mathematics. Part II of the book is the bibliography of resources recommended to support the disciplines of mathematics and statistics. These are grouped by type of material. Publication dates range from the 1800's onwards. Hundreds of electronic resources-some online, both dynamic and static, some in fixed media, are listed among the paper resources. Amazingly a majority of listed electronic resources are free.




Concordian Economics, Vol. 1


Book Description

This is the first part of a two-volume set on Concordian economics, a new paradigm whose core completes the Aristotelian-Aquinian project of economic justice. The book delves into the history of economics and presents Concordian economics as a response to the concerns and shortcomings of mainstream economics. Demand-side economics is represented in the process of consumption—the expenditure of monetary wealth to acquire real wealth and financial wealth of a different nature. In contrast, supply-side economics is represented in the production process, the process of producing real wealth, e.g. tables, chairs and foodstuffs. Institutionalists will also welcome this book because it ties the world of real wealth to that of monetary wealth through the process of distributing the value of ownership of both monetary and real wealth as they are created. The book begins with an introduction to Concordian economics, followed by a discussion of how to restore relevance to the field of economic studies. It also presents a revision of the Keynesian model designed to gradually address the major social, economic, and political causes of discord. Moreover, the author warns against the separation of economics from the world of physical things as well as the world of legal and moral issues. Following a discussion on the measurement of real wealth, econometrics is introduced in accordance with the categories of Concordian economics. Lastly, the book develops a theory of economic justice by defining a set of economic rights and responsibilities that guide economic behavior and policy. This book appeals to scholars and students of economics and related fields, as well as anyone interested in reintegrating economics into the social context.




Illegal Online File Sharing, Decision-Analysis, and the Pricing of Digital Goods


Book Description

Illegal online file sharing costs companies tens of billions of dollars of lost revenues around the world annually and results in lost productivity, various psychological issues, and significant reduction of incentives to create and innovate. Legislative, technical, and enforcement efforts have failed. This book presents psychological theories about why people illegally share files online; analyzes and characterizes optimal sanctions for illegal online file sharing; introduces new models for pricing of network-access and digital-content to help reduce illegal online file sharing; introduces new content control and P2P systems; and explains why game theory does not work in pricing of network access.




A Course in Stochastic Game Theory


Book Description

Stochastic games have an element of chance: the state of the next round is determined probabilistically depending upon players' actions and the current state. Successful players need to balance the need for short-term payoffs while ensuring future opportunities remain high. The various techniques needed to analyze these often highly non-trivial games are a showcase of attractive mathematics, including methods from probability, differential equations, algebra, and combinatorics. This book presents a course on the theory of stochastic games going from the basics through to topics of modern research, focusing on conceptual clarity over complete generality. Each of its chapters introduces a new mathematical tool – including contracting mappings, semi-algebraic sets, infinite orbits, and Ramsey's theorem, among others – before discussing the game-theoretic results they can be used to obtain. The author assumes no more than a basic undergraduate curriculum and illustrates the theory with numerous examples and exercises, with solutions available online.