Basic Posets PDF Download

Author: J. Neggers
Publisher: World Scientific
ISBN: 9789810235895
Category : Mathematics
Languages : en
Pages : 192

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Book Description
This book introduces the reader to the general theory of partially ordered sets, i.e., posets. The text is presented in a rather informal manner, with interesting examples and computations, which rely on the Hassle diagram to build graphical intuition for the structure of finite posits. The proofs of a small number of theorems is included in the appendix. Important examples especially the Letter N poset, which plays a role akin to that of the Petersen graph in providing a candidate counterexample to many propositions, are used repeatedly throughout the text.

Author: Marco Fattore
Publisher: Springer
ISBN: 3319454218
Category : Science
Languages : en
Pages : 305

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Book Description
TThis book illustrates recent advances in applications of partial order theory and Hasse diagram techniques to data analysis, mainly in the socio-economic and environmental sciences. For years, partial order theory has been considered a fundamental branch of mathematics of only theoretical interest. In recent years, its effectiveness as a tool for data analysis is increasingly being realized and many applications of partially ordered sets to real problems in statistics and applied sciences have appeared. Main examples pertain to the analysis of complex and multidimensional systems of ordinal data and to problems of multi-criteria decision making, so relevant in social and environmental sciences. Partial Order Concepts in Applied Sciences presents new theoretical and methodological developments in partial order for data analysis, together with a wide range of applications to different topics: multidimensional poverty, economic development, inequality measurement, ecology and pollution, and biology, to mention a few. The book is of interest for applied mathematicians, statisticians, social scientists, environmental scientists and all those aiming at keeping pace with innovation in this interesting, growing and promising research field.

Author: Krassimir T. Atanassov
Publisher: Springer
ISBN: 3319655450
Category : Technology & Engineering
Languages : en
Pages : 360

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Book Description
This book presents selected papers from two important conferences held on October 12–14, 2016 in Warsaw, Poland: the Fourteenth National Conference of Operational and Systems Research, BOS-2016, one of the premiere conferences in the field of operational and systems research not only in Poland but also at the European level; and the Fifteenth International Workshop on Intuitionistic Fuzzy Sets and General Nets, IWIFSGN-2016, one of the foremost conferences on fuzzy logic, notably addressing extensions of the traditional fuzzy sets, as well as the Generalized Nets (GNs), a powerful extension of the traditional Petri net paradigm. The scope of the BOS con ferences includes all types of problems related to systems modeling, systems analysis, broadly perceived operational research, optimization, decision making, and decision support, to name but a few. In all these areas, virtually all models used have to take into account not only uncertainty in its traditional sense, but also imprecision of information. That is, in addition to traditional probabilistic and statistical tools and techniques, the use of methods based on fuzzy sets can also be sensible. Even more so, employing certain extensions of the classic concept of a fuzzy set can be very useful. Applying intuitionistic fuzzy sets, which are at the core of the IWIFSGN conferences, is a good example. Both conferences, BOS-2016 and IWIFSGN-2016, offered ideal venues for the exchange of ideas, cross-fertilization, and mutual inspiration.

Author: Daniel Simson
Publisher: CRC Press
ISBN: 9782881248283
Category : Mathematics
Languages : en
Pages : 516

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Book Description
This volume provides an elementary yet comprehensive introduction to representations of partially ordered sets and bimodule matrix problems, and their use in representation theory of algebras. It includes a discussion of representation types of algebras and partially ordered sets. Various characterizations of representation-finite and representation-tame partially ordered sets are offered and a description of their indecomposable representations is given. Auslander-Reiten theory is demonstrated together with a computer accessible algorithm for determining in decomposable representations and the Auslander-Reiten quiver of any representation-finite partially ordered set.

Author: Chiara Bodei
Publisher: Springer
ISBN: 3319255274
Category : Computers
Languages : en
Pages : 386

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Book Description
This Festschrift volume is published in honor of Pierpaolo Degano on the occasion of his 65th birthday and is the outcome of a colloquium held in Pisa, Italy, in June 2015. Pierpaolo Degano has worked on a large variety of topics including formal program semantics, concurrency theory, systems biology and security. The volume contains 22 refereed papers and one extended abstract, including personal memoirs and regular research papers by close collaborators and friends and a laudatio illustrating his distinguished career and his main scientific contributions. The papers deal with the main research topics explored by Pierpaolo Degano and those still under his investigation.

Author: Krishnendu Chatterjee
Publisher: Springer
ISBN: 3642403131
Category : Computers
Languages : en
Pages : 869

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Book Description
This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.

Author: Ivan Rival
Publisher: Springer Science & Business Media
ISBN: 9400926391
Category : Computers
Languages : en
Pages : 491

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Book Description
This volume contains the texts of the principal survey papers presented at ALGORITHMS -and ORDER, held· at Ottawa, Canada from June 1 to June 12, 1987. The conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the University of Ottawa, and the Natural Sciences and Engineering Research Council of Canada. We are grateful for this considerable support. Over fifty years ago, the Symposium on Lattice Theory, in Charlottesville, U.S.A., proclaimed the vitality of ordered sets. Only twenty years later the Symposium on Partially Ordered Sets and Lattice Theory, held at Monterey, U.S.A., had solved many of the problems that had been originally posed. In 1981, the Symposium on Ordered Sets held at Banff, Canada, continued this tradition. It was marked by a landmark volume containing twenty-three articles on almost all current topics in the theory of ordered sets and its applications. Three years after, Graphs and Orders, also held at Banff, Canada, aimed to document the role of graphs in the theory of ordered sets and its applications. Because of its special place in the landscape of the mathematical sciences order is especially sensitive to new trends and developments. Today, the most important current in the theory and application of order springs from theoretical computer seience. Two themes of computer science lead the way. The first is data structure. Order is common to data structures.

Author: Ingo Althöfer
Publisher: Springer Science & Business Media
ISBN: 1475760485
Category : Technology & Engineering
Languages : en
Pages : 659

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Book Description
Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, `Numbers and Combinations', `Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and `Complexity'. Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on Combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to Natural Sciences are discussed.

Author: Rainer Brüggemann
Publisher: Springer Science & Business Media
ISBN: 3540339701
Category : Science
Languages : en
Pages : 404

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Book Description
This book explains the theory and practice of order relations in such a way that no specific mathematical skill is needed to understand the advantages of this algebraization. It acts as a primer in a mathematical technique which is useful in many expanding disciplines, like genomics, techniques of decision support, and sustainability. This book is recommended to those who are interested in the interface between sciences and management.

Author: Marcelo Firer
Publisher: Springer
ISBN: 3319938215
Category : Mathematics
Languages : en
Pages : 133

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Book Description
This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, were first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S. Graves and K. Mark Lawrence, and to date the relevant knowledge on this subject was spread over more than two hundred research papers. Poset metrics generalizes both the standard Hamming metric – the most important metric used in the context of coding theory – and the Niederreiter-Rosenbloom-Tsfasman metric, which is an ultrametric. Conceived to be as self-contained as possible, the book starts from basic concepts of coding theory and advances towards coding theory for poset metrics and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven results. This work will appeal to researchers and graduate students alike, particularly those in the fields of Mathematics, Electrical Engineering and Computer Sciences, with an interest in discrete geometry and coding theory.