Mathematica Scandinavica


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Modular Theory in Operator Algebras


Modular Theory in Operator Algebras

Author: Şerban Strǎtilǎ

language: en

Publisher: Cambridge University Press

Release Date: 2020-12-03


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Discusses the fundamentals and latest developments in operator algebras, focusing on continuous and discrete decomposition of factors of type III.

Formal Concept Analysis


Formal Concept Analysis

Author: Petko Valtchev

language: en

Publisher: Springer Science & Business Media

Release Date: 2011-04-26


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This book constitutes the refereed proceedings of the 9th International Conference on Formal Concept Analysis, ICFCA 2011, held in Nicosia, Cyprus, in May 2011. The 16 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 49 submissions. The central theme was the mathematical formalization of concept and conceptual hierarchy. The field has developed into a constantly growing research area in its own right with a thriving theoretical community and an increasing number of applications in data and knowledge processing including disciplines such as data visualization, information retrieval, machine learning, software engineering, data analysis, data mining, social networks analysis, etc.

Nonlinear Potential Theory of Degenerate Elliptic Equations


Nonlinear Potential Theory of Degenerate Elliptic Equations

Author: Juha Heinonen

language: en

Publisher: Courier Dover Publications

Release Date: 2018-05-16


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A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.