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Functions --- Abelian --- Integrals --- Hyperelliptic

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Regarding the set of all feature attributes in a given database as the universal set, this monograph discusses various nonadditive set functions that describe the interaction among the contributions from feature attributes towards a considered target attribute. Then, the relevant nonlinear integrals are investigated. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation, nonlinear multiregressions, and nonlinear classifications. Some methods of fuzzification are also introduced for nonlinear integrals such that fuzzy data can be

Fuzzy sets. --- Integrals. --- Fuzzy logic. --- Data mining.

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The goal of this book is to introduce students to path integrals within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.

Path integrals. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Integrals, Path --- Integrals --- Probabilities --- Quantum theory --- Statistical physics

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Quantum theory --- Path integrals --- Théorie quantique. --- Intégrales de chemin.

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Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Fractional calculus --- Differential equations --- Mathematics --- Mathematical Theory --- Calculus --- Physical Sciences & Mathematics --- Differential equations. --- Fractional calculus. --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- 517.91 Differential equations --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Integral equations. --- Ordinary Differential Equations. --- Integral Equations. --- Analysis. --- Equations, Integral --- Functional equations --- Functional analysis --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Differential Equations. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic