“…The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.…”
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“…This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. …”
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“…Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book - now in its third revised and augmented edition - has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. …”
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“…This book gives an introduction to Linear Functional Analysis, a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. …”
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“…The main topics discussed are: Linear and non linear Algebra Topology (Topological and Metric spaces, Convexity Connexity, Orthogonal Projection in Hilbert spaces, etc.) …”
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“…RESULTS: We propose a new algebraic topological framework, which obtains intrinsic information from MALDI data and transforms it to reflect topological persistence. …”
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“…Prerequisite knowledge of the basics of algebra, linear algebra, topology, and calculus of several variables will be useful.…”
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“…The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered as follows. A symbolic, algebraic-topological "quantum computer" (as introduced in Baianu, 1971b) is here suggested to provide one such potential means for adequate biological simulations based on QMV Quantum Logic and meta-Categorical Modeling as for example in a QMV-based, Quantum-Topos (Baianu and Glazebrook,2004.…”
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“…Content Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis Readership Graduate Students in Mathematics / Master of Science in Mathematics About the Author Prof. …”
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“…An interesting interplay of algebra, topology, and analysis is displayed. This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.…”
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“…Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.…”
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“…The magnitude of stride-to-stride fluctuations and corresponding changes over time—gait dynamics—reflects the physiology of gait, in quantifying the pathologic alterations in the locomotor control system of health subjects and patients with neuro-degenerative diseases. Motivated by algebra topology theory, a topological data analysis-inspired nonlinear framework was adopted in the study of the gait dynamics. …”
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“…Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. …”
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“…The latter are pitched at a more formal, abstract level than the applications and, therefore, encompass a number of concepts drawn from the abstract theory of sets and relations, network theory, automata theory, Boolean and n-valued logics, abstract algebra, topology and category theory. The purpose of these theoretical sections is to provide the ans for approaching a number of basic biological questions: (1) What are the essential characteristics of a biological organism as opposed to an automaton? …”
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