Research Topics In Analysis Volume I
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Research Topics in Analysis, Volume I
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Research Topics in Analysis, Volume II
This book, the second of two volumes, presents significant applications for understanding modern analysis. It empowers young researchers with key techniques and applications to explore various subfields of this broad subject and introduces relevant frameworks for immediate deployment. The applications list begins with Degree Theory, a useful tool for studying nonlinear equations. Chapter 2 deals with Fixed Point Theory, and Chapter 3 introduces Critical Point Theory. Chapter 4 presents the main spectral properties of linear, nonlinear, anisotropic, and double-phase differential operators. Chapter 5 covers semilinear and nonlinear elliptic equations with different boundary conditions, while Chapter 6 addresses dynamic systems monitored by ordinary and partial differential equations. Chapter 7 delves into optimal control problems, and Chapter 8 discusses some economic models, providing a brief presentation of Game Theory and Nash equilibrium. By offering a clear and comprehensive overview of modern analysis tools and applications, this work can greatly benefit mature graduate students seeking research topics, as well as experienced researchers interested in this vast and rich field of mathematics.
Citation Analysis in Research Evaluation
Author: Henk F. Moed
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-03-30
This book is written for members of the scholarly research community, and for persons involved in research evaluation and research policy. More specifically, it is directed towards the following four main groups of readers: – All scientists and scholars who have been or will be subjected to a quantitative assessment of research performance using citation analysis. – Research policy makers and managers who wish to become conversant with the basic features of citation analysis, and about its potentialities and limitations. – Members of peer review committees and other evaluators, who consider the use of citation analysis as a tool in their assessments. – Practitioners and students in the field of quantitative science and technology studies, informetrics, and library and information science. Citation analysis involves the construction and application of a series of indicators of the ‘impact’, ‘influence’ or ‘quality’ of scholarly work, derived from citation data, i.e. data on references cited in footnotes or bibliographies of scholarly research publications. Such indicators are applied both in the study of scholarly communication and in the assessment of research performance. The term ‘scholarly’ comprises all domains of science and scholarship, including not only those fields that are normally denoted as science – the natural and life sciences, mathematical and technical sciences – but also social sciences and humanities.