Author : F. F. Bonsall
Publisher : Cambridge University Press
Page : 189 pages
File Size : 49,99 MB
Release : 1973-08-02
Category : Mathematics
ISBN : 0521202272
The landlady, landlord, cat, trap, and cheese all take credit for catching the long-tailed rat who is really the only one who knows the truth of the matter.
Author : F. F. Bonsall
Publisher : CUP Archive
Page : 149 pages
File Size : 36,20 MB
Release : 1971-03-02
Category : Mathematics
ISBN : 0521079888
The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures.
Author : Karl E. Gustafson
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 50,44 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461384982
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
Author : Hwa-Long Gau
Publisher : Cambridge University Press
Page : 556 pages
File Size : 41,8 MB
Release : 2021-08-05
Category : Mathematics
ISBN : 1108787606
Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.
Author : Ulrich Daepp
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 39,84 MB
Release : 2018
Category : Mathematics
ISBN : 147044383X
Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.
Author : Mark Elin
Publisher : Springer
Page : 238 pages
File Size : 36,50 MB
Release : 2019-03-11
Category : Mathematics
ISBN : 3030050203
This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.
Author : Lianqing Qi
Publisher : Gulf Professional Publishing
Page : 268 pages
File Size : 37,55 MB
Release : 2020-10-22
Category : Business & Economics
ISBN : 0128226277
Development and Application of Classical Capillary Curve Theory shows readers how to improve chemical flooding recovery procedures in enhanced oil recovery (EOR) using sophisticated numerical modeling techniques for oil displacement that build on, and enhance, the accepted capillary curve in a novel way. The title presents research and technical data that amends the classical capillary curve, giving new impetus to chemical flooding research. By analyzing the capillary number experiment QL, the book models oil and water distribution in the micro-space of the reservoir core. Finally, the book discusses chemical flooding software, reservoir geological modeling, field tests, and a new technique of digital oil displacement testing being developed. - Describes how to improve chemical flooding recovery procedures using sophisticated numerical modeling techniques for oil displacement that build on, and enhance, accepted capillary curve theory - Presents the role of the capillary number experiment curve QL on oil-water distribution in the microscopic core of a reservoir - Details novel digital techniques for oil displacement testing and modeling with global applicability in enhanced oil recovery (EOR) - Gives information on chemical flooding software, reservoir geological modeling and field testing - Provides advanced digital modeling techniques alongside insights gained through many years of practical experience in Chinese oilfields
Author : David C. Geary
Publisher : Academic Press
Page : 401 pages
File Size : 12,95 MB
Release : 2014-11-04
Category : Psychology
ISBN : 0128008881
The first volume in this ground-breaking series focuses on the origins and early development of numerical cognition in non-human primates, lower vertebrates, human infants, and preschool children. The text will help readers understand the nature and complexity of these foundational quantitative concepts and skills along with evolutionary precursors and early developmental trajectories. - Brings together and focuses the efforts and research of multiple disciplines working in math cognition. - The contributors bring vast knowledge and experience to bear on resolving extant substantive and methodological challenges to help advance the field of basic number processing. - Introductory sections and summaries will be included to provide background for non-specialist readers.
Author : Mohamed Gad-el-hak
Publisher : World Scientific
Page : 445 pages
File Size : 27,29 MB
Release : 2005-12-27
Category : Technology & Engineering
ISBN : 9814479489
This volume contains articles based on lectures given at the Workshop on Transition and Turbulence Control, hosted by the Institute for Mathematical Sciences, National University of Singapore, 8-10 December 2004. The lecturers included 13 of the world's foremost experts in the control of transitioning and turbulent flows. The chapters cover a wide range of subjects in the broad area of flow control, and will be useful to researchers working in this area in academia, government laboratories and industry. The coverage includes control theory, passive, active and reactive methods for controlling transitional and turbulent wall-bounded flows, noise suppression and mixing enhancement of supersonic turbulent jets, compliant coatings, modern flow diagnostic systems, and swept wing instabilities.
Author : Christiane Tretter
Publisher : Imperial College Press
Page : 297 pages
File Size : 29,36 MB
Release : 2008
Category : Mathematics
ISBN : 1848161123
This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics.
