Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide.As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, ...

This book presents a novel framework design for the next generation Marine Wireless Communication Networks (MWCNs). The authors first provide an overview of MWCNs, followed by a discussion of challenges in the design and development of MWCNs in support of a diversity of marine services such as real-time marine monitoring, offshore oil exploration, drilling, marine tourism and fishing. The authors then propose cross layer networking solutions to achieve a high performance modern MWCN that e...

This textbook provides a comprehensive review of the evolution of mobile communications and networking from the birth of cellular networks to the forthcoming sixth-generation mobile communications, which is envisioned to be commercially deployed first in 2030. New students who are coming to wireless communications/electrical engineering/computer networking/telecommunications and network engineering can benefit from this book by quickly grasping the whole history of cellular networks, under...

This two-volume set (CCIS 1879 and 1880) constitutes the refereed proceedings of the 9th International Conference of Pioneering Computer Scientists, Engineers and Educators, ICPCSEE 2023 held in Harbin, China, during September 22–24, 2023.The 52 full papers and 14 short papers presented in these two volumes were carefully reviewed and selected from 244 submissions.The papers are organized in the following topical sections:Part I: Applications of Data Science, Big Da...

Taught at junior level math courses at every university, Linear Algebra is essential for students in almost every technical and analytic discipline.

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the re...

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is ...

A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fieldsFeaturing a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible, combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger’s equa...

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential ...

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for...

This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA grou...

This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin metho...