Copyright Year 2023
ISBN 9781032405155
December 22, 2022 Forthcoming by CRC Press
214 Pages
Basic formulation of waveguide cavity resonator equations especially when the cross sections of the guides and resonators have arbitrary shapes. The focus is on expressing the total field energy within such a cavity resonator as a quadratic form in the complex coefficients that determine the modal expansions of the electromagnetic field.
The reviews of basic statistical signal processing covering linear models, fast algorithms for estimating the parameters in such linear models, applications of group representation theory to image processing problems especially the representations of the permutation groups and induced representation theory applied to image processing problems involving the three dimensional Euclidean motion group.
The Hartree-Fock equations for approximately solving the two electron atomic problem taking spin-orbit magnetic field interactions into account has been discussed. In the limit as the lattice tends to a continuum, the convergence of the stochastic differential equations governing interacting particles on the lattice to a hydrodynamic scaling limit.
It will be useful to undergraduate and postgraduate students with courses on transmission lines and waveguides, and statistical signal processing.
Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Chapter 1: Remarks and problems on transmission lines and waveguides.
Chapter 2: Statistical Signal Processing
Chapter 3: Some study projects on applied signal processing
Harish Parthasarathy received B.tech degree in Electrical Engineering from IIT Kanpur and his Phd degree in Signal Processing from IIT Delhi in 1994. He worked as a visiting fellow in the Indian Institute of Astro Physics, Bangalore from 1993 to 1994. He has worked as a faculty in the Electrical Engineering departments at IIT Bombay and IIT Kanpur. Currently, he is a professor in the Electronics and Communication Division in NSIT, Delhi. He teaches courses on Signal processing Electromagnetics, transmission lines, wave guides & antennas and electives in quantum field theory, quantum robotics & quantum stochastic processes to undergraduate and postgraduate
students. He has published over 70 papers in international journals and conferences and he has also published 12 books on variety of topics in mathematical physics, signal processing and antenna theory.
Copyright Year 2023
ISBN 9781032357218 softcover
ISBN 9781032362151
December 16, 2022 Forthcoming by Chapman & Hall
312 Pages 28 B/W Illustrations
This book is written for the love of numbers. It tells their story, shows how they were invented and used to quantify our world, and explains what quantitative data mean for our lives. It aspires to contribute to overall numeracy through a tour de force presentation of the production, use, and evolution of data.
Understanding our physical world, our economies, and our societies through quantification has been a persistent feature of human evolution. This book starts with a narrative on why and how our ancestors were driven to the invention of number, which is then traced to the eventual arrival at our number system. This is followed by a discussion of how numbers were used for counting, how they enabled the measurement of physical quantities, and how they led to the estimation of man-made and abstract notions in the socio-economic domain. As data donft fall like manna from the sky, a unique feature of this book is that it explains from a teacherfs perspective how theyfre really conceived in our minds, how theyfre actually produced from individual observations, and how this defines their meaning and interpretation. It discusses the significance of standards, the use of taxonomies, and clarifies a series of misconceptions regarding the making of data. The book then describes the switch to a new research paradigm and its implications, highlights the arrival of microdata, illustrates analytical uses of data, and closes with a look at the future of data and our own role in it.
1. We Got Number 2. Measuring, With Instruments 3. Humanity's Numbers 4. The Socio-Economic Realm 5. The Art of Drawing Lines 6. The Old Guard 7. The New Era of Data 8.It's All About the Microdata 9. Data Analysis 10. The Future of Data
George Sciadas has worked in the public, private, and academic sectors. Hefs well-known in statistical circles in Canada and internationally, having worked for more than three decades at Statistics Canada and international organizations, including in several executive capacities. He has also taught at universities for many years. He earned his Ph.D. in Economics at McGill University, in Montreal. He has led many national and international projects, with research teams on all continents. He has authored numerous papers and monographs, and has been the editor of influential publications and compendia for many years.
This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.
Includes methodology for obtaining new Hardy inequalities
Applications for estimates from below of the 1-st eigenvalue of p-Laplacian are derived
Examples of the sharpness of Hardy inequality and the optimality of Hardy constant
Tsviatko Rangelov, Bulgarian Academy of Sciences, Bulgaria; Nikolai Kutev, Bulgarian Academy of Sciences, Bulgaria.
Analysis
Applied Mathematics
Differential Equations and Dynamical Systems
Mathematics
Volume 40 in the series De Gruyter Series in Nonlinear Analysis and Applications
The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.
Introduces differential equations and dynamical systems for applications in biology and ecology.
Covers the main components in cross diffusion systems:
Dynamics of solutions,
Coexistence of steady states
The persistence of evolution processes
Author information
Dung Le, University of Texas at San Antonio, USA.
Analysis
Differential Equations and Dynamical Systems
Mathematics
Publication Date 5 May 2022
ISBN print 978-3-98547-020-4
Long-Time Dispersive Estimates for Perturbations of a Kink Solution of One-Dimensional Cubic Wave Equations cover
A kink is a stationary solution to a cubic one-dimensional wave equation {(\partial_t^2-\partial_x^2)\phi = \phi-\phi^3}(Ý
t
2
?
?Ý
x
2
?
)?=???
3
that has different limits when {x}x goes to {-\infty}? and {+\infty}+, like {H(x) =\tanh(\frac{x}{\sqrt{2}})}H(x)=tanh(
2
?
x
?
). Asymptotic stability of this solution under small odd perturbation in the energy space has been studied in a recent work of Kowalczyk, Martel and Munoz. They have been able to show that the perturbation may be written as the sum {a(t)Y(x) + \psi(t,x)}a(t)Y(x)+Õ(t,x), where {Y}Y is a function in Schwartz space, {a(t)}a(t) a function of time having some decay properties at infinity, and {\psi(t,x)}Õ(t,x) satisfies some local in space dispersive estimate. These results are likely to be optimal when the initial data belong to the energy space. On the other hand, for initial data that are smooth and have some decay at infinity, one may ask if precise dispersive time decay rates for the solution in the whole space-time, and not just for {x}x in a compact set, may be obtained. The goal of this work is to attack these questions.
Our main result gives, for small odd perturbations of the kink that are smooth enough and have some space decay, explicit rates of decay for {a(t)}a(t) and for {\psi(t,x)}Õ(t,x) in the whole space-time domain intersected by a strip {|t| \leq \epsilon^{-4+c}}?t???
?4+c
, for any {c>0}c>0, where {\epsilon}? is the size of the initial perturbation. This limitation is due to some new phenomena that appear along lines {x=\pm\frac{\sqrt{2}}{3}t}x=}
3
2
?
?
t that cannot be detected by a local in space analysis. Our method of proof relies on construction of approximate solutions to the equation satisfied by {\psi}Õ, conjugation of the latter in order to eliminate several potential terms, and normal forms to get rid of problematic contributions in the nonlinearity. We use also Fermifs golden rule in order to prove that the {a(t)Y}a(t)Y component decays when time grows.