Debnath Lokenath Debnath – författare

This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler''s works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics.The book is written to provide a definitive impression of Euler''s personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author''s historically motivated method of teaching, special attention is given to demonstrate that Euler''s work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler''s extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research.Erratum

This is perhaps the first book containing biographical information of Sir James Lighthill and his major scientific contributions to the different areas of fluid mechanics, applied mathematics, aerodynamics, linear and nonlinear waves in fluids, geophysical fluid dynamics, biofluiddynamics, aeroelasticity, boundary layer theory, generalized functions, and Fourier series and integrals. Special efforts is made to present Lighthill''s scientific work in a simple and concise manner, and generally intelligible to readers who have some introduction to fluid mechanics. The book also includes a list of Lighthill''s significant papers.Written for the mathematically literate reader, this book also provides a glimpse of Sir James'' serious attempt to stimulate interest in mathematics and its diverse applications among the general public of the world, his profound influence on teaching of mathematics and science with newer applications, and his deep and enduring concern on enormous loss of human lives, economic and marine resources by natural hazards. By providing detailed background information and knowledge, sufficient to start interdisciplinary research, it is intended to serve as a ready reference guide for readers interested in advanced study and research in modern fluid mechanics.

In 1934, G. H. Hardy et al. published a book entitled “Inequalities”, in which a few theorems about Hilbert-type inequalities with homogeneous kernels of degree-one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof. Bicheng Yang in their four published books.This monograph deals with half-discrete Hilbert-type inequalities. By means of building the theory of discrete and integral Hilbert-type inequalities, and applying the technique of Real Analysis and Summation Theory, some kinds of half-discrete Hilbert-type inequalities with the general homogeneous kernels and non-homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed.The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.