Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to
This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.
Advanced Heat Transfer, Second Edition provides a comprehensive presentation of intermediate and advanced heat transfer, and a unified treatment including both single and multiphase systems. It provides a fresh perspective, with coverage of new emerging fields within heat transfer, such as solar energy and cooling of microelectronics. Conductive, radiative and convective modes of heat transfer are presented, as are phase change modes. Using the latest solutions methods, the text is ideal for the range of engineering majors taking a second-level heat transfer course/module, which enables them to succeed in later coursework in energy systems, combustion, and chemical reaction engineering.
This book constitutes the proceedings of the 20th International Workshop on Computer Algebra in Scientific Computing, CASC 2018, held in Lille, France, in September 2018. The 24 full papers of this volume presented with an abstract of an invited talk and one paper corresponding to another invited talk were carefully reviewed and selected from 29 submissions. They deal with cutting-edge research in all major disciplines of computer algebra in sciences such as physics, chemistry, life sciences, and engineering. Chapter “Positive Solutions of Systems of Signed Parametric Polynomial Inequalities” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.
A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.
This book provides a unique and comprehensive overview of the latest advances, challenges and accomplishments in the rapidly growing field of theoretical and computational materials science. Today, an increasing number of industrial communities rely more and more on advanced atomic-scale methods to obtain reliable predictions of materials properties, complement qualitative experimental analyses and circumvent experimental difficulties. The book examines some of the latest and most advanced simulation techniques currently available, as well as up-to-date theoretical approaches adopted by a selected panel of twelve international research teams. It covers a wide range of novel and advanced materials, exploring their structural, elastic, optical, mass and electronic transport properties. The cutting-edge techniques presented appeal to physicists, applied mathematicians and engineers interested in advanced simulation methods in materials science. The book can also be used as additional literature for undergraduate and postgraduate students with majors in physics, chemistry, applied mathematics and engineering.
Evgenii Mikhailovich Lifshitz is perhaps best known for his long association with his mentor Lev D Landau, with whom he co-wrote the classic Course of Theoretical Physics, but he was a noted and respected Soviet physicist in his own right. Born in the Ukraine to a scientific family, his long and distinguished career will be remembered for three things - his collaboration with Landau on the internationally acclaimed Course of Theoretical Physics, his work as editor of the Journal of Experimental and Theoretical Physics, and his scientific papers. As well as his work with Landau, E\M\Lifshitz collaborated with many noted Soviet scientists such as I\M\Khalatnikov, I\E\Dyzaloshinskii, V\V\Sudakov, V\A\Belinskii and the editor of this book, L\P\Pitaevskii. Many of the papers presented in this book include their contribution. Collected together they give a comprehensive and penetrating insight into the man and his work, clearly showing Lifshitz's contribution to physics and the influences on his work.