“…The first edition of this book emerged from a set of notes written in the 1970sfor a sophomore-junior level course at the University at Albany entitled "Classical Algebra." The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre­ ciate the basic concepts of abstract algebra. …”
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“…Based on a discussion of multipliers on locally compact groups in the third chapter all the well-known observables of classical quantum theory like linear momenta, orbital and spin angular momenta, kinetic and potential energies, gauge operators etc., are derived solely from Galilean covariance in the last chapter. …”
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“…Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert’s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. …”
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“…We perform our investigations using coarse-grained particle-level simulations with Brownian dynamics, classical density functional theory, and the mean-field Poisson–Boltzmann theory. …”
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“…In this study, we employed an ab initio computational study on solid carbon dioxide phases I and VII at high pressure and predicted their structures, energies and phase transition using the second-order Møller–Plesset perturbation (MP2) theory. Compared to the classical force field method and density-functional theory (DFT), MP2 is capable of describing covalent, ionic, hydrogen-bonds, and dispersion interactions accurately. …”
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“…The book - proves the empirical nucleation nature of traffic breakdown in networks - discusses the origin of the failure of classical traffic and transportation theories - shows that the three-phase theory is incommensurable with the classical traffic theories, and - explains why current state-of-the art dynamic traffic assignments tend to provoke heavy traffic congestion, making it a valuable reference resource for a wide audience of scientists and postgraduate students interested in the fundamental understanding of empirical traffic phenomena and related data-driven phenomenology, as well as for practitioners working in the fields of traffic and transportation engineering.…”
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“…We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. …”
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“…A classical force field approach was used to characterize the solvation dynamics of high-density CO(2)(g) by monoethanolamine (MEA) at the air–liquid interface. …”
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“…Based on the Fermi Golden Rule, the particle–substrate coupling is derived in terms of the photon absorption probability assuming a local dipole field. An increase in photocurrent gain is achieved through the optical coupling. …”
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“…With the rise of smart robots in the field of industrial automation, the motion control theory of the robot servo controller has become a research hotspot. …”
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“…A mounting number of studies have revealed that the classical nucleation theory is not suitable for all nucleation process of biominerals, and phase-separated structures such as polymer-induced liquid precursors (PILPs) play essential roles in the non-classical nucleation processes. …”
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“…As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. …”
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“…The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. …”
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“…Assuming randomness of the electrical field phase of the input beam, we reformulated and significantly simplified the rigorous conical refraction theory. …”
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“…The Skorokhod Embedding Problem is one of the classical problems in the theory of stochastic processes, with applications in many different fields [cf.  …”
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“…The one-century-old theory of orthogonal genetic variance decomposition originated the field of quantitative genetics and has kept on being improved ever since. …”
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“…Cartan theory remains a touchstone in modern differential geometry, and Clelland's book provides a fine new introduction that includes both classic and contemporary geometric developments and is supplemented by Maple symbolic software routines that enable the reader to both tackle the exercises and delve further into this fascinating and important field of contemporary mathematics. …”
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“…The first part of the volume is devoted to the description of scattering processes in the context of relativistic quantum field theory. The use of the semi-classical approximation allows us to illustrate the relevant computation techniques in a reasonably small amount of space. …”
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“…It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. …”
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“…The spatial boundary conditions for the quark fields are chosen such that the massless Dirac operator in the classical background field has a large smallest eigenvalue. …”
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