“…His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). …”
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“…A key ingredient in this proof is the study of the Fourier transforms of distributions on \mathfrak g, the Lie algebra of G. In particular, Harish-Chandra shows that if the support of a G-invariant distribution on \mathfrak g is compactly generated, then its Fourier transform has an asymptotic expansion about any semisimple point of \mathfrak g. …”
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“…Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential. .…”
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“…The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.…”
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“…Integrates modern cryptography, physical-layer security, QKD, covert communication, and cyber security technologies and shows students how they can work together to solve issues Does not require prior knowledge in corresponding fields or prerequisite material except basic concepts on vector algebra at undergraduate level. Can be used in multiple courses, such as modern cryptography, physical-layer security, QKD, or a combination of these.…”
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“…This book would be an ideal textbook for advanced courses, for it requires background only at the level of standard courses in mathematical analysis and linear algebra and some familiarity with elementary concepts and results in the theory of Banach spaces. …”
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“…He gives a useful review of probability, making the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics is slowly and carefully developed, in order to make self-study easier. …”
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“…They also allow us to use methods from calculus and analysis to obtain results in algebra and number theory. This book is an elementary introduction to p-adic numbers. …”
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“…Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics Review of the first edition: This book presents an introduction to differential geometry and the calculus on manifolds with a view on some of its applications in physics. … The present author has succeeded in writing a book which has its own flavor and its own emphasis, which makes it certainly a valuable addition to the literature on the subject. …”
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“…Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. …”
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“…It provides various tools, utilities, and facilities for statistics, algebra, visualization, multi-varied methods, data serialization, parallelized data computation, etc. …”
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“…Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. …”
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“…The first two talks (2 May at 11.00 hrs and 11 May* at 14.00 hrs) will be by way of mathematical introduction for those whose matrix algebra and solution of differential equations may need refreshing. …”
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“…We explain all details of the calculations and mathematical tools: Lagrangian and Hamiltonian formalism for the systems with finite degree of freedom and for fields, Geometric Optics, the Hamilton-Jacobi equation and WKB approximation, Noether theory of invariants including the theorem on currents, four conservation laws (energy, momentum, angular momentum and charge), Lie algebra of angular momentum and spherical functions, scattering theory (limiting amplitude principle and limiting absorption principle), the Lienard-Wiechert formulas, Lorentz group and Lorentz formulas, Pauli theorem and relativistic covariance of the Dirac equation, etc. …”
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“…This is not only a shift in the designation but a real change of mathematical structure, with a new underlying algebra. Diffusion processes commonly start with a stroke at one vertex and diffuse over the network. …”
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“…In fact, given a variational problem, GBM establishes the corresponding Euler equations by means of a systematic procedure, which is easy to recall, based in both elementary calculus and algebra without having to memorize the known formulas. …”
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“…The anchoring of this method in a framework of integral geometry and linear algebra highlights its possibilities and limitations.…”
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“…RESULTS: We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model. …”
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“…It aims at minimizing code duplication by cleanly separating pixel-algebra, data access and data representation in memory. …”
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“…Using structural magnetic resonance imaging of 48 healthy adults in conjunction with voxel-based morphometry and diffeomorphic anatomical registration using exponentiated lie algebra (VBM-DARTEL), positive associations between self-esteem and regional grey matter volume were indeed found in the anterior cingulate cortex (ACC), right lateral prefrontal cortex (LPFC), right hippocampus, and left hypothalamus. …”
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