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eebo-0021

Arithmetic --- Square root --- Numbers, Natural

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La relation entre l’hypoténuse et les autres côtés d’un triangle rectangle est l’une des découvertes scientifiques les plus importantes de l’humanité. Le théorème qui la décrit a pris le nom de Pythagore, l’un des personnages les plus fascinants et les plus surprenants de l’histoire de la science.

Pythagorean theorem --- Théorème de Pythagore --- Square root. --- Racine carrée. --- Théorème de Pythagore. --- Racine carrée. --- Théorème de Pythagore.

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The book continues with an experimental analysis conducted to obtain accurate and complete information about electric vehicles in different traffic situations and road conditions. For the experimental analysis in this study, three different electric vehicles from the Edinburgh College leasing program were equipped and tracked to obtain over 50 GPS and energy consumption data for short distance journeys in the Edinburgh area and long-range tests between Edinburgh and Bristol. In the following section, an adaptive and robust square root cubature Kalman filter based on variational Bayesian approximation and Huber’s M-estimation is proposed to accurately estimate state of charge (SOC), which is vital for safe operation and efficient management of lithium-ion batteries. A coupled-inductor DC-DC converter with a high voltage gain is proposed in the following section to match the voltage of a fuel cell stack to a DC link bus. Finally, the book presents a review of the different approaches that have been proposed by various authors to mitigate the impact of electric buses and electric taxis on the future smart grid.

adaptive --- electric vehicle --- state of charge (SOC) --- high voltage gain --- lithium-ion battery --- climate change --- ssustainable transport --- driving cycle --- smart grid --- robust --- battery powered vehicle --- Huber’s M-estimation --- electric taxi --- public transportation --- sustainable development --- DC-DC converter --- square root cubature Kalman filter (SRCKF) --- coupled inductor --- fuel cell vehicles --- charging approaches --- ripple minimization current --- variational Bayesian approximation --- electric propulsion --- electric bus

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"Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number P can be computed in time bounded by a fixed power of the logarithm of P. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations"-- "This book represents a major step forward from explicit class field theory, and it could be described as the start of the 'explicit Langlands program'"--

Galois modules (Algebra) --- Class field theory. --- Algebraic number theory --- Galois module structure (Algebra) --- Galois's modules (Algebra) --- Modules (Algebra) --- Arakelov invariants. --- Arakelov theory. --- Fourier coefficients. --- Galois representation. --- Galois representations. --- Green functions. --- Hecke operators. --- Jacobians. --- Langlands program. --- Las Vegas algorithm. --- Lehmer. --- Peter Bruin. --- Ramanujan's tau function. --- Ramanujan's tau-function. --- Ramanujan's tau. --- Riemann surfaces. --- Schoof's algorithm. --- Turing machines. --- algorithms. --- arithmetic geometry. --- arithmetic surfaces. --- bounding heights. --- bounds. --- coefficients. --- complex roots. --- computation. --- computing algorithms. --- computing coefficients. --- cusp forms. --- cuspidal divisor. --- eigenforms. --- finite fields. --- height functions. --- inequality. --- lattices. --- minimal polynomial. --- modular curves. --- modular forms. --- modular representation. --- modular representations. --- modular symbols. --- nonvanishing conjecture. --- p-adic methods. --- plane curves. --- polynomial time algorithm. --- polynomial time algoriths. --- polynomial time. --- polynomials. --- power series. --- probabilistic polynomial time. --- random divisors. --- residual representation. --- square root. --- square-free levels. --- tale cohomology. --- torsion divisors. --- torsion.

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The description for this book, Contributions to Fourier Analysis. (AM-25), will be forthcoming.

Fourier analysis. --- Analysis, Fourier --- Mathematical analysis --- Absolute value. --- Almost periodic function. --- Approximation. --- Bessel function. --- Bilinear map. --- Boundary value problem. --- Characterization (mathematics). --- Coefficient. --- Compact space. --- Comparison theorem. --- Conservative vector field. --- Constant function. --- Continuous function. --- Corollary. --- Counterexample. --- Diagonalization. --- Diagram (category theory). --- Diameter. --- Dimension. --- Dirichlet kernel. --- Dirichlet problem. --- Dirichlet's principle. --- Distribution function. --- Exponential polynomial. --- Exponential sum. --- Fourier series. --- Fourier transform. --- Harmonic function. --- Hilbert space. --- Hölder's inequality. --- Integer. --- Interpolation theorem. --- Linear combination. --- Lp space. --- Measurable function. --- Measure (mathematics). --- Partial derivative. --- Partial differential equation. --- Periodic function. --- Poisson formula. --- Polynomial. --- Power series. --- Quantity. --- Rectangle. --- Remainder. --- Semicircle. --- Several complex variables. --- Sign (mathematics). --- Simple function. --- Special case. --- Sphere. --- Square root. --- Step function. --- Subsequence. --- Subset. --- Theorem. --- Theory. --- Triangle inequality. --- Two-dimensional space. --- Uniform continuity. --- Uniform convergence. --- Variable (mathematics). --- Vector field. --- Vector space.