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61“…The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambien…”
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62“…We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. …”
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63“…Contents include the properties of the triangle and the quadrilateral; equations, sub-multiple angles, and inverse functions; hyperbolic, logarithmic, and exponential functions; and expansions in power-series. Further topics encompass the special hyperbolic functions; projection and finite series; complex numbers; de Moiv…”
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64“…his book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition. …”
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65“…A simple model verifies analytically that our experimental scheme provides an integrator generating a power series that is third order in time. The model identifies two parameters that govern the kinetics and shows how the initial concentrations of the substrates are the coefficients in the power series.…”
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66por Tartakoff, David S“…The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. …”
Publicado 2011
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67por Koblitz, Neal“…After reviewing the basics (the construction of p-adic numbers and the p-adic analog of the complex number field, power series and Newton polygons), the author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration. p-adic gamma functions are introduced, and their relationship to L-series is explored. …”
Publicado 1980
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68por Abhyankar, Shreeram Shankar“…The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. …”
Publicado 1964
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69por Pauli, Wolfgang“…Källén is working on the question to look behind the veil of Dyson's power series. The new Swiss "infant prodigy", Alder, is working on angular correlation, shell model and related problems and Shafrot on superconductivity. …”
Publicado 2000
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70“…Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron-Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply poly…”
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71“…We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. …”
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72por Goertz, Florian“…We discuss the remaining model dependence (which is inherent even in the EFT approach to have control over the error due to the truncation of the power series), as well as prospects to test paradigms of UV physics. …”
Publicado 2017
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73por Gullberg, JanTabla de Contenidos: “…Numbers and language -- Systems of numeration -- Types of numbers -- Cornerstones of mathematics -- Combinatorics -- Symbolic logic -- Set theory -- Introduction to sequences and series -- Theory of equations -- Introduction to functions -- Overture to the geometries -- Elementary geometry -- Trigonometry -- Hyperbolic functions -- Analytic geometry -- Vector analysis -- Fractals -- Matrices and determinants -- Embarking on calculus -- Introduction to differential calculus -- Introduction to integral calculus -- Power series -- Indeterminate limits -- Complex numbers revisited -- Extrema and critical points -- Arc length -- Centroids -- Area -- Volume -- Motion -- Harmonic analysis -- Methods of approximation -- Probability theory -- Differential equations.…”
Publicado 1997
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74“…Solutions of the equations are obtained in terms of power series and of K-transforms and determine in the general case their asymptotic behaviour for large fireball mass. …”
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75por Munteanu, Bogdan Gheorghe“…In this paper, a statistical simulation algorithm for the power series distribution, called the Max Erlang Binomial distribution, is proposed, analyzed, and tested for bladder cancer remission time data. …”
Publicado 2021
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76por Said-Houari, Belkacem“…After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. …”
Publicado 2015
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77“…It furnishes a gauge invariant infrared cut off, and yields for small values of the phases a systematic procedure for obtaining a power series in the coupling g and glog(1/g). It breaks the centergroup symmetry of the gauge group only at high temperature so leads to domain walls disappearing at low temperatures. …”
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78por Chao, A W“…The topics covered are: (1) Panofsky-Wenzel and Planar Wake Theorems; (2) Echo Effect; (3) Crystalline Beam; (4) Fast Ion Instability; (5) Lawson-Woodward Theorem and Laser Acceleration in Free Space; (6) Spin Dynamics and Siberian Snakes; (7) Symplectic Approximation of Maps; (8) Truncated Power Series Algebra; and (9) Lie Algebra Technique for nonlinear Dynamics. …”
Publicado 2002
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79“…It follows that the S-matrix has unitary adiabatic limit as an operator-valued formal power series in Fock space. (4 refs).…”
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80“…In this paper, we obtain some improved exponential approximation inequalities for the functions [Formula: see text] and [Formula: see text] , and we prove them by using the properties of Bernoulli numbers and new criteria for the monotonicity of quotient of two power series.…”
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