“…As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. …”
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“…Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. …”
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“…Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. …”
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“…Classical work on the theory to noncommutative power series has been augmented more recently to areas such as representation theory, combinatorial mathematics and theoretical computer science. …”
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“…D 99, 104077 (2019)] we studied the quasinormal mode spectrum of spacetimes for which the radial potentials are slightly modified from their general relativistic form, writing generic small modifications as a power-series expansion in the radial coordinate. We assumed that the perturbations in the quasinormal frequencies are linear in some perturbative parameter, and that there is no coupling between the perturbation equations. …”
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“…The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. …”
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“…We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. …”
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“…The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. …”
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“…Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. …”
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“…Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. …”
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“…The book allows aspiring researchers to update their understanding of prime rings, generalized derivations, generalized semiderivations, regular semigroups, completely simple semigroups, module hulls, injective hulls, Baer modules, extending modules, local cohomology modules, orthogonal lattices, Banach algebras, multilinear polynomials, fuzzy ideals, Laurent power series, and Hilbert functions. All the contributing authors are leading international academicians and researchers in their respective fields. …”
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“…The accelerator model is represented as a product of unperturbed and perturbed exponential operators with the exponent of the perturbed operator given as a power series in the perturbation parameter. Normal forms can be applied to this representation and the lattice parameters are used to control the normal form Hamiltonian and normal form transformation. …”
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“…In the article, we present new bounds for the function [Formula: see text] on the interval [Formula: see text] and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function.…”
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“…Starting with elementary results, the book advances to topics such as: uniform coherence, regular rings, rings of small homological dimensions, polynomial and power series rings, group rings and symmetric algebra over coherent rings. …”
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“…In such regions W can be expressed as a power series, the coefficients of which being the, multipole components of the field with respect to the origin of the series expansion. …”
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“…We choose the smallest diffusion coefficient as a small parameter in a power series expansion whose components fulfill relatively simple equations. …”
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“…Furthermore, the gradient coefficient is employed as the representation of the relation with the layer thickness and the material parameters, and the power series method is applied to solve the variable coefficients governing the equations. …”
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“…In the modified Riemann Liouville (mRL) frame, we formulate the fractional TOV (FTOV) equations and introduce an analytical solution. Using power series expansions in solving FTOV equations yields a limited physical range to the convergent power series solution. …”
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“…Given a power series expansion in two parameters alpha and t (with, for instance, alpha =O(1/10) and t>>>1), the sum of the leading asymptotic part in t of each individual term in the series does not in general give the correct asymptotic behaviour of the whole sum of the series. …”
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