“…This scheme is developed based on Sumudu transform and the residual power series method (RPSM) that generates the solution in the form of a series. …”
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“…We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., [Formula: see text]) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor [Formula: see text] in the n term of the power series expansion with respect to the fugacity z. …”
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“…The alternative direction multiplier method is chosen to optimize the model, and the k-terms power series is applied in order to derive the LogDet function into the augmented Lagrange form. …”
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“…Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. …”
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“…The Spaces R, Rk, and CThe Real Numbers RThe Real Spaces RkThe Complex Numbers CPoint-Set Topology Bounded SetsClassification of Points Open and Closed SetsNested Intervals and the Bolzano-Weierstrass Theorem Compactness and Connectedness Limits and Convergence Definitions and First Properties Convergence Results for SequencesTopological Results for Sequences Properties of Infinite SeriesManipulations of Series in RFunctions: Definitions and Limits DefinitionsFunctions as MappingsSome Elementary Complex FunctionsLimits of FunctionsFunctions: Continuity and Convergence Continuity Uniform Continuity Sequences and Series of FunctionsThe DerivativeThe Derivative for f: D1 → RThe Derivative for f: Dk → RThe Derivative for f: Dk → RpThe Derivative for f: D → CThe Inverse and Implicit Function TheoremsReal IntegrationThe Integral of f: [a, b] → RProperties of the Riemann Integral Further Development of Integration TheoryVector-Valued and Line IntegralsComplex IntegrationIntroduction to Complex Integrals Further Development of Complex Line Integrals Cauchy's Integral Theorem and Its Consequences Cauchy's Integral Formula Further Properties of Complex Differentiable Functions Appendices: Winding Numbers Revisited Taylor Series, Laurent Series, and the Residue Calculus Power SeriesTaylor Series Analytic FunctionsLaurent's Theorem for Complex FunctionsSingularitiesThe Residue Calculus Complex Functions as MappingsThe Extended Complex PlaneLineal Fractional TransformationsConformal MappingsBibliographyIndexExercises appear at the end of each chapter.…”
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“…In this work, a deep learning approach with multi-head attention and a multi-scale hierarchical learning mechanism based on encoder-decoder architecture is developed to accurately forecast voltage and power series. By using the predicted voltage without ISCs as the standard and detecting the consistency of the collected and predicted voltage series, we develop a method to detect ISCs quickly and accurately. …”
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“…Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. …”
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“…This system is then solved to obtain the coefficients of the power series solution. The main advantage of the proposed technique is that it does not require an index reduction nor a linearization. …”
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“…To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. …”
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“…The Owen-Naylor integral equation for absorption of rays in the walls of cylindrical radium sources has been evaluated by a power series expansion of the integrand. Absorption coefficients and correction factors for platinum and Moael metal (materials commonly used for source capsules) have been computed for the NBS chamber.…”
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“…By characterizing the spectral radius of appropriate matrix power series, we explore how the universality results on the limiting behaviour of classical walk-based centrality measures extend to these non-cycling cases. …”
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“…Our contribution lies in the derivation of a generalised Lagrangian, in the form of a power series expansion, that satisfies these constraints. …”
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“…The solution is created by constructing a single second-order nonlinear differential equation in [Formula: see text] and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. …”
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“…Given a locally integrable structure [Formula: see text] over a smooth manifold [Formula: see text] and given [Formula: see text] we define the Borel map of[Formula: see text] atp as the map which assigns to the germ of a smooth solution of [Formula: see text] at p its formal Taylor power series at p. In this work we continue the study initiated in Barostichi et al. …”
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“…Motivated by a conjecture on the convexity of the ratio [Formula: see text] for [Formula: see text] , using the monotonicity rules for a ratio of two power series and an elementary technique, we present fully the convexity of the functions [Formula: see text] , [Formula: see text] and [Formula: see text] for [Formula: see text] on [Formula: see text] in different value ranges of [Formula: see text] , which give an answer to the conjecture and extend known results. …”
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“…In addition, to determine the reinforcing effect of restrained nano-/micro-rods, a new system of linear equations with the concept of the infinite power series is presented. After performing the mathematical processes known as Fourier sine series, Stokes’ transformation and successive integration, we finally obtain a coefficient matrix in terms of infinite series for various rigid or deformable boundary conditions. …”
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“…We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. …”
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“…We pay special attention to the power series coefficients of Heun functions, which are also important in fields such as quantum mechanics and general relativity, as well as the binary choice models studied here. …”
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“…As an application of 3° we have a generalization of Bernstein's theorem on absolute convergence of power series that belong to a Hölder class.…”
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“…What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. …”
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