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Proceedings of the American Mathematical Society, 1960 Then G is a rationalfunction of x if and only if a is a rational number. As usual, [x] denotes the integral part of x and { x } the fractional part of x, so that x = [x] + { x }. We first prove LEMMA 1. Let a be a real irrational number, and let R be a finite set of non-integral real numbers. Then there are infinitely many positive integers m such that
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Exponentiated Extended Weibull-Power Series Class of Distributions [PDF]
, 2015 In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series ...
Jafari, Ali Akbar, Tahmasebi, Saeid
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Natural Frequencies of Axisymmetric Vibrations of Thin Hyperbolic Circular Plates with Clamped Edges
International Journal of Applied Mechanics and Engineering, 2017 A free vibration analysis of homogeneous and isotropic circular thin plates with nonlinear thickness variation and clamped edges is considered. The limited independent solutions of differential Euler equation were expanded in the power series based on ...
J. Jaroszewicz
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Factorisation theorems for generalised power series [PDF]
, 2017 Fields of generalised power series (or Hahn fields), with coefficients in a field and exponents in a divisible ordered abelian group, are a fundamental tool in the study of valued and ordered fields and asymptotic expansions.
L'Innocente, Sonia, Mantova, Vincenzo
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STATCOM Model Using Holomorphic Embedding
IEEE Access, 2019 Convergence characteristics of existing Newton-Raphson (N-R) load-flow based FACTS devices models are affected by the choice of initial conditions. Many a time, a solution is either spurious or fails to converge.
Pradeep Singh, Rajive Tiwari
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Irrational Power Series. III [PDF]
Proceedings of the American Mathematical Society, 1965 Several writers (see [1 ] for references) have shown that if f(y) satisfies various conditions, then F(x) is not a rational function of x, and some have shown that the circle x| = 1 is a line of essential singularities for F(x). I notice a very simple way of dealing with such questions. The method is really that of Hecke, but its possibilities have not
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Mathematics, 2021 In this paper, we deal with some applications of the network simulation method (NMS) to the non-linear differential equations derived of a parametric family associated to stated problems by Newton in and others like the parabolic mirror and van der Pol ...
Joaquín Solano +2 more
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Power Series Method For Solving Nonlinear Volterra Integro-Differential Equations of The Second Kind [PDF]
Engineering and Technology Journal, 2010 In this work, we present the power series method for solving special typesof the first order nonlinear Volterra integro-differential equations of the second kind.
Hanan Mahmood Hasson
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Applied Mathematics in Science and Engineering, 2022 A class of nonlinear variational problems describing incompressible fluids and solids by stationary Stokes equations given in a planar domain with a crack (infinitely thin flat plate in fluids) is considered.
Victor A. Kovtunenko, Kohji Ohtsuka
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MANAS: Journal of EngineeringIn this paper, we apply Laplace-Padé Series method to solve linear and non-linear differentialalgebraicequations (DAEs). Firstly, The basic properties of the Laplace-Padé Series method aregiven.
Nooriza Myrzabekova, Ercan Celık
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