Search Results - Polynomials and rational functions of one complex variable

A brief account of Klein’s icosahedral extensions by Solanilla, Leonardo, Barreto, Erick S., Morales, Viviana

“…We present an alternative relatively easy way to understand and determine the zeros of a quintic polynomial whose Galois group is isomorphic to the group of rotational symmetries of a regular icosahedron…”
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A Remark on Holomorphic Functions Rational in Some Variables by Ivanova, O. A., Melikhov, S. N.

“… We use the Kronecker method for establishing some criterion for the rationality of a holomorphic function of one complex variable…”
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The rational Heun operator and Wilson biorthogonal functions by Tsujimoto, Satoshi, Vinet, Luc, Zhedanov, Alexei

“…We consider the rational Heun operator defined as the most general second-order q -difference operator which sends any rational function of type [ ( n - 1 ) / n…”
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Some remarks on approximation in several complex variables by Falcó, Javier, Gauthier, Paul M., Manolaki, Myrto, Nestoridis, Vassili

“…)$ which is smaller than the classical one $A(K)$ . In the present paper, we investigate when these two algebras coincide and compare them with the classes of all plausibly approximable functions by polynomials or rational functions or functions…”
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Frontiers in complex dynamics: in celebration of John Milnor's 80th birthday by Bonifant, Araceli, Lyubich, Misha, Sutherland, Scott

“…John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize…”
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The Mother Body Phase Transition in the Normal Matrix Model by Bleher, Pavel M., Silva, Guilherme L. F.

“… & López, we consider multiple orthogonal polynomials associated…”
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On algebraic dependencies between Poincaré functions by PAKOVICH, FEDOR

“…Let A be a rational function of one complex variable of degree at least two, and $z_0$ its repelling fixed point with the multiplier…”
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Current Trends in Symmetric Polynomials with their Applications by Kim, Taekyun

“… Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric…”
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Ellipsoidal designs and the Prouhet–Tarry–Escott problem: Ellipsoidal designs and the Prouhet–Tarry–Escott problem by Matsumura, Hideki, Sawa, Masanori

“…) as a natural generalization of the classical one-dimensional PTE problem ( PTE 1 ). We first provide a combinatorial criterion for the construction of solutions of the PTE 2 from a pair of ellipsoidal designs…”
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Dynamics in One Complex Variable. (AM-160): Third Edition. (AM-160) by Milnor, John

“… The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology…”
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On the Blaschke Factors in Polydisk by Durakov, Matvey E

“… We construct inner rational functions for the case of three complex variables, in particular, using the Lee-Yang polynomial from the theory of phase transitions…”
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ON THE EQUATION P(f) = Q(g), WHERE P, Q ARE POLYNOMIALS AND f, g ARE ENTIRE FUNCTIONS by Pakovich, F.

“…In 1922 Ritt described polynomial solutions of the functional equation P(f) = Q(g). In this paper we describe solutions of the equation above in the case when P, Q are polynomials while f, g are allowed to be arbitrary entire functions…”
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The Maximum Number of Zeros of r(z)-z¯ Revisited by Liesen, Jörg, Zur, Jan

“…Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions f ( z ) = p ( z ) q ( z ) - z…”
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The nearest complex polynomial with a zero in a given complex domain by Luo, Zhongxuan, Hu, Wenyu, Sheen, Dongwoo

“…Given a univariate complex polynomial f and a closed complex domain D , whose boundary C is a curve parameterized by a piecewise rational function, we propose two computational algorithms for finding…”
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More infinite products: Thue–Morse and the gamma function by Allouche, J.-P., Riasat, S., Shallit, J.

“… . The purpose of this paper is twofold. On the one hand, we try to find other rational functions for which similar infinite products involving the ± 1 Thue…”
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On amenable semigroups of rational functions by Pakovich, Fedor

“…We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation…”
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An upper bound for the number of gravitationally lensed images in a multiplane point-mass ensemble by Perry, Sean

“… . Our proof uses the theory of resultants applied to a complex variable representation of the so-called lensing map…”
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Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples by Platte, Rodrigo B., Trefethen, Lloyd N., Kuijlaars, Arno B. J.

“…It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions…”
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On axially rational regular functions and Schur analysis in the Clifford-Appell setting by Alpay, Daniel, Colombo, Fabrizio, De Martino, Antonino, Diki, Kamal, Sabadini, Irene

“…: the Fueter mapping theorem and the generalized Cauchy–Kovalevskaya (GCK) extension. These results allow one to obtain axially regular functions starting from analytic functions of one real or complex variable…”
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Lyapunov function computation for autonomous systems with complex dynamic behavior by Polcz, Péter, Szederkényi, Gábor

“… is given in the form of rational functions (i.e., fraction of polynomials). The Lyapunov function is searched in a parameterized quadratic form of rational terms of the state variables…”
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