Results 21 to 30 of about 387,708 (163)
Zeros of Convex Combinations of Elementary Families of Harmonic Functions
Mathematics, 2023 Brilleslyper et al. investigated how the number of zeros of a one-parameter family of harmonic trinomials varies with a real parameter. Brooks and Lee obtained a similar theorem for an analogous family of harmonic trinomials with poles. In this paper, we
Jennifer Brooks +4 more
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Generalizations of the Eneström–Kakeya Theorem Involving Weakened Hypotheses
AppliedMath, 2022 The well-known Eneström–Kakeya Theorem states that, for P(z)=∑ℓ=0naℓzℓ, a polynomial of degree n with real coefficients satisfying 0≤a0≤a1≤⋯≤an, then all the zeros of P lie in |z|≤1 in the complex plane. Motivated by recent results concerning an Eneström–
Robert Gardner, Matthew Gladin
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Mathematics, 2019 In this paper, we study differential equations arising from the generating function of the ( r , β ) -Bell polynomials. We give explicit identities for the ( r , β ) -Bell polynomials. Finally, we find the zeros of the ( r , &#
Kyung-Won Hwang +2 more
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Unnormalized differences between zeros of L-functions [PDF]
, 2014 We study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function. We establish a precise measure which explains the phenomenon, that the location of each Riemann zero is encoded in ...
Ford, Kevin, Zaharescu, Alexandru
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AxiomsOrthogonal polynomials on radial rays in the complex plane were introduced and studied intensively in several papers almost three decades ago. This paper presents an account of such kinds of orthogonality in the complex plane, as well as a number of new ...
Gradimir V. Milovanović
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Machines, 2022 This paper deals with the stability characteristics of zeros for sampled-data models with a class of triangle sample and hold realized by a traditional zero-order hold.
Minghui Ou +6 more
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REFINEMENT OF SOME BERNSTEIN TYPE INEQUALITIES FOR RATIONAL FUNCTIONS
Проблемы анализа, 2022 In this paper, we establish some Bernstein-type inequalities for rational functions with prescribed poles. These results refine prior inequalities on rational functions and strengthen many well-known polynomial inequalities.
Idrees Qasim
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Higher Monotonicity Properties for Zeros of Certain Sturm-Liouville Functions
Mathematics, 2023 In this paper, we consider the differential equation y″+ω2ρ(x)y=0, where ω is a positive parameter. The principal concern here is to find conditions on the function ρ−1/2(x) which ensure that the consecutive differences of sequences constructed from the ...
Tzong-Mo Tsai
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Convexity of the zeros of some orthogonal polynomials and related functions
, 2008 We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions ...
Ahmed +17 more
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On the Zeros of Polynomials with Restricted Coefficients
Annales Mathematicae Silesianae, 2023 Let P(z)=∑j=0najzjP\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}} be a polynomial of degree n such that an ≥ an−1 ≥ . . . ≥ a1 ≥ a0 ≥ 0. Then according to Eneström-Kakeya theorem all the zeros of P (z) lie in |z| ≤ 1.
Zargar B. A., Gulzar M. H., Ali M.
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