Results 61 to 70 of about 2,960 (152)

Unicity Results Concerning of difference monomials of L-function and a meromorphic function

Ratio Mathematica
In this paper, we study the value distribution of $\mathcal{L}$-function in the extend Selberg class and a non-constant transcendental meromorphic $\mathsf{f}$ function with finitely many zeros of finite order, sharing a polynomial with its difference ...
Harina Waghamore P, Roopa M.
doaj   +1 more source

Some Bounds for the Polar Derivative of a Polynomial

International Journal of Mathematics and Mathematical Sciences, 2018
The polar derivative of a polynomial p(z) of degree n with respect to a complex number α is a polynomial np(z)+α-zp′(z), denoted by Dαp(z). Let 1≤R≤k. For a polynomial p(z) of degree n having all its zeros in z≤k, we investigate a lower bound of modulus ...
Jiraphorn Somsuwan, Keaitsuda Maneeruk Nakprasit   +1 more
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A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems

Mathematics, 2018
In this paper, by transforming the given over-determined system into a square system, we prove a necessary and sufficient condition to certify the simple real zeros of the over-determined system by certifying the simple real zeros of the square system ...
Xiaojie Dou, Jin-San Cheng
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On the Zeros of Polynomials

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1977
1. Govil and Rahman [1, Theorem 1] have proved the fol- lowing theorem.n Theorem A. Let p (z) = £ aj^ k“0 z’^ ( 0) be a polynomiai ofdegree n with complex coefficients such that for some a>«-1 I a^ •11-2 a' I »ol-Then p (z) has ali its zeros in |z Kj, where Kj is the greatest positive root of the trinomial equation K"+ı - 2K" + 1 =
openaire   +4 more sources

Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients

International Journal of Differential Equations, 2015
We consider the equation u″=P(z)u+F(z)  (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let zk(u)  (k=1,2,…) be the zeros of a solution u(z) to that equation. Lower estimates for the products ∏k=1j|zk(u)|  (j=1,2,…) are derived.
Michael Gil’
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Zeros of difference polynomials

Journal of Approximation Theory, 1992
Studies --- both analytic and numerical --- on polynomials have been of immense interest for long. Here the authors deal in detail with various questions relating to the zeros of difference polynomials. Particularly, defining the difference operator by \(\Delta f(x)=f(x+1)-f(x)\), the polynomial \(\Delta^ mx^ n\) of degree \((n-m)\) having \((n-m ...
Evans, Ronald J, Wavrik, John J
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Inequalities Involving the Derivative of Rational Functions With Prescribed Poles

Journal of Applied Mathematics
This paper gives an upper bound of a modulus of the derivative of rational functions. rz=z−z0shz/wz∈Rm,n, where rz has exactly n poles a1,a2,⋯,an and all the zeros of rz lie in Dk∪Dk+,k≥1 except the zeros of order s at z0 ...
Preeti Gupta
doaj   +1 more source

Real Wronskian zeros of polynomials with nonreal zeros

Journal of Mathematical Analysis and Applications, 1991
Let f be a polynomial with real coefficients and let \[ Wf(z)=f(z)f''(z)- (f'(z))^ 2 \] be the ``Wronskian'' of f. This paper is devoted to studying the relationship between the geometry of the zeros of f and that of Wf. The results are aimed at a conjecture of Craven, Csordas and Smith which states that the number of real zeros of Wf never exceeds ...
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Choice of Collocation Points for Axisymmetric Nonlinear Two-Point Boundary Value Problems In Statics Of Shallow Spherical Shells

Engineering Transactions, 1983
The present work investigates the optimum choice of collocation points which gives for а given accuracy the minimum number of collocation points. А convergence study has been conducted for the axisymmetric nonlinear analysis of а shallow spherical shell ...
Y. Nath, P.C. Dumir, M.L. Gandhi
doaj  

Computation of the zeros of a quaternionic polynomial using matrix methods

Arab Journal of Basic and Applied Sciences
In a recent paper, Ishfaq Dar (2024), worked on the problem of locating the zeros of quaternion polynomials by introducing various matrix techniques.
N. A. Rather, Tanveer Bhat, Ishfaq Dar, Bilal Khan, Arjika Sama   +4 more
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