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zeros AND FIXED POINTS OF DIFFERENCE OPERATORS OF MEROMORPHIC FUNCTIONS

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Acta Mathematica Scientia 2013年第3期33卷 773-780页

作者：崔巍巍杨连忠 School of Mathematics Shandong University

Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of o... 详细信息

关键词： Entire functions meromorphic functions complex difference fixed points zeros

On the Role of zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems

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Journal of Systems Science & Complexity 2022年第2期35卷 535-542页

作者： ZHOU Bin DUAN Guang-Ren Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China Center for Control Science and Technology Southern University of Science and TechnologyShenzhen 518055China

It is well known that for a linear system in state space form,controllability is equivalent to arbitrary pole assignment by state *** brief points out that for a scalar high-order fully actuated linear system,the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account,that is,controllability cannot guarantee arbitrary pole assignment by state feedback.

关键词： High-order fully actuated systems pole assignment state feedback zeros

The distribution of the zeros of L-functions and the least prime in some arithmetic progression

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Science China Mathematics 2000年第9期43卷 937-944页

作者：蒙在照 Department of Mathematics and Institute of Mathematics Peking University Beijing 100871 China

This paper gives some new estimations to the distribution of the zeros of L-functions and proves that the least prime in an arithmetic progression with a prime differenceq is ?q 4.5.

关键词： distribution of zeros least prime Laplace transform.

A general method to generate parallel iterations for finding all zeros of polynomial simultaneously

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Chinese Science Bulletin 1997年第22期42卷 1849-1852页

作者： Han, DF Wang, XH Hangzhou Univ Dept Math Hangzhou 310028 Peoples R China

SINCE there are many difficulties in finding a single root of a polynomial, it becomes moreand more important for parallel iterations to determine all roots simultaneously. Among theproposed methods, the iterative fami1y produced by paralleling the iterative family of Halleyusing Bell’s polynomial appears the most systematic and richest. In fact the paper becomesthe main contents of the monograph.

关键词： all zeros of a polynomial parallel iteration generating method.

ON THE zeros OF QUOTIENTS OF BESSEL FUNCTIONS

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Chinese Annals of Mathematics,Series B 2000年第3期21卷 285-296页

作者： A.FRIEDMAN B.HU J.J.L.VELAZQUEZ DepartmentofMathematics UniversityofMinnesotaMinneapolisMN55455USA. DepartmentofMathematics UniversityofNotreDameNotreDameIN46556USA. DepartamentodeMatematicaAplicada FacultaddeMatematicasUniversidadComplutense28040MadridSpain.

The paper studies the zeros of 2mIm/Im-1- (m+1)I1 /I0, where Im are the Bessel functions.

关键词： zeros Quotient Bessel function

Some Integral Mean Estimates for Polynomials with Restricted zeros

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Analysis in Theory and Applications 2015年第1期31卷 81-91页

作者： Abdullah Mir Q.M.Dawood Bilal Dar Department of Mathematics University of Kashmir

Let P（z） be a polynomial of degree n having all its zeros in ｜z｜≤ k. For k = 1, it is known that for each r 〉 0 and ｜a｜≥1,n（｜a｜-1）{∫0^2π｜P（e^iθ）｜^rdθ}^1/r≤{∫0^2π｜1＋e^iθ｜^rdθ}^1/rmax｜z｜=1｜DzP（z）｜.In this paper, we shall first consider the case when k≥1 and present certain generaliza- tions of this inequality. Also for k≤ 1, we shall prove an interesting result for Lacunary type of polynomials from which many results can be easily deduced.

关键词： Polynomial zeros polar derivative.

Estimated Bounds for zeros of Polynomials from Traces of Graeffe Matrices

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Advances in Linear Algebra & Matrix Theory 2014年第4期4卷 210-215页

作者： Ousmane Moussa Tessa Maimouna Salou Morou Amidou Département de Mathématiques et d’informatique Université A. Moumouni de Niamey Niamey Niger Institut de Recherche sur l’Enseignement des Mathématiques Université A. Moumouni de Niamey Niamey Niger

In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant ... 详细信息

关键词： Graeffe Matrices Numerical Approximation of Eigenvalues Dandelin-Graeffe’s Method Bounds of zeros of Polynomial

Transcendental Meromorphic Functions Whose First Order Derivatives Have Finitely Many zeros

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Advances in Pure Mathematics 2019年第11期9卷 925-933页

作者： Feng Guo Department of Mathematics Yunnan Normal University Kunming China

Let f be a meromorphic function in C. If the order of f is greater than 2,has finitely many zeros and f takes a non-zero finite value finitely times, and then ?is unbounded.

关键词： Transcendental Meromorphic Functions Derivatives zeros

A SIMPLE ITERATIVE PROCEDURE FOR FINDING ALL zeros OF A POLYNOMIAL WITHOUT REPEATED EVALUATION

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1996年第2期5卷 234-240页

作者：郑士明 Department of Mathematics Hangzhou UniversityHangzhou 310028PRC.

In this note a simple iterative method for simultaneously finding all zeros of a polynomial is *** method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally convergent for quadr... 详细信息

关键词： Iterative method zeros of polynomial repeated evaluation global convergence.