The author proves that if f ： C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
Let k be a positive integer,let h(z)■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P(f)(z)-h(z) has a...Let k be a positive integer,let h(z)■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P(f)(z)-h(z) has at most k+l-1 distinct zeros(ignoring multiplicity) in D,where P(f)(z)=f(k)(z)+a1(z)f((k-1)(z)+…+ak(z)f(z) is a differential polynomial of f and aj(z)(j=1,2,···,k) are holomorphic functions in D,then F is normal in D.展开更多
In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the l...In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.展开更多
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational...The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.展开更多
In this paper we prove some interesting extensions and generalizations of Enestrom- Kakeya Theorem concerning the location of the zeros of a polynomial in a complex plane. We also obtain some zero-free regions for a c...In this paper we prove some interesting extensions and generalizations of Enestrom- Kakeya Theorem concerning the location of the zeros of a polynomial in a complex plane. We also obtain some zero-free regions for a class of related analytic functions. Our results not only contain some known results as a special case but also a variety of interesting results can be deduced in a unified way by various choices of the parameters.展开更多
In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L f (s,χ),where f is a holomorphic cusp form and χ a Dirichlet character of mod q.
Let f(z) be a function transcendental and meromorphic in the plane of growth order less than 1. This paper focuses on discuss and estimate the number of the zeros of a certain homogeneous difference polynomials of deg...Let f(z) be a function transcendental and meromorphic in the plane of growth order less than 1. This paper focuses on discuss and estimate the number of the zeros of a certain homogeneous difference polynomials of degree k in f(z), and obtains that this certain homogeneous difference polynomials has infinitely many zeros.展开更多
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...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 order σ（f）=1. Examples show that some of the results are sharp.展开更多
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.
The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematica...The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.展开更多
In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result:Let f(z)and g(z)be two transcendental meromorphic functions,p(z)a polynomial o...In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result:Let f(z)and g(z)be two transcendental meromorphic functions,p(z)a polynomial of degree k,n≥max{11,k+1}a positive integer.If fn(z)f(z)and gn(z)g(z)share p(z)CM,then either f(z)=c1ec p(z)dz, g(z)=c2e ?c p(z)dz ,where c1,c2 and c are three constants satisfying(c1c2) n+1 c2=-1 or f(z)≡tg(z)for a constant t such that tn+1=1.展开更多
The value distribution of differential polynomials is studied. The results in this paper improve and generalize some previous theorems given by Yang Chungchun （On deficiencies of differential polynomials, Math. Z., ...The value distribution of differential polynomials is studied. The results in this paper improve and generalize some previous theorems given by Yang Chungchun （On deficiencies of differential polynomials, Math. Z., 116（1970）, 197- 204）, H. S. Gopalakrishna and S. S. Bhoosnurmath （On distribution of values of differential polynomials, Indian 3. Pure Appl. Math., 17（1986）, 367-372）, I. Lahiri （A note on distribution of nonhomogeneous differential polynomials, Hokkaido Math. J., 31（2002）, 453-458） and Yi Hongxun （On zeros of differential polynomials, Adv. in Math., 18（1989）, 335-351） et al. Examples show that the results in this paper are sharu.展开更多
This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zer...This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.展开更多
Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this p...Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this paper through a linear differential equation satisfied by its probability generating function [1] [2].展开更多
基金supported by the National Natural Science Foundation of China(11201395)supported by the Science Foundation of Educational Commission of Hubei Province(Q20132801)
文摘The author proves that if f ： C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
文摘Let k be a positive integer,let h(z)■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P(f)(z)-h(z) has at most k+l-1 distinct zeros(ignoring multiplicity) in D,where P(f)(z)=f(k)(z)+a1(z)f((k-1)(z)+…+ak(z)f(z) is a differential polynomial of f and aj(z)(j=1,2,···,k) are holomorphic functions in D,then F is normal in D.
文摘In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.
文摘The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.
文摘In this paper we prove some interesting extensions and generalizations of Enestrom- Kakeya Theorem concerning the location of the zeros of a polynomial in a complex plane. We also obtain some zero-free regions for a class of related analytic functions. Our results not only contain some known results as a special case but also a variety of interesting results can be deduced in a unified way by various choices of the parameters.
基金Supported by the NNSF of China（11071186）Supported by the Science Foundation for the Excellent Youth Scholars of Shanghai（ssc08017）Supported by the Doctoral Research Fund of Shanghai Ocean University
文摘In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L f (s,χ),where f is a holomorphic cusp form and χ a Dirichlet character of mod q.
文摘Let f(z) be a function transcendental and meromorphic in the plane of growth order less than 1. This paper focuses on discuss and estimate the number of the zeros of a certain homogeneous difference polynomials of degree k in f(z), and obtains that this certain homogeneous difference polynomials has infinitely many zeros.
基金supported by the NSF of Shandong Province, China (ZR2010AM030)the NNSF of China (11171013 & 11041005)
文摘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 order σ（f）=1. Examples show that some of the results are sharp.
文摘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.
基金Supported by Natural Science Foundation of Zhejiang Province P. R. China (Y105141)Natural Science Foundation of Fujian Province P.R.China (A0510025)Technological Project of Zhejiang Education Department,P. R. China(20050291)
文摘The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.
基金Supported by the Natural Science Foundation of Jiangsu Education Department（07KJD110086）
文摘In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result:Let f(z)and g(z)be two transcendental meromorphic functions,p(z)a polynomial of degree k,n≥max{11,k+1}a positive integer.If fn(z)f(z)and gn(z)g(z)share p(z)CM,then either f(z)=c1ec p(z)dz, g(z)=c2e ?c p(z)dz ,where c1,c2 and c are three constants satisfying(c1c2) n+1 c2=-1 or f(z)≡tg(z)for a constant t such that tn+1=1.
文摘The value distribution of differential polynomials is studied. The results in this paper improve and generalize some previous theorems given by Yang Chungchun （On deficiencies of differential polynomials, Math. Z., 116（1970）, 197- 204）, H. S. Gopalakrishna and S. S. Bhoosnurmath （On distribution of values of differential polynomials, Indian 3. Pure Appl. Math., 17（1986）, 367-372）, I. Lahiri （A note on distribution of nonhomogeneous differential polynomials, Hokkaido Math. J., 31（2002）, 453-458） and Yi Hongxun （On zeros of differential polynomials, Adv. in Math., 18（1989）, 335-351） et al. Examples show that the results in this paper are sharu.
基金supported by the Development of airborne gravity gradiometer(No.2017YFC0601601)open subject of Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences(No.KLOR2018-8)
文摘This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.
文摘Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this paper through a linear differential equation satisfied by its probability generating function [1] [2].
