The nature and extent of the geographic market for hogs in the United States

This paper looks at the question of whether hogs sold at different locations in the United States are part of a single geographic market covering the entire country. An answer to this question is sought using an approach to defining a geographic market based on the notion of instantaneous causality. The empirical results, based on prices for hogs at sixteen different locations over the period October 1989 to May 1992, suggest that there was but a single identifiable geographic market covering the entire United States. The implications of this finding are explored.     

Uniqueness theorems of entire functions sharing a nonzero complex number with their difference operators

In this paper, we deal with a uniqueness question of entire functions sharing a nonzero complex number with their difference operators. The results in this paper improve Theorem 1.1 in Liu and Yang (Arch. Math. 92 (2009), 270–278) and deal with Question 1 in Liu and Yang (2009), where the entire functions are of finite orders.     

Notes on entire functions sharing an entire function of a smaller order with their difference operators

In this paper, we study a uniqueness question of entire functions sharing an entire function of smaller order with their difference operators. The results in this paper extend Theorem 1.1 in [19] by Liu and Yang and deal with Question 1 in [19], where the entire functions are of finite order. Moreover, we repair certain statements in [21] by Li et al., which in turn had depended on questionable assertions of Lemma 2.6 in [20]. Examples are provided to show that the results in this paper are best possible.     

Entire functions sharing one polynomial with their derivatives

In this paper, we study the growth of solutions of ak-th order linear differential equation and that of a k + 1-th order linear differential equation. From this we affirmatively answer a uniqueness question concerning a conjecture given by Brück in 1996 under the restriction of the hyper order less than 1/2, and obtain some uniqueness theorems of a nonconstant entire function and its derivative sharing a finite nonzero complex number CM. The results in this paper also improve some known results. Some examples are provided to show that the results in this paper are best possible.     

亚纯函数的唯一性

§ 1.　Introduction　　Inthispaper,unlessspecified ,allthefunctionsarenonconstantmeromorphicfunctions.WeshallusethestandardnotatiosofNevanlinnatheoryofmeromorphicfunctionssuchasT(r,f) ,m(r ,f) ,N(r ,f) , N(r,f) ,… .SetE(r ,f) =∪α∈S{z｜f(z) -a},whereaze ropointwithmultiplicitymiscountedmtimesintheset.AsetSsuchthatforanytwonon constantentirefunctionsf(z)andg(z)theconditionE(S ,f) =E(S ,g)impliesf≡ giscalledauniquerangesetsofentirefunctions.In 1 976,GROSSF [1 ]askedthefollowingquesti…     

关于I. Laine和杨重骏的一个问题

本文主要研究线性差分方程 $A_n(z)f(z+n)+\cdots+A_1(z)f(z+1)+A_0(z)f(z)=0$亚纯解的增长级.当上述方程的系数中没有起控制作用的系数时,我们给出了一些约束条件,得到了一些结果,所得结果部分回答了I. Laine和杨重骏的一个问题.     

涉及导数与公共值的整函数

本文研究整函数f与f'具有一个公共值时的R.Brck问题,用一种较简便的方法证明了:若f与f'以有穷非零复数a为IM公共值,且存在正数M,使f(z)=a时0<│f'(z)│≤M,则f'a/f-a≡c,其中c为非零常数、此结论改进了G.Jank等人的结果。     

关于Gundersen问题的若干结果

对Gundersen问题“设非常数整函数f(z)与g(z)有三个判别的IM分担值.那么 这三个值是否皆为f(z)与g(z)的CM分担值?”,作者进行了研究,得到若干结果,部 分解决了该问题.     

超越整函数的某些动力学性质

本文研究了由m个超越整函数{fl,f2,…,fm}生成的随机迭代系统的Fatou集分支的某些动力学性质.运用复动力系统理论与双曲度量理论,得到了随机迭代系统有界Fatou分支不存在的一个判别准则,同时回答了Baker所提出的问题,且给出了随机迭代系统Fatou分支为单连通的一个充分条件,推广了Bergweiler的结果.     

整函数与其两个导数CM共享一个值

该文研究了与两个导数共享一个非零、有穷值的整函数的唯一性问题，给出了函数确定的表达式，回答了仪洪勋，杨重骏提出的一个问题     

The uniqueness of an entire function sharing a small entire function with its derivatives

In this paper, we prove a theorem on the growth of a solution of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its derivatives sharing a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.     

A unified approach to the study of certain growth estimates of entire functions

Summary Growth properties of entire functions represented by Taylor series or Dirichlet series have been studied in this paper by considering a positive, non decreasing and unbounded function. The results thus obtained are applicable to entire functions of slow growth also. A number of earlier results have been improved in this paper.Finally, the authors wish to thank the referee for his helpful suggestions and comments.     

On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.     

On in‐out splitting of incident fields and the far‐field behaviour of Herglotz wavefunctions

It is easy to write down entire solutions of the Helmholtz equation: Examples are plane waves and Herglotz wavefunctions. We are interested in the far‐field behaviour of these solutions motivated by the following question: When is it legitimate to split the far field of such an entire solution into the sum of an incoming spherical wave and an outgoing spherical wave? We review the relevant literature (there are disjoint physical and mathematical threads), and then we answer the question for Herglotz wavefunctions, using a combination of the 2‐dimensional method of stationary phase and some explicit examples.     

On the nature of the de Branges Hamiltonian

We prove the theorem announced by the author in 1995 in the paper “A criterion for the discreteness of the spectrum of a singular canonical system” (Funkts. Anal. Prilozhen., 29, No. 3).In developing the theory of Hilbert spaces of entire functions (we call them Krein-de Branges spaces), de Branges arrived at a certain class of canonical equations of phase dimension 2. He showed that, for any given Krein-de Branges space, there exists a canonical equation of the class indicated that restores a chain of Krein-de Branges spaces imbedded one into another. The Hamiltonians of such canonical equations are called de Branges Hamiltonians. The following question arises: Under what conditions will the Hamiltonian of a certain canonical equation be a de Branges Hamiltonian? The main theorem of the present work, together with Theorem 1 of the paper cited above, gives an answer to this question.     

Bruck猜想的一类微分和差分方程

运用值分布以及Wiman-Valiron理论研究了整函数与它的k阶导数分担某些小函数问题,得到了一些涉及到Bruck猜想的唯一性结果.     

A characterization of graphs with rank 4

The rank of a graph G is defined to be the rank of its adjacency matrix. In this paper, we consider the following problem: What is the structure of a connected graph with rank 4? This question has not yet been fully answered in the literature, and only some partial results are known. In this paper we resolve this question by completely characterizing graphs G whose adjacency matrix has rank 4.     

Uniqueness of entire functions sharing an entire function of smaller order with their derivatives

In this paper, we prove some uniqueness theorems of entire functions and their derivatives that share an entire of function whose order is less than their order. The results in this paper improve those given by G. G. Gundersen and L. Z. Yang, J. P. Wang, J. M. Chang, and Y. Z. Zhu, X. M. Li and H. X. Yi, and others. Some examples are provided to show that the results in this paper are the best possible.     

一类解析的零级Laplace-Stieltjes变换

本文研究了Laplace-Stieltjes变换所定义的零级整函数的增长性.利用牛顿多边形,得到了这类整函数关于增长性及正规增长性的充要条件,推广了文献[3]中的结果.     

A question of Eremenko and Lyubich concerning completely invariant domains and indirect singularities

We give an example of an entire function with a completely invariant Fatou component which has an indirect singularity not contained in this Fatou component. The question of whether such a function exists has been raised by Eremenko and Lyubich.