多复变函数的Picard定理

本文给出了多复变函数的Ｋ－拟亚纯函数的定义,并且得到了一个关于多复变函数的Ｋ－拟亚纯函数的正规定则,从这个正规定则,我们证明了多复变函数的全纯函数Ｐｉｃａｒｄ定理。     

与分担函数相关的正规定则

本文研究了与分担函数相关的亚纯函数族的正规性的问题.利用Nevanlinna理论的方法,得到了一个正规定则,推广了庞学诚和Zalcman~[3]的一个结果.     

Montel正规定则的推广(英文)

用简单的方法证明了全纯函数族的一个正规定则,推广了Montel正规定则.设F为区域D上的一个全纯函数族,其零点是重级的,a为有限复数.如果f,g∈F,有(f-1)f′与(g-1)g′分担a,则F正规.     

涉及例外函数的正规定则

讨论了一个涉及例外函数的亚纯函数正规定则,一定程度上推广和改进了方明亮~([2])等人的相关结果.     

一类亚纯函数的正规定则

该文研究了一类亚纯函数的一般性的正规定则.其结果推广了以前与之相关的一系列结果.     

涉及Picard例外值的亚纯函数正规族

本文研究了徐炎等人在文(Xu Y,Wu F Q,Liao L W.Picard values and normal families of meromorphic functions,Proc.R.Soc.Edinburgh,2009,139:1091-1099.)中提出的一个有关亚纯函数正规族猜想,得到了两个正规定则,并且证明了一个涉及分担值的正规定则,推广了前人的一些结果.     

亚纯函数族的一个正规定则

本文研究了涉及一类微分多项式的亚纯函数族的正规性问题.利用Zalcman-Pang的方法,得到一个正规定则,推广了2011年袁文俊等得到的结果.     

Montel定则的进一步推广

本文研究了全纯函数族的正规性问题.利用Zalcman引理,证明了全纯函数族的几个正规定则,推广了Montel正规定则.     

涉及极点重级与分担值的亚纯函数正规定则

运用分担值的思想证明了涉及极点重数的亚纯函数族的正规定则,所得结论推广了相关文献的主要结果.     

代数体函数族的Marty正规定则

Marty正规定则在亚纯函数的正规族理论中具有十分重要的作用,然而该定则对代数体函数是不成立的.本文首先深入考察了亚纯函数的Marty正规定则,然后基于Ahlfors覆盖曲面理论,在形式上对该正规定则进行了推广,最后证明了此推广形式的Marty正规定则对一类代数体函数也是成立的.     

Bi‐commutators of fractional integrals on product spaces

Recently Lacey extended Chanillo's boundedness result of commutators with fractional integrals to a higher parameter setting. In this paper, we extend Lacey's result to higher dimensional spaces by a different method. Our method is in terms of the dual relationship between product BMO and product Hardy space and the maximal function characterization of product Hardy spaces obtained by S.‐Y.Chang and R. Fefferman. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A NEW PROOF FOR THE CONVEXITY OF THE BERNSTEIN-BEZIER SURFACES OVER TRIANGLES

A neceassary and sufficient condition for the convexity of the Bezier net is presented'The convex Bezier net implies the convexity of the corresponding Bernstein-Bezier surfaceover triangles', a theorem established by Chang Geng-zhe and Philip J. Davis, is reprovedby a new approach.     

A note on meromorphic functions that share a set with their derivatives

In this paper, we study a problem of meromorphic functions that share an arbitrary set having three elements with their derivatives. A uniqueness result is derived which is an improvement of some related theorems given by Fang and Zalcman (J. Math. Anal. Appl. 280 (2003), 273–283) and Chang, Fang, and Zalcman (Arch. Math. 89 (2007), 561–569). As an application, we generalize the famous Brück conjecture with the idea of sharing a set.     

Technical note – On optimization approach for multidisk vertical allocation problems

Multidisk vertical allocation (MDVA) problems intend to find an allocation of relations to disks such that the expected query cost is minimized. Recently, Chang [European Journal of Operational Research 143 (2002) 210] modified Rotem et al.'s [IEEE Transactions on Knowledge and Data Engineering 5 (1993) 882] method for solving an MDVA problem using a smaller number of binary variables. Chang's method however is unable to treat MDVA problems with possible replication of relations. This paper proposes another method to solve MDVA problems, which is more effective than Rotem et al.'s and is able to treat replication problems insolvable by Chang's method.     

On the local gevrey and quasi-analytic hypoellipticity of □b

This paper contains a variational treatment of the Ambrosetti–Prodi problem, including the superlinear case. The main result extends previous ones by Kazdan–Warner, Amann–Hess, Dancer, K. C. Chang and de Figueiredo. The required abstract results on critical point theory of functionals in Hilbert space are all proved using Ekeland's variational principle. These results apply as well to other superlinear elliptic problems provided an ordered pair of a sub– and a supersolution is exhibited.     

Analysis of G/D/1 Queueing Systems with Inputs Satisfying Large Deviation Principle under Weak* Topology

The large deviation principle (LDP) which has been effectively used in queueing analysis is the sample path LDP, the LDP in a function space endowed with the uniform topology. Chang [5] has shown that in the discrete-time G/D/1 queueing system under the FIFO discipline, the departure process satisfies the sample path LDP if so does the arrival process. In this paper, we consider arrival processes satisfying the LDP in a space of measures endowed with the weak^* topology (Lynch and Sethuraman [12]) which holds under a weaker condition. It is shown that in the queueing system mentioned above, the departure processes still satisfies the sample path LDP. Our result thus covers arrival processes which can be ruled out in the work of Chang [5]. The result is then applied to obtain the exponential decay rate of the queue length probability in an intree network as was obtained by Chang [5], who considered the arrival process satisfying the sample path LDP.     

Singular values of nonnegative rectangular tensors

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. Some properties concerning the singular values of a real rectangular tensor were discussed by K. C. Chang et al. [J. Math. Anal. Appl., 2010, 370: 284–294]. In this paper, we give some new results on the Perron-Frobenius Theorem for nonnegative rectangular tensors. We show that the weak Perron-Frobenius keeps valid and the largest singular value is really geometrically simple under some conditions. In addition, we establish the convergence of an algorithm proposed by K. C. Chang et al. for finding the largest singular value of nonnegative primitive rectangular tensors.     

A note on random fixed point theorem in probabilistic analysis

In this paper we first prove that the assumptions between basic Theorem 1 and 2, hence main Theorem 3 and 4, in Chang [ 1 ] are equivalent. We then give several common fixed point theorems which are proved under considerably weaker conditions. We finally point out three mistakes in Chang [ 1 ] and correct them. The method used in this paper defers from the method used by Chang [ 1 ]     

New results on the Erdös–Szemerédi sum-product problems

In this Note, we present several contributions (or solutions) to problems related to the sizes of sum sets and product sets of integers (or complex numbers), considered in [8]. We also introduce some new methods in this area of research. To cite this article: M.-C. Chang, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Making sparse matrices sparser: Computational results

Many optimization algorithms involve repeated processing of a fixed set of linear constraints. If we pre-process the constraint matrixA to be sparser, then algebraic operations onA will become faster. We consider the problem of making a given matrix as sparse as possible, theSparsity Problem (SP). In a companion paper with S. Frank Chang, we developed some theoretical algorithms for SP under a non-degeneracy assumption (McCormick and Chang, 1988). Here we investigate what must be done to make those algorithms applicable in practice. We report encouraging computational results in making linear programming constraint matrices sparser. We also find that the Simplex Algorithm can solve the reduced LPs faster. Comparisons are made to a heuristic algorithm for SP of Adler et al. (1989).This work was partially supported by NSF Grants ECS-84-04350 and CDR-84-21402, and by ONR Contract N0014-87-K0214.