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R!kpe_(u!kpeN}!kpe!kpe\OUSMO@Normal Families of Holomorphic Functions Concerning Zero NumbersYang Qi;In this paper, we study the normal families related with a Hayman conjecture of higher derivative concerning zero numbers, and get one normal criteria.Our result improve some earlier related result.59016pef[xvz(On the Group of endotrivial GmodulesHuang Wenlin;LIn this paper, we define a group T_(G) of pendotrivial Gmodules and a generalized Dade group D_(G) for a finite group G. We prove that T_(G)? T_(H)whenever the subgroup H contains a normalizer of a Sylow psubgroup of G, in this case, K(G)? K(H). We also prove that the group D_(G) can be embedded into T_(G) as a subgroup.45109Theorems of Helly's Type for Partiallyclosed HalfspacesLiu JianGuo;Guo Qi;In this article, under quite weaker conditions, theorems of Helly's type for(not necessarily finite) family of partially closed halfspaces are presented in both analytic and geometric forms. Examples are also provided to show that these conditions cannot be omitted in general.465=Some Normality Criteria for Families of Meromorphic FunctionsChen Junfan;Cai Xiaohua;Let be a positive integer and F be a family of meromorphic functions in a domain D such that for each f " F, all poles of f are of multiplicity at least 2,and all zeros of f are of multiplicity at least + 1. Let and b be two distinct finite complex numbers. If for each f " F, all zeros of f~() are of multiplicity at least 2,and for each pair of functions f, g " F, f~()and g~() share b in D, then F is normal in D.44,Cotorsion Dimension of Weak Crossed ProductsChen Huaxi;Liang Jinrong;"Let H be a finitedimensional weak Hopf algebra over a field and A an associative algebra, and A#_H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of A#_H in terms of the corresponding data for H and A.387:Theorems of Helly''s Type for Partiallyclosed Halfspaces35IUlamHyers Stability of Trigonometric Functional Equation with Involution
Cheng Lihua;sThe present work aims to determine the solution of trigonometric functional equation f with involution from group to field by using the properties of involution function, and the solution and UlamHyers stability of the trigonometric functional equation are also discussed. Furthermore, this method generalizes the main theorem and gives the supplement in some reference.373DOn Meromorphic Solutions of Nonlinear Complex Differential EquationsSu Xianfeng;Zhang Qingcai;Applying the Nevanlinna theory of meromorphic function, we investigate the nonadmissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result. Meanwhile, we prove that the meromorphic solutions of some types of the systems of nonlinear complex differential equations are nonadmissible. Moreover, the form of the systems of equations with admissible solutions is discussed.kHopf Bifurcation of Delayed Predatorprey System with Reserve Area for Prey and in the Presence of Toxicity#Zhang Zizhen;Chu Yugui;Zhang Xin;$A kind of three species delayed predatorprey system with reserve area for prey and in the presence of toxicity is proposed in this paper. Local stability of the coexistence equilibrium of the system and the existence of a Hopf bifurcation is established by choosing the time delay as the bifurcation parameter. Explicit formulas to determine the direction and stability of the Hopf bifurcation are obtained by means of the normal form theory and the center manifold theorem. Finally, we give a numerical example to illustrate the obtained results.349@Weakly Diskbusting Curves in the Boundary of a Compression BodySun Meng;Liang Liang;Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?_+V is called weakly diskbusting if ?_+VJ has only one compressing disk <up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly diskbusting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.362(Spanning Predisks in a Compression Body1Liang Liang;Han Youfa;Li Fengling;Zhao Luying;A properly embedded essential planar surface P(not a disk) in a compression body V is called a spanning predisk with respect to J, if one boundary component of P is lying in ?_+V and all other boundary components of P are lying in?_V and coplanar with J. In this paper, we show that the number of boundary components of spanning predisks in a compression body is unbounded. But the number of a maximal collection of spanning predisks is bounded.1eFeketeSzeg? Problem for a Subclass of Meromorphic Functions Defined by the DziokSrivastava Operator&Guo Dong;Li Zongtao;Xiong Liangpeng;+By using the hypergeometric function defined by the DziokSrivastava operator, a new subclass of meromorphic function is introdued. We obtain FeketeSzeg? inequalities for the meromorphic function f(z) for which (1 + {1 +z[_lI_mf(z)]2 2 /[_lI_mf(z)]2 }/z[_lI_mf(z)]2 /_lI_mf(z))? (z)(" C{1/2, 1}).396Communications in Mathematical Research Aims and Scope<ck>Communications in Mathematical Research(CMR)is a comprehensive mathematical journal carrying original papers on pure and applied mathematics.It was launched in September,1985.The journal is formerly Northeastern Mathematical Journal(NMJ),and publishes quarterly.The primary purpose is to present the latest achievements in mathematical research and to promote of the journal international academic exchange.The Editorial24Instructions to Contributors<ck>1.Papers to be published in CMR are required to be written in English.2.Manuscripts submitted to CMR are expected to be clear in exposition,valid in argument,concise in wording,and reliable in data.They should be submitted electronically along with the LaTex format and pdf files.3.A manuscript should begin with the title of the article,the authors name,and the address(including the affiliation,the city,the province and the postcode).The title should29
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