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25 October 2007, Volume 27 Issue 5 Previous Issue    Next Issue

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On Class w F (p,r,q) Operators Yang Changsen;Yuan Jiangtao Acta mathematica scientia,Series A. 2007, 27 (5):  769-780.  Abstract ( 1947 )   RICH HTML PDF (309KB) ( 1230 )   Save The class of wF(p,r,q) operators is introduced, as a continuation of the study of class wA(p,r) operators. This class contains all A(p,r) operators and belongs to classF(p,r,q). The authors show several properties of this class, such as its characterizations, inclusion relations, normality, powers and so on. Related Articles | Metrics

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Generalization and Application of Super-Poincare Inequality on Lp-space Liu Wei; Sun Guozheng Acta mathematica scientia,Series A. 2007, 27 (5):  781-787.  Abstract ( 2072 )   RICH HTML PDF (292KB) ( 1171 )   Save The authors establish the super-Poincare inequality on Lp-space with respect to a measure space, and obtain some necessary and sufficient conditions about semicompact and compact property of semigroup and the perturbation result. Meanwhile, a sufficient condition for super-Poincare inequality is shown, which generalizes some known results obtained on the L2-space. As applications, the essential spectrum of a class of non-symmetric diffusion operators on Riemannian manifold is studied. Related Articles | Metrics

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Strong Consistency of a Class of Estimators in Partial Linear Model under Martingale Difference Sequence Li Guoliang; Liu Luqin Acta mathematica scientia,Series A. 2007, 27 (5):  788-801.  Abstract ( 2182 )   RICH HTML PDF (329KB) ( 1142 )   Save Consider the heteroscedastic regression model: yi=xi β +g(ti)+σiei ,i=1,2,...,n,where Here σi=f(ui), (xi,ti,ui)Here the design points (xiti,ui) are known and nonrandom, g and f are unknown functions , and β is the parameter needed to be estimated,ei is the random error and a martingale difference sequence in relation to the undecreasing σ-algebra series {Fi,i≥1}. For the least squares estimator βn and the weighted least squares estimator βn of β given in [1] based on the family of nonparametric estimates of g(.) and f(.), the authors establish their strong consistency under suitable conditions, thereby improve the the result where ei is iid in [6]. Related Articles | Metrics

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Some Notes on the May Spectral Sequence Liu Xiugui Acta mathematica scientia,Series A. 2007, 27 (5):  802-810.  Abstract ( 2116 )   RICH HTML PDF (320KB) ( 1063 )   Save Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p , where p>5 is an arbitrary odd prime. In this paper, some important propositions on the May spectral sequence are first given, and then a new nontrivial family of homotopy elements is detected in the stable homotopy groups of spheres by the May spectral sequence and the Adams spectral sequence. The new one is of degree p(p-1)(pn+sp2+sp+s)-7) and is represented by bn-1g0γs in the E2s+4,﹡-term of the Adams spectral sequence, where n 4≥ and 3≤ s<p-2. The main theorem obtained in this paper is an obvious generalization of Theorem I in [1]. Related Articles | Metrics

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Stochastic Recursive Optimal Control and Mixed Optimal Control Problems Wei Gang;Wu Zhen Acta mathematica scientia,Series A. 2007, 27 (5):  811-818.  Abstract ( 2149 )   RICH HTML PDF (328KB) ( 1264 )   Save The existence results of the optimal strategy are obtained for the stochastic recursive optimal control problem i.e. the cost function is described by the solution of a certain backward stochastic differential equation and the recursive mixed optimal control problem i.e. the controller has to decide the optimal stopping time also. The minimal and maximal mathematic expectations for the recursive optimal value function under one kind of equivalent probability measures set are also given in the paper. Related Articles | Metrics

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The Calculation of Differential Representations of Dynamical Lorentz Group SO(3,1) as an Example Zhao Dun;Wang Shunjin;Luo Honggang Acta mathematica scientia,Series A. 2007, 27 (5):  819-829.  Abstract ( 1741 )   RICH HTML PDF (356KB) ( 1102 )   Save The authors present a symbolic computation method for calculating the differential representations for dynamical groups, including the right and the left differential representations, and the adjoint differential representations in the group parameter space and in its coset spaces. As an example, the corresponding representations of Lorentz SO(3,1) group with 6-parameters and 3-parameters are calculated. Especially, two different kinds of 3-parameter adjoint differential representations are obtained. At the same time, the right and the left differential representations, and the adjoint differential representations of Wigner's little group SO(2,1) and SO(3) with 6-parameters and 3-parameters are also obtained respectively. These representations are the relativistic generalization of the differential representations of the SO(3) rotation group in the Euler angles and in the polar angles. They may find their applications in the study of relativistic quantum top. Related Articles | Metrics

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Fτ-Coherent Risk Measures Chen Wencai ; Ye Zhongxing Acta mathematica scientia,Series A. 2007, 27 (5):  830-838.  Abstract ( 2167 )   RICH HTML PDF (327KB) ( 1082 )   Save The authors present in this paper a new concept of risk measure defined at an arbitrary stopping time τ, the Fτ-coherent risk measure. For an Fτ-coherent risk adjusted value (the negative of a Fτ-coherent risk measure) фт: L∞ (F) →L∞ (Fτ), which satisfies the Fatou property, its representation theorem is obtained by using a special Fτ-convex set of probability measures. It is also proven that an Fτ-coherent risk adjusted value can be represented by its acceptance set. Related Articles | Metrics

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The Maximal Dilatation and Boundary Dilatation of Quasi-symmetric Mapping Qi Yi ;Wu Yan Acta mathematica scientia,Series A. 2007, 27 (5):  839-844.  Abstract ( 1916 )   RICH HTML PDF (334KB) ( 1106 )   Save To study the relationship between the maximal dilatation of quasi-symmetric self-homoemorphism of the unit circle and the maximal dilatation of its extremal extension, it was proved in [1] that if the maximal dilatation Kq(h) of a qusi-symmetric self-homoemorphism h cannot be arrive at some quadrilateral with the unit disk △ as its domain and vertices on the unit circle $\pd$, then Kq(h)≤ H(h), where H(h) is the boundary dilatation of h. The main resluts in [1] quite depend on this result. But its proof there is very complicated. In this paper, the authors give another elementary and simple proof. Furthermore, they use this result to study the problem when the maximal dilatation of a qusi-symmetric self-homoemorphism of the unit circle could be arrive at some quadrilateral. Related Articles | Metrics

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Positive Solutions for a Class of Two-point Boundary Value Problems with Nonlinearity Lu Huiqin Acta mathematica scientia,Series A. 2007, 27 (5):  845-854.  Abstract ( 1890 )   RICH HTML PDF (297KB) ( 973 )   Save Exact number of solutions and behaviour of continuum of the solution set are obtained for a class of nonlinear boundary value problems. The results in the paper generally answer an open problem in paper [1]. Related Articles | Metrics

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Domain Oscillation Criteria for a Forced Second Order Elliptic Differential Equations Zhuang Rongkun;Yao Zhengan Acta mathematica scientia,Series A. 2007, 27 (5):  855-861.  Abstract ( 1893 )   RICH HTML PDF (277KB) ( 1079 )   Save In this paper, new oscillation criteria are obtained for nonlinear elliptic differential equations of the form ∑ i,j=1n Di[Aij(x)Djy]+∑i=1n bi(x)Diy+q(x)f(y)=e(x) where x∈ Rn. These criteria are only based on the information of a sequence of subdomain of Ω С Rnand different from most known ones. Related Articles | Metrics

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On the Correlation Dimension of the Spectral Measure for the m-multiplicative Sequence Niu Min; Wen Zhixiong Acta mathematica scientia,Series A. 2007, 27 (5):  862-870.  Abstract ( 1724 )   RICH HTML PDF (294KB) ( 1053 )   Save Using the relation between the decay rate of the correlation function and the characteristics of singular Fourier spectra, the authors give the exact value for the correlation dimension of the spectral measure for the infinite m-multiplicative sequence. Related Articles | Metrics

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G-functions and Estimates of Spectral Radius of Iterative Matrices Huang Tingzhu; Li Houbiao; Shen Shuqian Acta mathematica scientia,Series A. 2007, 27 (5):  871-878.  Abstract ( 2114 )   RICH HTML PDF (293KB) ( 993 )   Save In this paper, some new bounds for the spectral radius of iterative matrices are obtained, which generalize and improve the results in [1--6]. These results are suited to extended matrices. Numerical examples show that these new bounds are better than the earlier ones in [1--6] under same conditions. Related Articles | Metrics

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Domain Decomposition Upwind Difference Schemes for Multidimensional Parobolic Problems Li Changfeng ;Yuan Yirang Acta mathematica scientia,Series A. 2007, 27 (5):  879-889.  Abstract ( 1908 )   RICH HTML PDF (387KB) ( 1092 )   Save Combining the domain decomposition with upwind difference method, the authors present the convection part of multidimensional parabolic problems is discretized by the 1-order upwind method and the modified 2-order upwind method. The proposed schemes rely on implicit procedures in subdomains and explicit calculation on the inter-domain boundaries. With certain stability conditions, convergence analysis is presented by the maximum principle and embedding theorem. Finally, numerical examples illustrating the value, accuracy and parallelism are shown. Related Articles | Metrics

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On the Singular Direction of Meromorphic Function Liu Xuekun; Wu Zhaojun Acta mathematica scientia,Series A. 2007, 27 (5):  890-897.  Abstract ( 1890 )   RICH HTML PDF (294KB) ( 1266 )   Save In this paper, by using Ahlfors' theory of covering surface, the singular directions of meromorphic functions are discussed. The existence of T direction concerning a rational function is established, which confirms a Zheng's conjecture. Related Articles | Metrics

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Modeling the Interactions between the HIV-1 Phenotypes and the Cytokines Lou J; Ma Zhien ;Shao Yiming Acta mathematica scientia,Series A. 2007, 27 (5):  898-906.  Abstract ( 1632 )   RICH HTML PDF (443KB) ( 1197 )   Save In this paper, the authors present a model illustrateing the interactions between the two HIV-1 phenotypes and cytokines. By introducing the important cytokines, IL-2 and CAF, in the HIV-1 dynamics model, the authors study the evolution of the two different HIV-1 phenotypes: the M-tropic (NSI) and the T-cell-tropic (SI). Using the type Km monotone system theory, the authors obtain two results. First, the number of steady states of the system is odd, the odd indexed equilibria are asymptotically stable, and the even ones are unstable. Secondly, some detailed information about the bases of attraction of these steady states has been obtained. These results indicate that the two phenotypes will coexist in the infected patient for long time. Moreover, all these results can be explained by the pathogenesis of AIDS and are consistent with the results of clinical studies. Related Articles | Metrics

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Hartman-Stampacchia Variational Inequalities on Non-compact Sets with Applications Guo Weiping Acta mathematica scientia,Series A. 2007, 27 (5):  907-914.  Abstract ( 1628 )   RICH HTML PDF (249KB) ( 1080 )   Save In this paper, two multivalued versions of the Hartman-Stampacchia variational inequalities on non-compact sets are proved and as applications, the complementarity problems for multivalued operators are discussed. Related Articles | Metrics

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Operator-Valued Unitary Random Matrices and Asymptotic Freeness Meng Bin;Guo Maozheng;Cao Xiaohong Acta mathematica scientia,Series A. 2007, 27 (5):  915-922.  Abstract ( 2014 )   RICH HTML PDF (318KB) ( 1071 )   Save In this paper a notion of semi-standard unitary random matrix is introduced in operator-valued noncommutative probability space and the semi-standard unitary random matrices to be the asymptotic free matrix models for operator-valued Haar unitary elements is proved. Related Articles | Metrics

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Cross-estimate and Tightness for Non-symmetric Markov Processes Jiang Yiwen Acta mathematica scientia,Series A. 2007, 27 (5):  923-930.  Abstract ( 2160 )   RICH HTML PDF (314KB) ( 1126 )   Save The author extends the cross-estimate of Lyons-Zheng Markov processes from the symmetric case to the general stationary situation. The main tool is the forward-backward martingale decomposition. As a corollary the author obtains a tightness result for laws of Markov processes. Finally the author gives an example to show how to obtain the crucial cross-estimate. Related Articles | Metrics

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A Nonlinear Model of El Nino Atmospheric Physics Mo Jiaqi; Wang Hui; Lin Wantao Acta mathematica scientia,Series A. 2007, 27 (5):  931-934.  Abstract ( 1795 )   RICH HTML PDF (233KB) ( 1155 )   Save A El Nin''o atmospheric physics oscillator model is considered. Using the homotopic method, the approximate expansion of solution of corresponding problem is constructed. Related Articles | Metrics

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On Limit Sets and Nonelementary Transformation Groups in Rn Dai Binlin Acta mathematica scientia,Series A. 2007, 27 (5):  935-940.  Abstract ( 1392 )   RICH HTML PDF (248KB) ( 1075 )   Save This paper studies the nonelementary groups of Mò'bius Transformations in Rn and some important properties are obtained. This paper also gives several theorems about discreteness criteria and algebraic convergence. Related Articles | Metrics

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Existence of Strong Global Attractors for the Nonlinear Beam Equations Ma Qiaozhen; Sun Chunyou; Zhong Chengkui Acta mathematica scientia,Series A. 2007, 27 (5):  941-948.  Abstract ( 1855 )   RICH HTML PDF (291KB) ( 1169 )   Save The nonlinear beam equations represent the viberation of the rode bed in downward direction. The authors discuss the global attractors of the strong solution by using a new method obtaining the compactness introduced in [3]. Related Articles | Metrics

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A Necessary and Sufficient Condition for Quasiconformal Mappings Chu Yuming;Huang Manzi Acta mathematica scientia,Series A. 2007, 27 (5):  949-954.  Abstract ( 1934 )   RICH HTML PDF (290KB) ( 1336 )   Save Let f : Rn→ Rn be a homeomorphism. In this paper, the authors prove that f is a quasiconformal mapping if and only if f(D) is a John domain for any John domain D in Rn. Related Articles | Metrics

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The Flow-capturing Location-allocation Model with Risk Bottleneck Limitation Yang Jun;Yang Chao;Wu Yun Acta mathematica scientia,Series A. 2007, 27 (5):  955-960.  Abstract ( 1598 )   RICH HTML PDF (290KB) ( 1002 )   Save This paper considers the flow-capturing location-allocation model (FCLM) with risk bottleneck limitation. Suppose each edge in the network has two attributes: length and risk. A variant of FCLM with one origin and multi-destinations is considered with objection of minimizing the total cost for setting up facilities as well as an additional security cost. The security cost F(r) is a nondecreasing function about risk. If the security cost F(r) is expended, maximal risk that all the flows can resist is r∈ R. The authors formulate this model and propose the algorithm based on the postorder traversal substitute algorithm. Related Articles | Metrics