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Current Issue   2008 51 (2)  Mar. 15, 2008       2       2     209 Xian Meng MENG and Zhen CUI   On Hua's Five Prime Squares Theorem with One Prime in Arithmetic Progressions     Let $N$ be a sufficiently large positive integer satisfying $N\equiv 5\bmod 24$, $l$ and $d$ be integers satisfying $(l, d)=1$. Denote by $A_0$ and $A>1$ the positive constants, satisfying $A_0=600A+2000$. For all integers $0<d\leq D_0= N^{\f{1}{4}}...      51 (2): 209-218 [Abstract ] ( 114 ) [HTML 0KB] [PDF 433KB ]( 232 ) 219 Ai Li YANG and Jian Hua ZHANG   Jordan Isomorphisms on Nest Subalgebras of Factor von Neumann Algebras     This paper is devoted to the study of Jordan isomorphisms on nest subalgebras of factor von Neumann algebras. It is shown that every Jordan isomorphism $\varphi$ between two nest subalgebras $\mbox{alg}_M\beta$ and $\mbox{alg}_M\gamma$ is either an isomor...      51 (2): 219-224 [Abstract ] ( 93 ) [HTML 0KB] [PDF 354KB ]( 123 ) 225 Cai Xia DENG, Yu Ling QU and Jie HOU   Characterization of Image Space of Gauss Wavelet Transform     For the Gauss wavelet which is often used in edge detection and is of a good performance, the expression of the reproducing kernel function of image space of Gauss wavelet transform is shown on the bases of the image space of the continuous wavelet transf...      51 (2): 225-234 [Abstract ] ( 91 ) [HTML 0KB] [PDF 532KB ]( 117 ) 235 Sheng Kui YE and Sheng CHEN   Several Classes of Upper Bounds for the Laplacian Spectral Radius of a Graph     Several classes of upper bounds for Laplacian spectral radius of a graph are obtained. By an appropriate choice of diagonal matrices, some bounds which are in some sense better than the previous ones are presented....      51 (2): 235-240 [Abstract ] ( 96 ) [HTML 0KB] [PDF 287KB ]( 116 ) 241 Bo HOU and Yun Ge XU   Hochschild (Co)-Homology Groups of $Z_n$-Galois Coverings of Exterior Algebras in Two Variables     Let $\Lambda$ be the exterior algebras in two variables over a field $k$ satisfying char$k\nmid n$, $\widetilde{\Lambda}$ be the ${\mathbb Z}_n$-Galois covering of $\Lambda$. In this paper we construct a minimal projective bimodule resolution of $\widetil...      51 (2): 241-252 [Abstract ] ( 77 ) [HTML 0KB] [PDF 510KB ]( 105 ) 253 Shou Chuan ZHANG, Min WU and Heng Tai WANG   Classifications of Ramification System for Symmetric Group     Ramification systems with characters can be applied to classify the quiver Hopf algebras. In this paper, we obtain the formula to compute the number of elements in isomorphic classes of ramification systems with characters over group $S_n\ (n\ne 6)$....      51 (2): 253-264 [Abstract ] ( 95 ) [HTML 0KB] [PDF 548KB ]( 102 ) 265 Hong Bin WANG, Xiao Jin ZHANG and Zong Guang LIU   The Endpoint Estimates for the Commutator of Marcinkiewicz Integral     We obtain the$(H^1,L^{1,\infty})$, $(H^1_b,L^1)$ and $(H^{1,\infty}_b,L^{1,\infty})$ type estimates for the commutator of Marcinkiewicz integral with the kernel satisfying the logarithmic type Lipschitz conditions....      51 (2): 265-274 [Abstract ] ( 78 ) [HTML 0KB] [PDF 396KB ]( 110 ) 275 Li Xin LIU and Shi Hong CHENG   The Strong Law of Large Numbers of Negatively Associated Random Variables and Its Applications     We give some results on the strong law of large numbers for sequence of negatively associated random variables with different distributions. On the Basis of a these results, the Egorov's results for independent random variables are generalized to the case...      51 (2): 275-280 [Abstract ] ( 76 ) [HTML 0KB] [PDF 437KB ]( 118 ) 281 Ping Yan CHEN and Xiang Dong LIU   Complete Moment Convergence for Sequence of Identically Distributed $\rho$-Mixing Random Variables     In this paper, the sufficient and necessary conditions of complete moment convergence for sequence of identically distributed $\rho$-mixing random variables are obtained, which extent and generalize the well-known results....      51 (2): 281-290 [Abstract ] ( 81 ) [HTML 0KB] [PDF 406KB ]( 99 ) 291 Xue Gang HU and Chun Lai MU   Localization and Asymptotic Behavior of Solutions to Degenerate Parabolic Equations with Variable Density and Absorption     For a wide class of nonlinear parabolic equations with variable density and absorption, this paper obtains the conditions for the localization of solutions to the Cauchy problem with nonnegative compactly initial data, and proves the asymptotic behavior. ...      51 (2): 291-298 [Abstract ] ( 82 ) [HTML 0KB] [PDF 493KB ]( 105 ) 299 Shu Jin LI and Sheng Hong LI   Exotic Options Pricing Formulae with Stochastic Interest Rates     A general pricing formula for compound call option is derived when the interest rate is stochastic by the change of measure in this paper. At the same time, an analytic pricing formula for compound call option is also given in an extended Vasicek's intere...      51 (2): 299-310 [Abstract ] ( 85 ) [HTML 0KB] [PDF 635KB ]( 110 ) 311 Zji Min LI, Li Bo LUO and Xiang LI   On the Computational Complexity of the Theory of Complete Binary Trees     The first-order theory of a complete binary tree is decidable by the quantifier elimination, we also know the $CB$ rank of elements of a complete binary tree. In this paper, by using the bounded Ehrenfeucht--Fra\"{\i}ss\'{e} game, we demonstrate that the ...      51 (2): 311-318 [Abstract ] ( 86 ) [HTML 0KB] [PDF 523KB ]( 99 ) 319 Yan Hui ZHANG and Guan Tie DENG   Growth Properties for a Class of Subharmonic Functions in Half Space     We prove that the Poisson integral with Dirichlet data under the natural integral condition for convergence satisfying the growth property $u(x)=o(|x|)$ when $|x|\rightarrow \infty$ in $\R^n$, and subharmonic functions of half space $\{x\in \R^n,\, x>0...      51 (2): 319-326 [Abstract ] ( 79 ) [HTML 0KB] [PDF 407KB ]( 109 ) 327 Xue TONG, Rong Fang BIE and Yong Qiang LI   Relations between Strongly Minimal Sets in Models     This paper studies relations between strongly minimal sets in any model of a complete theory. We get the following theorem: If $T$ is a complete theory, $\Psi_{1}(x)$ and $\Psi_{2}(x)$ are two strongly minimal formulas of $T$, then $\Psi_{1}(x)$ can be $X...      51 (2): 327-334 [Abstract ] ( 76 ) [HTML 0KB] [PDF 391KB ]( 94 ) 335 Xiao Hong CAO   Hypercyclicity for Operator Matrices     The relation between hypercyclic operators and the operators which have topological uniform descent is discussed. Also, we explore the hypercyclicity and the supercyclicity for operator matrices....      51 (2): 335-342 [Abstract ] ( 87 ) [HTML 0KB] [PDF 387KB ]( 113 ) 343 Fei HE   Drop Theorem and Drop Property in Topological Linear Spaces     In this paper, Drop theorem in topological linear spaces is established. From this, we obtained that every sequentially compact convex set in topological linear spaces has the Drop property; every countably compact closed convex set in topological linear ...      51 (2): 343-350 [Abstract ] ( 81 ) [HTML 0KB] [PDF 392KB ]( 106 ) 351 Ji Ming YANG   The Number of Solutions of the Generalized Ramanujan--Nagell Equation ${x^2}-D=3^n$     Let $D$ be a positive integer with $D\not\equiv0\ (\mod3)$. ln this paper we prove that if $D>10^{12}$ and the Pell equation ${U^2}-D{V^2}=-1$ has solutions $(U,V)$, then the equation ${x^2}-D=3^n$ has at most two positive integer solutions $(x, n)$....      51 (2): 351-356 [Abstract ] ( 85 ) [HTML 0KB] [PDF 289KB ]( 99 ) 357 Tian Zhou XU   Covariant Projective Representation for Covariant Completely Multi-Positive Linear Maps     The covariant completely multi-positive linear maps between $C^*$-algebras are studied. We show that a covariant completely multi-positive linear map between $C^*$-algebras induces a covariant projective representation of a $C^*$-algebra on Hilbert $C^*$-...      51 (2): 357-364 [Abstract ] ( 74 ) [HTML 0KB] [PDF 382KB ]( 94 ) 365 Yong Hong   On the Norm of a Series Operator with a Symmetric and Homogeneous Kernel and Its Application     For a series operator $T$ with a symmetric and homogemecus rernel $k(m,n)$ defined by $ T\{a_{n}\}{=}\sum_{n=1}^{\infty}K(m,n)a_{n},\, \{a_{n}\}{\in} l_{\omega(n)}$, $lw(n)=\{\{a_{n}\}\,|\,a_{n}\geq0,\, \sum_{n=1}^{\infty}\omega(n)\cdot$ $a_{n}<+\infty...      51 (2): 365-370 [Abstract ] ( 80 ) [HTML 0KB] [PDF 319KB ]( 94 ) 371 Li Ping HUANG   Matrix Having Strong Normal Form over Division Ring     Let $D$ be a division ring, $A\in D^{n\times n}$. Then $\lambda I-A$ can be reduced by some elementary operations into a diagonal form $\Lambda={\rm diag}(1, \ldots, 1, \varphi_1, \ldots, \varphi_r)$, where $\varphi_i$ is a monic polynomial with $\varphi_...      51 (2): 371-380 [Abstract ] ( 86 ) [HTML 0KB] [PDF 492KB ]( 89 ) 381 Sen Hua LAN and Pu ZHANG   A Molecular Characterization of Anisotropic Hardy Spaces and Its Applications     Given an expansive matrix $A$, a molecular characterization of some aniso-tropic Hardy spaces $H^p(\mathbb{R}^n)$ associated with $A$ is obtained in this paper. As its applications, the boundedness on $H^p(\mathbb{R}^n)$ for Calder$\acute{\mbox{o}}$n--Zyg...      51 (2): 381-390 [Abstract ] ( 76 ) [HTML 0KB] [PDF 509KB ]( 91 ) 391 Jian Zhong XIAO and Yuan TAO   Property of Surjection for Monotonic Random Operator and its     The monotonic random operators are studied in Banach spaces. The random acute angle principle, random surjection theorem and random bijection theorem for the continuous monotonic random operators are established. Some new random fixed point theorems for c...      51 (2): 391-400 [Abstract ] ( 77 ) [HTML 0KB] [PDF 483KB ]( 100 ) 401 Qing Liu YAO   Positive Solutions to a Class of Semipositive Fourth-Order Boundary Value Problems with Parameters     The existence of $n$ solutions and/or positive solutions is considered for a class of nonlinear fourth-order boundary value problems with two parameters, where the nonlinear term is allowed to possess a nonpositive lower bound of function type. In mechani...      51 (2): 401-410 [Abstract ] ( 90 ) [HTML 0KB] [PDF 452KB ]( 138 ) 411 Hong Ya GAO, Yu Ming CHU and Guang Ze GU   Local Regularity Results for Minima of Functionals and Solutions of Nonlinear Elliptic Equations     Local regularity results for minima of functionals of the calculus of variation and weak solutions of nonlinear elliptic equations in more general conditions are proved by using the imbedding inequality of Giaquinta and Giusti and the Sobolev space method...      51 (2): 411-416 [Abstract ] ( 99 ) [HTML 0KB] [PDF 400KB ]( 137 )
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