SHORT COMMUNICATION SECTION Some Geometric Flows on Kahler Manifolds

We define a kind of KdV （Korteweg-de Vries） geometric flow for maps from a real line or a circle into a Kahler manifold （N,J,h） with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note.     

Path-following interior point algorithms for the Cartesian <Emphasis Type="Italic">P</Emphasis><Subscript>*</Subscript>(κ)-LCP over symmetric cones

In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P _*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P _*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)     

基于次梯度选取的非光滑优化强次可行方向法

本文结合次梯度选取技术及割平面法和强次可行方向法的思想,提出了一个求解目标函数非光滑约束优化问题的强次可行方向算法.通过设计一个新的寻找搜索方向子问题和构造新型线搜索,算法不仅能接受不可行的初始点,而且能保持迭代点的强次可行性,同时避免在可行域外目标函数值的不适度增加.算法具备全局收敛性,且初步的数值试验表明算法是稳定有效的.     

An improved partial SPIHT with classified weighted rate-distortion optimization for interferential multispectral image compression

Based on the property analysis of interferential multispectral images, a novel compression algorithm of partial set partitioning in hierarchical trees (SPIHT) with classified weighted rate-distortion optimization is presented.After wavelet decomposition, partial SPIHT is applied to each zero tree independently by adaptively selecting one of three coding modes according to the probability of the significant coefficients in each bitplane.Meanwhile the interferential multispectral image is partitioned into two kinds of regions in terms of luminous intensity, and the rate-distortion slopes of zero trees are then lifted with classified weights according to their distortion contribution to the constructed spectrum.Finally a global ratedistortion optimization truncation is performed.Compared with the conventional methods, the proposed algorithm not only improves the performance in spatial domain but also reduces the distortion in spectral domain.     

MERIT FUNCTION AND GLOBAL ALGORITHM FOR BOX CONSTRAINED VARIATIONAL INEQUALITIES

1 IntroductionWe consider tlie variational inequality problelll, deuoted by VIP(X, F), wliicli is to find avector x* E X such thatF(X*)"(X -- X-) 2 0, VX E X, (1)where F: R" - R" is any vector-valued f11uction and X is a uonelllpty subset of R'.This problem has important applicatiolls. in equilibriun1 modeIs arising in fields such asecououtics, transportatioll scieuce alld operations research. See [1]. There exist mauy lllethodsfor solviug tlie variational li1equality problem VIP(X. …     

An adaptive trust region method and its convergence

In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.     

On the Hartogs-Bochner phenomenon for CR functions in

Let be a compact, connected, -smooth and globally minimal hypersurface in which divides the projective space into two connected parts and . We prove that there exists a side, or , such that every continuous CR function on extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.

     

Global existence and nonexistence for degenerate parabolic systems

The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system

in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .

     

Global Attractivity of the Equilibrium of a Nonlinear Difference Equation

The authors consider the nonlinear difference equation x_n+1=x_n+x_n-kf(x_n-k),n=0,1,(0.1) where (0,1), k 0,1, and f C¹[[0,), [0,)] with f(x) < 0.They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.