一类具幂零奇点的五次系统中心条件及极限环分支

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.     

构造二元向量值有理插值函数的一种新方法

At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.     

平环和的Heegaard亏格的一个下界

Let Mi, i = 1,2, be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of OMi. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper, we give a lower bound for the genus of the annulus sum M in the condition of the Heegaard distances of the submanifolds M1 and M2     

与$\zeta(2k 1)$函数有关的两类快速收敛级数

Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.     

子群的S-条件置换性对有限群结构的影响

Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma（P） denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф（P）, the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md（P） on the structure of finite groups. Some new results are obtained and some known results are generalized.     

投影的约化极小模和空间的夹角

Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of （I - PN）PM,     

全函数空间和置换空间的一些性质

In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.     

非Lipschitz条件Hilbert空间上扩散过程的短时间大偏差原理

Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.     

基于J-C本构模型的Comp.B炸药落锤冲击数值模拟

为研究Comp.B炸药在惯性冲击下的力学响应特性, 基于Johnson-Cook本构模型, 对 点火前的Comp.B炸药大落锤(400kg)冲击实验进行了数值模拟. 在不同应力加载条件下模 拟计算得到了用状态方程和不用状态方程的$\sigma$-$t$曲线, 对比应力峰值、应 力上升时间等主要力学参数, 结果表明考虑了状态方程的数值模 拟结果与实验吻合最好, 可以很好地模拟炸药惯性冲击下的力学响应.     

A biomass carbon material with microtubule bundling and natural O-doping derived from goldenberry calyx and its electrochemical performance in supercapacitor

A promising biomass carbon material,manufactured by the carbonation of Physalis peruviana L.calyx at 700℃,is presented in this wo rk.Morphology characterization shows that the carbon material possesses long microtubule bundling and above 30%natural O-atom component on the surface.After KOH chemical etching,the materials maintain the oxygen content but exhibit more micropores and higher specific surface area up to 1732.6 m^2/g.Using as an electrode material for supercapacitor,the active carbon material exhibits high specific capacitance up to 339.7 F/g at 0.5 A/g in 3 mol/L KOH aqueous solution through three-electrode system.The active carbon material also exhibits excellent cycling stability(97%retention)by 10,000 cycles at 10 A/g.The outstanding electrochemical performances are attributing to the unique long microtubule bundling with much more pores and the abundant Oelement on the surface.This biomass carbon material with excellent electrochemical properties could be a useful material for multiple applications.