赋权矩阵及其性质

本文给出了以S为行权和向量的权矩阵类T_＋(S)中每个权矩阵都可逆的一个充要条件．     

B值鞅型序列的一些极限定理

本文讨论了一些B值鞅型序列的强大数定律 ,弱大数定律 ,Lr收敛性及完全收敛性 ,推广了许多熟知的结果 .     

Augmented Spinor Space

In this paper, based on the Pauli matrices, a notion of augmented spinor space is introduced, and a uniqueness of such augmented spinor space of rank n is proved. It may be expected that this new notion of spaces can be used in mathematical physics and geometry.     

Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

On superlinear convergence of quasi-Newton methods for nonsmooth equations

We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.     

谱约束下对称正交对称矩阵束的最佳逼近

讨论了对称正交对称矩阵的广义逆特征值问题，得到了通解表达式和最佳解的表达式。     

示差半微分循环伏安法研究琥珀酰胆碱在水/硝基苯界面的传递行为

研究了油/水界面电解的示差半微分循环伏安行为。在0.01mol/L LiCl(w)-0.01mol/L TBATCIPB(nb)体系“电位窗”比TBATPB(nb)向正方向扩展约50mV,残余电流基本消除,使“电位窗”内的平台向左右拓宽约50mV。算得界面电容约为16μF/cm~2。考察了琥珀酰胆碱离子在w/nb界面的传递伏安特性,结果与一般半微分循环伏安法相似。但峰形改善,检测限降低一个数量级(1×10~(-6)mol/L),相对标准偏差在5％以内,可用于定量测定琥珀酰胆碱。     

触销式双障碍买权价值过程鞅性

主要证明了在不存在交易成本的完全市场条件下连续时间欧式触销式双障碍买权贴现到0时刻的价值过程为鞅,并且给出了对应单障碍买权价值过程的鞅性质.同时还讨论了执行价格为随机的触销式双障碍买权的鞅性质,给出了任意时刻 t(0≤ t≤T)其内在价值的表达式.     

一类周期种群系统的适定性及最优控制

本文研究了一类非线性周期种群系统的适定性及最优控制问题 .利用压缩不动点原理讨论了该种群系统的周期解的存在唯一性 .并用变分法给出了最优控制所满足的必要条件 .