关于一般Hilbert二重级数定理的改进

应用Ｅｌｕｅｒ求和公式．证明对任意正整数ｎ及实数ｐ＞１．有这里，由此改进了一般Ｈｉｌｂｅｒｔ二重级数定理．     

部分线性变系数模型改进的加权混合Profile-Liu估计

研究半参数部分线性变系数模型的有偏估计,当回归模型参数部分自变量存在多重共线性时,在随机线性约束条件下,融合Profile最小二乘估计、加权混合估计和Liu估计构造回归模型参数分量改进的加权混合Profile-Liu估计,并在一定正则条件下证明估计量的渐近性质,最后利用蒙特卡洛数值模拟验证所提出估计量的有限样本表现性.     

Efficient and Adaptive Lagrange-Multiplier Methods for Nonlinear Continuous Global Optimization

Lagrangian methods are popular in solving continuous constrained optimization problems. In this paper, we address three important issues in applying Lagrangian methods to solve optimization problems with inequality constraints.First, we study methods to transform inequality constraints into equality constraints. An existing method, called the slack-variable method, adds a slack variable to each inequality constraint in order to transform it into an equality constraint. Its disadvantage is that when the search trajectory is inside a feasible region, some satisfied constraints may still pose some effect on the Lagrangian function, leading to possible oscillations and divergence when a local minimum lies on the boundary of the feasible region. To overcome this problem, we propose the MaxQ method that carries no effect on satisfied constraints. Hence, minimizing the Lagrangian function in a feasible region always leads to a local minimum of the objective function. We also study some strategies to speed up its convergence.Second, we study methods to improve the convergence speed of Lagrangian methods without affecting the solution quality. This is done by an adaptive-control strategy that dynamically adjusts the relative weights between the objective and the Lagrangian part, leading to better balance between the two and faster convergence.Third, we study a trace-based method to pull the search trajectory from one saddle point to another in a continuous fashion without restarts. This overcomes one of the problems in existing Lagrangian methods that converges only to one saddle point and requires random restarts to look for new saddle points, often missing good saddle points in the vicinity of saddle points already found.Finally, we describe a prototype Novel (Nonlinear Optimization via External Lead) that implements our proposed strategies and present improved solutions in solving a collection of benchmarks.     

一类对称函数不等式的加细和推广

利用控制不等式理论加细和推广了一类对称函数不等式,并给出一个几何应用。     

Synchronization of master-slave markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin's formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.     

Diversity study of 12 X‐chromosomal STR loci in Hui ethnic from China

X‐chromosomal STRs (X‐STRs) have been used as complements of autosomal STR application in recent years. In this work, we present population genetic data of 12 X‐STRs including DXS101, DXS10159, DXS10162, DXS10164, DXS6789, DXS7133, DXS7423, DXS7424, DXS8378, DXS981, GATA165B12, and GATA31E08 loci in a sample of 231 unrelated healthy individuals from the Hui ethnic group in Ningxia Hui Autonomous Region, China. Allelic frequencies of the 12 X‐STR loci and haplotypic frequencies of the reported linkage groups (DXS7424‐DXS101 and DXS10159‐DXS10164‐DXS10162) were investigated in the group, respectively. No STR loci showed significant deviations from the Hardy–Weinberg equilibriums and no linkage disequilibriums of pairwise loci were found after Bonferroni correction, respectively. A combined power of discrimination in female individuals was 0.999999999985 and that in male individuals was 0.99999967, respectively. The combined mean exclusion chance in deficiency cases, normal trios and duo cases were 0.999934, 0.995754, and 0.999796, respectively. Significant differences were observed from 0 to 8 loci, when making comparisons between the data of Hui ethnic group and previously reported data from other 16 populations. The results indicated the new panel of 12 X‐STR loci might be useful for forensic science application.     

GA-凸函数的Hadamard型不等式的推广

对GA-凸函数的Hadamard型不等式加权推广,定义了与GA-凸函数定积分有关的函数,证明了它们具有某种准线性,从而得到这些函数的单调性.     

Morita Invariance of the Filter Dimension and of the Inequality of Bernstein

It is proved that the filter dimension is Morita invariant. A direct consequence of this fact is the Morita invariance of the inequality of Bernstein: if an algebra A is Morita equivalent to the ring of differential operators on a smooth irreducible affine algebraic variety X of dimension n ≥ 1 over a field of characteristic zero then the Gelfand–Kirillov dimension for all nonzero finitely generated A-modules M. In fact, a stronger result is proved, namely, a Morita invariance of the holonomic number for finitely generated algebra. A direct consequence of this fact is that an analogue of the inequality of Bernstein holds for the (simple) rational Cherednik algebras H _c for integral c: for all nonzero finitely generated H _c -modules M. For these class of algebras, it gives an affirmative answer to a question of Ken Brown about symplectic reflection algebras. Presented by Alain Verschoren.     

An SQP-filter method for inequality constrained optimization and its global convergence

In this paper, we combine the filter technique with a modified sequential quadratic programming (SQP) method. The optimization solution is obtained by reducing step length, which is obtained by an exact linear search. Furthermore, this method can start with an infeasible initial point. The method uses a filter to promote global convergence.