Enhanced and restored signals as a generalized solution for shock filter models. Part II—numerical study

In Part I of this paper, we proposed a well-posed generalized model for signal enhancement and restoration based on shock filters. A theoretical study of the Cauchy problem in the framework of generalized functions algebra was developed in detail. In Part II, we investigate the numerical aspects of the model. We derive an efficient, explicit numerical scheme in both one and two dimensions, and investigate the schemes' stability and convergence. Through experimental tests, we demonstrate the effectiveness of the numerical schemes when restoring and enhancing signals in various situations with a limited number of iterations. Moreover, we show the impact of the coefficients introduced in the model on the procedure's processing time.     

Regular connections among generalized connections

The properties of the space of regular connections as a subset of the space of generalized connections in the Ashtekar framework are studied. For every choice of compact structure group and smoothness category for the paths, it is determined whether is dense in or not. Moreover, it is proven that has Ashtekar–Lewandowski measure zero for every non-trivial structure group and every smoothness category. The analogous results hold for gauge orbits instead of connections.     

解第一类算子方程的一种新的正则化方法

对算子与右端都为近似给定的第一类算子方程提出一种新的正则化方法，依据广义Ａｒｃａｎｇｅｌｉ方法选取正则参数，建立了正则解的收敛性。这种新的正则化方法与通常的Ｔｉｋｈｏｎｏｖ正则化方法相比较，提高了正则解的渐近阶估计。     

联邦滤波理论在组合导航系统设计中的应用

为了解决导航信息大量冗余情况下组合导航系统计算量过大及故障数据互相污染的问题，本文探讨了具有容错结构的无复位联邦滤波器的设计方法，包括公共参考系统的选定及信息的合理分配原则，并对集中滤波器和联邦滤波器作了对比仿真计算。仿真结果表明：融合周期为滤波周期的１０倍时，联邦滤波精度与集中滤波精度几乎相同。     

Generalized R-KKM theorems in topological space and their applications

In this paper, we introduce generalized R-KKM mapping and discuss some new generalized R-KKM theorem under the nonconvexity setting of topological space. As applications, some new minimax inequalities, saddle point theorem are proved in topological space. Our theorems unified and extend many known results in recent literature.     

Optimality conditions and duality for a class of nondifferentiable multi-objective fractional programming problems

A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,θ,ρ,d)-convex class about the Clarke’s generalized gradient. Under the above generalized convexity assumption, necessary and sufficient conditions for optimality are given. Finally, a dual problem corresponding to (MFP) is formulated, appropriate dual theorems are proved.      

Analysis of a two-stage telecommunication supply chain with technology dependent demand

We analyze a two-stage telecommunication supply chain consisting of one operator and one vendor under a multiple period setting. The operator faces a stochastic market demand which depends on technology investment level. The decision variables for the operator are the initial technology investment level and the capacity of the network for each period. The capacity that the operator installs in one period also remains available in subsequent periods. The operator can increase or decrease the available capacity at each period. For this model, an algorithm to find the centralized optimal solution is proposed. A profit sharing contract where firms share both the revenue and operating costs generated throughout the periods along with initial technology investment is suggested. Also a coordinating quantity discount contract where the discount on the price depends on the total installed capacity is designed. The case where the vendor decides on the technology investment level and the operator decides on the capacity of the network is also analyzed and it is shown that this game has a unique Nash equilibrium.     

岛津GC-16A型气相色谱仪故障排除一例

岛津GC－16A型气相色谱仪因CRT显示器控制电路故障而导致主机死机，进而造成CR－7A型数据处理机无法与主机联机而死机。通过分析故障现象和电路结构，对主机部分电路进行改造，完全拆除主机上的CRT显示器控制电路，直接通过CR－7A型数据处理机控制主机，使主机不受CRT显示器控制电路的影响而稳定地工作。经改造后，气相色谱仪工作正常，不再出现死机现象。     

Solvability of nonlinear variational-hemivariational inequalities

In this paper we study nonlinear elliptic differential equations driven by the p-Laplacian with unilateral constraints produced by the combined effects of a monotone term and of a nonmonotone term (variational-hemivariational inequality). Our approach is variational and uses the subdifferential theory of nonsmooth functions and the theory of accretive and monotone operators. Also using these ideas and a special choice of the monotone term, we prove the existence of a strictly positive smooth solution for a class of nonlinear equations with nonsmooth potential (hemivariational inequality).     

广义线性回归拟似然估计的渐近正态性

研究了形如n∑i=1xi(yi-μ(xi′β))=0拟似然方程,在一定的条件下证明了拟似然估计βn的渐近正态性;并进一步证明了可用于β0大样本统计推断的渐近正态性结果．