Incremental subgradient method for nonsmooth convex optimization with fixed point constraints

This paper proposes an incremental subgradient method for solving the problem of minimizing the sum of nondifferentiable, convex objective functions over the intersection of fixed point sets of nonexpansive mappings in a real Hilbert space. The proposed algorithm can work in nonsmooth optimization over constraint sets onto which projections cannot be always implemented, whereas the conventional incremental subgradient method can be applied only when a constraint set is simple in the sense that the projection onto it can be easily implemented. We first study its convergence for a constant step size. The analysis indicates that there is a possibility that the algorithm with a small constant step size approximates a solution to the problem. Next, we study its convergence for a diminishing step size and show that there exists a subsequence of the sequence generated by the algorithm which weakly converges to a solution to the problem. Moreover, we show the whole sequence generated by the algorithm with a diminishing step size strongly converges to the solution to the problem under certain assumptions. We also give examples of real applied problems which satisfy the assumptions in the convergence theorems and numerical examples to support the convergence analyses.     

山西省近50年风速变化及突变特征分析

利用线性拟合、M-K方法对山西省22个气象观测站1960—2010年的逐日风速资料进行了倾向、突变、逐年代变化等特征分析。研究表明,近50年来山西省平均风速存在明显的下降趋势,平均风速由20世纪60年代的2.16 m/s下降到21世纪初的1.86 m/s;不同时间段呈现不同的变化特征,1979—1989年风速出现显著下降,年均递减率达到0.046 m/s,变率远超出其他时段;对近50年山西省平均风速进行M-K检验后发现,在1982年出现明显的突变点。山西省四季平均风速均呈下降趋势,四季风速下降速率最快的为春季,冬季次之,夏季风速下降速率最慢。同样,四季风速均发生突变,突变时间点分布在1980—1985年间。除8月外,山西省各个月份风速也呈下降趋势,且均出现突变现象。     

二阶自治广义Birkhoff系统的奇点分析

建立二阶自治广义Birkhoff系统的微分方程.给出该系统的线性化方程,得到该线性方程转化为梯度系统的条件,利用梯度系统的性质对线性系统的奇点进行了分析,然后再利用Perron定理探讨了相应的非线性系统的奇点类型.结果表明,如果线性系统能成为梯度系统,那么相应的非线性系统的奇点可能是结点或者鞍点.     

Point-augmented biquadratic C1 subdivision surfaces

Shape artifacts, especially for convex input polyhedra, make Doo and Sabin’s generalization of bi-quadratic (bi-2) subdivision surfaces unattractive for general design. Rather than tuning the eigenstructure of the subdivision matrix, we improve shape by adding a point and enriching the refinement rules. Adding a guiding point can also yield a polar bi-2 subdivision algorithm. Both the augmented and the polar bi-2 subdivision are complemented by a new Primal Bi-2 Subdivision scheme. All surfaces are $C^1$ and can be combined.     

On the Controllability of Nonlocal Second‐Order Impulsive Neutral Stochastic Integro‐Differential Equations with Infinite Delay

In this paper, we investigate the controllability for a class of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay in Hilbert spaces. More precisely, a set of sufficient conditions for the controllability results of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay are derived by means of the Banach fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. As an application, an example is provided to illustrate the obtained theory.     

太阳能LED路灯控制系统的设计

设计了一套基于STC12单片机的太阳能LED路灯控制系统,系统采用变步长的电导增量法跟踪太阳能电池板最大功率点,充分利用太阳能电池板的能量,对铅酸蓄电池充电。同时实时监测铅酸蓄电池的电压防止蓄电池过充、过放等现象;对LED路灯采用多段式的恒流控制,通过环境照度的监测控制LED路灯在不同电流强度下工作,以增强LED路灯的使用寿命,实现节约用电的目的。     

Complete controllability for abstract measure differential systems

In this paper, we investigate the complete controllability for abstract measure differential systems. Firstly, we introduce several new concepts about complete controllability for abstract measure differential systems. Then, on the basis of the Sadovskii fixed‐point theorem, we give sufficient conditions for complete controllability for a class of abstract measure differential systems. The compactness of the semigroup generated by some operator is unnecessary in this paper, and we show that our results, dealing with complete controllability problem for an ordinary differential system in infinite‐dimensional Banach space, are also less conservative than that in the previous literature. Copyright © 2012 John Wiley & Sons, Ltd.     

瓦斯突变预警上限值确定方法的研究

针对现有煤矿安全监控系统采用超限原理,以瓦斯传感器测量值为判断依据,无法及时发现预定报警值以下范围内瓦斯异常变化的问题,提出了一种不超限瓦斯突变预警方法,介绍了静态预警和动态预警两种不超限瓦斯突变报警方法。结合余吾煤业N2202工作面探头数据,分别对不超限瓦斯突变预警基础数据的静态数据和动态数据进行了分层抽样及分布的验证和拟合,得出静态预警和动态预警的基础数据基本符合正态分布的结论。提出采用假设检验和区间估计等实时计算静态预警和动态预警上限值的方法,并采用N2202工作面探头数据进行了验证。     

提升机综合后备保护装置减速点的设置方法

依次给出了提升机综合后备保护装置减速点到停车位距离的粗略计算公式、某段(点)到停车位的安全制动距离计算公式、某段(点)到停车位的超速持续判断安全制动距离的计算公式及减速点到停车位的超速持续判断安全制动距离的计算公式,在井口下与井口相距该安全制动距离的点即设置为减速点。该方法适用于提升机电控系统减速点随载重量自动调整时后备保护减速点的设置。应用结果表明,根据该方法设置的提升机综合保护装置减速点可保证在提升机电控系统减速点失效后使提升容器在井口以下安全停车,可靠性高。     

光伏电池最大功率点跟踪方法比较

根据太阳能光伏电池的工程数学模型,在Matlab环境下建立了光伏电池仿真模型,分析了光照强度和温度变化对光伏电池输出特性的影响。针对扰动观察法采用固定的扰动步长而难以获得较高跟踪精度和响应速度的问题,提出了一种基于变步长的改进的扰动观察法,并通过对光伏电池控制系统进行仿真,比较了这2种最大功率点跟踪方法的仿真曲线。结果表明,采用改进的扰动观察法的光伏电池控制系统能更快速跟踪最大功率点,且在最大功率点处稳定性较好。