An efficient optimal algorithm for the quantity discount problem in material requirement planning

An optimal algorithm based on branch-and-bound approach is presented in this paper to determine lot sizes for a single item in material requirement planning environments with deterministic time-phased demand and constant ordering cost with zero lead time, where all-units discounts are available from vendors and backlog is not permitted. On the basis of the proven properties of optimal order policy, a tree-search procedure is presented to construct the sequence of optimal orders. Some useful fathom rules have been proven, which make the algorithm very efficient. To compare the performance of this algorithm with the other existing optimal algorithms, an experimental design with various environments has been developed. Experimental results show that the performance of our optimal algorithm is much better than the performance of other existing optimal algorithms. Considering computational time as the performance measure, this algorithm is considered the best among the existing optimal algorithms for real problems with large dimensions (i.e. large number of periods and discount levels).     

The labeled maximum matching problem

Given a graph G where a label is associated with each edge, we address the problem of looking for a maximum matching of G using the minimum number of different labels, namely the labeled maximum matching problem. It is a relatively new problem whose application is related to the timetabling problem. We prove it is NP-complete and present four different mathematical formulations. Moreover, we propose an exact algorithm based on a branch-and-bound approach to solve it. We evaluate the performance of our algorithm on a wide set of instances and compare our computational times with the ones required by CPLEX to solve the proposed mathematical formulations. Test results show the effectiveness of our procedure, that hugely outperforms the solver.     

Least trace extended set-membership filter

To improve the consistency of estimation result, a least-trace extended set-membership filter (LTESMF) is presented for a class of nonlinear stochastic systems, which has linear output and unknown- but-bounded noise. Feedback technique is used instead of the intersection of ellipsoid-sets in the measurement update. The feedback parameter is optimized in order to minimize the trace of error bounded ellipsoid’s envelop matrix. A new stability analysis method was developed to prove the stochastic system’s stab...     

六角网格系统下的多边形填充算法

针对六角网格系统下图形、图像处理及显示时像素之间相邻的唯一性,挺出六角网格系统下的多边形填充算法,其中包括边界填充算法和扫描线填充算法,采用图示与伪代码的方法描述箅法。与矩形网格上的图像处理算法相比,六角网格系统上的图像处理算法具有更好的唯一性和简便性。     

电阻型半导体甲醛传感器研究进展

甲醛是潜在致癌物和重要的环境污染物.电阻型半导体甲醛传感器因灵敏度高、工艺简单、操作方便、体积小而成为研究热点.从电阻型半导体甲醛传感器的气敏材料和器件结构两个方面展开分析,研究了国内外有代表性的最新研究成果,并展望了未来的发展方向.     

交互式凸组合法的混合时滞不确定中立系统的稳定性

针对带分布时滞和离散时滞的不确定中立型系统进行稳定性研究. 基于交互式凸组合方法和下界引理, 通过构造恰当的李雅普诺夫泛函, 适当分割时滞区间, 处理一组由凸参数逆加权的正函数线性组合(交互式凸组合), 给出线性矩阵不等式形式的系统鲁棒稳定性判据. 该方法允许离散时滞为变时滞, 增强了系统的鲁棒性能. 数值算例验证了所得结果的有效性和合理性.

     

Decentralised sampled-data control for large-scale systems with nonlinear interconnections

This paper presents a decentralised sampled-data control technique for a class of large-scale systems, which are considered to consist of linear subsystems and nonlinear interconnections. The decentralised sampled-data controller design problem is established using a closed-loop subsystem. Based on the controller design problem, the stability condition is derived for a closed-loop large-scale system, and the maximum interconnection bound is guaranteed to satisfy the stability condition. Also, its sufficient condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed technique is verified by using an example of the multi-machine power system.     

On Convergence of Volterra Series Expansion of a Class of Nonlinear Systems

A fundamental issue in conducting the analysis and design of a nonlinear system via Volterra series theory is how to ensure the excitation magnitude and/or model parameters will be in the appropriate range such that the nonlinear system has a convergent Volterra series expansion. To this aim, parametric convergence bounds of Volterra series expansion of nonlinear systems described by a NARX model, which can reveal under what excitation magnitude or within what parameter range a given NARX system is able to have a convergent Volterra series expansion subject to any given input signal, are investigated systematically in this paper. The existing bound results often are given as a function of the maximum input magnitude, which could be suitable for single‐tone harmonic inputs but very conservative for complicated inputs (e.g. multi‐tone or arbitrary inputs). In this study, the output response of nonlinear systems is expressed in a closed form, which is not only determined by the input magnitude but also related to the input energy or waveform. These new techniques result in more accurate bound criteria, which are not only functions of model parameters and the maximum input magnitude but also consider a factor reflecting the overall input energy or wave form. This is significant to practical applications, since the same nonlinear system could exhibit chaotic behavior subject to a simple single‐tone input but might not with respect to other different input signals (e.g. multi‐tone inputs) of the same input magnitude. The results provide useful guidance for the application of Volterra series‐based theory and methods from an engineering point of view. The Duffing equation is used as a benchmark example to show the effectiveness of the results.     

中国微米纳米 花状Au-SnO2复合材料的制备及其对甲醛气敏性能的研究

利用水热法合成了花状SnO2微米材料,并以它作为基体,对其进行Au纳米颗粒修饰,得到了花状Au-SnO2复合材料.利用X射线衍射(XRD)、扫描电子显微镜(SEM)、X射线光电子能谱(XPS)分析等表征手段对所制备的Au-SnO2复合材料进行了表征分析,结果表明,这种花状结构的材料是由厚度为30 nm～60 nm的SnO2纳米片自组装而成,其尺寸为1 μm～2 μm.同时,我们用花状SnO2和Au修饰的花状SnO2复合材料对1×10-6～500×10-6的甲醛进行了气敏性能测试.结果表明,通过Au修饰,花状SnO2对甲醛的气敏性能有了极大的提高.当甲醛浓度为200×10-6时,其灵敏度(Ra/Rg)约为120,是花状SnO2敏感材料的8倍,表现出很高的响应.另外,由Au修饰的花状SnO2复合材料制成的敏感元件对甲醛表现出良好的选择性.这可能归因于Au纳米颗粒高效的催化活性促进了甲醛气体的扩散和O2的吸附,从而使其表现出更加优异的气敏性能.     

The ski-rental problem with multiple discount options

We propose the ski-rental problem with multiple discount options in which there are n options to rent an equipment. Every option has a rental duration; the longer the duration, the more the discount. This generalizes the standard ski-rental problem where one can only rent or buy. We present a 4-competitive on-line algorithm for our problem and show that no deterministic algorithm can have a smaller competitive ratio when n is large enough. Comparing with the original ski-rental problem, the competitive ratio becomes larger when there are more options.