Semisimple algebras of almost minimal rank over the reals

A famous lower bound for the bilinear complexity of the multiplication in associative algebras is the Alder–Strassen bound. Algebras for which this bound is tight are called algebras of minimal rank. After 25 years of research, these algebras are now well understood. Here we start the investigation of the algebras for which the Alder–Strassen bound is off by one. As a first result, we completely characterize the semisimple algebras over R$\mathbb{R}$ whose bilinear complexity is by one larger than the Alder–Strassen bound. Furthermore, we characterize all algebras A$A$ (with radical) of minimal rank plus one over R$\mathbb{R}$ for which A/radA$A/radA$ has minimal rank plus one. The other possibility is that A/radA$A/radA$ has minimal rank. For this case, we only present a partial result.     

插值边界的四边网格离散极小曲面建模方法

如何实现极小曲面的快速三维建模,是几何设计与计算领域中的难点和热点问题.给定一条封闭的边界离散折线,本文研究如何构造以其为边界的四边网格离散极小曲面.首先从曲面的内蕴微分几何度量出发,给出了离散四边网格极小曲面的数学定义;然后利用保长度边界投影、四边网格生成、径向基函数插值映射和非线性优化技术,提出了由给定边界离散折线快速构造离散四边网格极小曲面的一般技术框架.最后通过若干建模实例验证了本文方法的有效性.该方法可实现四边网格极小曲面的高质量建模,在建筑几何领域具有一定的应用价值.     

Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. When failures occur, the repair of both component 1 and component 2 are not ‘as good as new’. The consecutive operating times of component 1 after repair constitute a decreasing geometric process, while the repair times of component 1 are independent and identically distributed. For component 2, its failure is rectified by minimal repair, and the repair time is negligible. Component 1 has priority in use when both components are good. The replacement policy N is based on the failure number of component 1. Under policy N, we derive the explicit expression of the long-run average cost rate C(N) as well as the average number of repairs of component 2 before the system replaced. The optimal replacement policy N*, which minimises the long-run average cost rate C(N), is obtained theoretically. If the failure rate r(t) of component 2 is increasing, the existence and uniqueness of the optimal policy N* is also proved. Finally, a numerical example is given to validate the developed theoretical model. Some sensitivity analyses are provided to show the influence of some parameters, such as the costs for replacement and repair, and the parameters of the lifetime and repair time distributions of both components, to the optimal replacement policy N* and corresponding average cost rate C(N*).     

Supervisory control based on minimal cuts and Petri net sub-controllers coordination

This paper addresses the synthesis of Petri net (PN) controller for the forbidden state transition problem with a new utilisation of the theory of regions. Moreover, as any method of control synthesis based on a reachability graph, the theory of regions suffers from the combinatorial explosion problem. The proposed work minimises the number of equations in the linear system of theory of regions and therefore one can reduce the computation time. In this paper, two different approaches are proposed to select minimal cuts in the reachability graph in order to synthesise a PN controller. Thanks to a switch from one cut to another, one can activate and deactivate the corresponding?PNcontroller. An application is implemented in a flexible manufacturing system to illustrate the present method. Finally, comparison with previous works with experimental results in obtaining a maximally permissive controller is presented.     

过测地线的调和Bézier曲面设计

极小曲面和测地线是建筑几何领域中2类重要的几何元素,而调和曲面常作为极小曲面的一种线性近似.文中将测地线和调和曲面结合起来,提出一种过给定测地线的调和Bézier曲面设计方法.首先给出了一种构造调和Bézier曲面的新方法,证明了调和Bézier曲面的形状由第一层和第二层的控制顶点完全决定;然后根据测地线的性质,证明了过给定测地线的调和Bézier曲面的形状由该测地线和第二层的首末2个控制顶点完全决定.最后通过若干实例验证了该方法的有效性.文中方法充分利用了测地线和调和曲面的特殊几何性质,对张拉膜建筑结构的几何设计具有一定的实用价值.     

求解最小闭包球问题改进的SMO-型算法

研究n维空间中m个点的最小闭包球(MEB)问题。通过结合确定并删除内部点的技术到序列最小最优化(SMO)方法中,提出一种近似求解MEB问题的改进的SMO-型算法。证明了该算法具有线性收敛性。数值结果表明对于一些mn的大规模数据集,改进的算法与原算法相比速度可以提高10倍以上。尤其,当n等于100且m等于100000时,改进的SMO-型算法仅需执行8s。此外,对于n等于10000且m等于1000的大规模数据集,改进的算法也仅需执行150s。     

公交线路查询算法

公共交通不仅是衡量城市现代化程度的重要标志也是解决交通拥堵问题的途径. 而公交线路查询系统的关键技术是公交线路查询算法, 它对提高公交资源的利用率有着重要的意义. 总结了国内外城市公交最优路径算法并在此基础上分析了高效运行城市公交系统的条件和影响因素. 介绍了最短路径问题及Dijkstra算法及其在查询系统应用中的弊端. 然后提出了基于换乘最小的广度优先算法的数学模型, 给出了算法的实现, 并以银川市公共交通公司的公交部分数据为基础, 完成了公交信息查询系统的设计与开发.     

Integrating spectral indices with environmental parameters for estimating heavy metal concentrations in rice using a dynamic fuzzy neural-network model

A generalized dynamic fuzzy neural network (GDFNN) was created to estimate heavy metal concentrations in rice by integrating spectral indices and environmental parameters. Hyperspectral data, environmental parameters, and heavy metal content were collected from field experiments with different levels of heavy metal pollution (Cu and Cd). Input variables used in the GDFNN model were derived from 10 variables acquired by gray relational analysis. The assessment models for Cd and Cu concentration employed five and six input variables, respectively. The results showed that the GDFNN for estimating Cu and Cd concentrations in rice performed well at prediction with a compact network structure using the training, validation, and testing sets (for Cu, fuzzy rules=9, R² greater than 0.75, and RMSE less than 2.5; for Cd, fuzzy rules=9, R² greater than 0.75, and RMSE less than 1.0). The final GDFNN model was then compared with a back-propagation (BP) neural network model, adaptive-network-based fuzzy interference systems (ANFIS), and a regression model. The accuracies of GDFNN model prediction were usually slightly better than those of the other three models. This demonstrates that the GDFNN model is more suitable for predicting heavy metal concentrations in rice.     

芹菜素和山萘酚对细胞色素CYP1A2抑制机理研究

目的:我们先前的体外肝微粒体抑制活性实验,已证实芹菜素和山萘酚对细胞色素CYP 1A2有较强的抑制作用。然而,其抑制机理仍然未知。分子模拟方法能更好了解这2个天然产物对1A2的抑制机理。方法:采用分子对接、分子动力学模拟及结合自由能计算的方法,研究它们对1A2的抑制作用。结果:芹菜素和山萘酚对1A2的预测结合自由能分别是-18.01和-16.40 kcal/mol,这与实验抑制活性结果一致。在1A2结合口袋中,残基呈平面性排列,与平面芹菜素和山萘酚存在紧密的范德华和疏水相互作用,因而小分子有较强的抑制作用。此外,活性位点残基也与小分子发生氢键和盐桥等相互作用,使小分子在结合口袋中的位置得到固定。     

无线传感器网络中基于最小跳数路由的节点休眠算法

结合无线传感器网络中的最小跳数路由协议,根据功能的不同将传感器节点分为只进行数据采集的终端节点和既进行数据采集又要转发数据的中间节点两类;提出一种节点休眠算法,对前述两种节点采取不同的休眠/唤醒策略以降低能耗。理论分析和仿真结果表明：所提节点休眠算法节约了节点能量,延长了无线传感器网络的寿命。