关键词： Symplectic similitude group   Orthogonal similitude group   Word problem   Gaussian elimination   Spinor norm   Double coset decomposition  

摘要： This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double coset decomposition with respect to a Siegel maximal parabolic subgroup, which is important in computing infinite-dimensional representations for some algebraic groups.

关键词： Monitoring area coverage optimization algorithm   Nodes perceptual mathematical model   Wireless sensor networks  

摘要： With the rapid development of microelectronics technology, wireless communication technology and sensor technology, micro-structured sensors that can sense and communicate at the same time have emerged. This tiny device can sense all kinds of information in the surrounding environment, collect it to the sink node, and then transmit it to the data center. Wireless sensor networks are widely used in civil, industrial, agricultural, military and other fields. In order to meet the demand of monitoring area coverage effect, this paper firstly analyzes the research status of wireless sensor networks at home and abroad, points out the main problems existing in the current research process, and establishes a reasonable mathematical model according to the research status. Secondly, to solve the problem of poor coverage effect of existing algorithms, a monitoring area coverage optimization algorithm based on perceived probability around nodes is proposed. By designing a reasonable scheme of moving nodes, the algorithm can gradually disperse the nodes and improve the coverage effect in the monitoring area. Finally, the simulation results show that the algorithm has a good performance, which can reduce the moving distance of nodes, improve the coverage of the network and prolong the service time of the whole network.

关键词： 算法多样化   比较优化   个性学习   创新意识  

摘要： 数学课程标准倡导算法多样化,尊重学生的个体差异,实现不同的人在数学上都得到不同的发展。在"十几减9"的教学中,教师尊重学生的想法,积极肯定他们的创意和进步,发展学生的数学思维和合作交流能力,从而激发学生的创新意识,提高学生的数学素养。

关键词： 非拟牛顿法   Wolfe-Powell不精确线性搜索   Goldstein非精确线性搜索  

摘要： 在目标函数一致凸的条件下,探讨了非拟牛顿法在Wolfel线性搜索和Goldstein线性搜索下的全局收敛性予以证明,得出在求解无约束优化问题当δk充分小时,用B k+1替代2f(x k),使非拟牛顿方程不仅利用了函数梯度值信息,还利用了函数值的信息。

关键词： two-dimensional integrable lattice   x-integral   integrable reduction   cutoff condition   open lattice   Darboux-integrable system   characteristic Lie algebra  

摘要： We study the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables. By integrability, we mean the presence of reductions of a chain to a system of hyperbolic equations of an arbitrarily high order that are integrable in the Darboux sense. Darboux integrability admits a remarkable algebraic interpretation: the Lie-Rinehart algebras related to both characteristic directions corresponding to the reduced system of hyperbolic equations must have a finite dimension. We discuss a classification algorithm based on the properties of the characteristic algebra and present some classification results. We find new examples of integrable equations.

关键词： logistics   milk-run   routing   mixed integer linear formulation   first   best-fit strategy   grouping evolution strategy  

摘要： The operational planning of distribution network for automotive industry is complex with many conditions to consider, including heterogeneous fleet, enforcing the feasibility of 3D-packing of pallets into vehicles to address the vehicle's capacity in terms of weight and volume, compatibility of orders in a vehicle, returning empty pallets from assembly-plants backwards to suppliers, and delivery time windows. A mathematical model (MILP) is proposed that takes account of these conditions to minimise total transportation costs. The network structure can be a combination of direct shipment and milk-run for both forward and reverse flow of pallets. The model is solved optimally for small-size problems. For solving larger problems, a heuristic algorithm (in two versions) is proposed that uses a similarity measure to generate a reasonable list of orders. Best/first-fit strategies are employed to generate a feasible solution with the aid of a relaxed version of the proposed MILP. Improvement heuristics are also designed. Unlike most of existing constructive heuristics, our aim for developing the heuristic approach is to force routing decision, with all of its considerations, being made optimal. We also use the proposed best-fit strategy in the body of grouping evolution strategy (GES) algorithm to attain an effective meta-heuristic approach. The effectiveness of heuristics is tested on generated instances which demonstrates they are optimal for small-size problems. They are also tested on the data of daily auto-parts shipments gathered from the largest Iranian automobile company. Results demonstrate there exists a significant potential for cost saving through milk-run strategy compared with the direct shipping strategy.

关键词： Optimization   genetic algorithm   solar energy   Jarghoyeh power plant   solar technology type  

摘要： With growing proliferation of environmental pollution and reduction of energy sources, human being has been always looking for a solution to reduce pollution. One of these solutions is to use solar energy. In this research, a mathematical model is developed for optimization location decision of solar cells to minimize the operational and investment costs. The location of placement and the type of solar technology is planned and optimized by Genetic Algorithm (GA). To show the validity of the model, an accurate solving method is applied for small dimensions. Then, the GA efficiency is shown by comparing GAMS and GA results in large dimensions using the optimum values of the GA parameters. Finally, the applicability of the proposed model is presented for Jarghoyeh power plant in Iran. The results indicate that GA with spending less time could find better answers in comparison with GAMS. The results show the effectiveness of the proposed model.

关键词： 算法多样化   数学思维   策略方法  

摘要： 算法多样化可以让学生在掌握基本运算方法时,获得解决问题、创新思维、发展思维的能力。运用算法多样化,可以活跃课堂学习氛围,学生积极参与,实现师生互动,提高学生数学素养。

关键词： 算法思想   高中数学   教学应用  

摘要： 高中数学教学顺应新课程改革提出的教学理念,正不断地丰富和发展着教学内容和积极的转变教学模式、更新教育理念等。算法在当前的教育背景下,越来越成为高中数学教学的重要部分,算法思想是数学学科核心素养的组成部分,是贯穿于数学发展始终,能够很好的应用于数学实践。因此,在高中数学教学中有效地应用算法思想有助于学生核心素养的培养和推进学生综合素质的有效提升。

关键词： 小学数学课堂教学   引导学生   学科核心素养   数学思维   方格图   乘法分配律  

摘要： 义务教育数学课程标准(2011版)提出了10个关键词,运算能力赫然在列。普通高中数学课程标准(2017版)明确提出数学学科核心素养包括:数学抽象、逻辑推理、数学建模、直观想象、数学运算和数据分析。数学运算再次名列其中,由此可见,数学运算及其能力作为后续学习和将来生活所必需的能力基础是何其重要。