关键词： 小学数学   算法   多样化   认识   思考  

摘要： 小学数学的特点决定单一的数学算法无法满足学生学习的需要,而且由于数学科目所涉及的算法较多,因此只有掌握多样化的数学知识以及数学算法,才能够更好地解决实际数学问题,为提高学生的数学成绩以及各方面综合能力奠定基础。本文针对小学数学算法多样化的认识与思考进行相应的分析以及研究。

关键词： Axial algebra   Nonassociative algebra   Majorana algebra   Finite groups   Algorithm  

摘要： An axial algebra A is a commutative non-associative algebra generated by primitive idempotents, called axes, whose adjoint action on A is semisimple and multiplication of eigenvectors is controlled by a certain fusion law. Different fusion laws define different classes of axial algebras. Axial algebras are inherently related to groups. Namely, when the fusion law is graded by an abelian group T, every axis a leads to a subgroup of automorphisms T-a of A. The group generated by all T-a is called the Miyamoto group of the algebra. We describe a new algorithm for constructing axial algebras with a given Miyamoto group. A key feature of the algorithm is the expansion step, which allows us to overcome the 2-closedness restriction of Seress's algorithm computing Majorana algebras. At the end we provide a list of examples for the Monster fusion law, computed using a MAGMA implementation of our algorithm. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Grid-connected photovoltaic plants   Modeling   Optimization   Genetic algorithm  

摘要： The increasing penetration of photovoltaic (PV) technology calls for the development of an effective method for optimization of grid-connected photovoltaic power plants. This paper presents a simultaneous optimization method of ten important design parameters of a PV plant, including the module power, inverter sizing, support structure dimensions, cable losses, module orientation and row spacing. A mathematical PV performance model taking into account the important effects and losses and an economic cost model were developed and presented in detail. The objective function is the internal rate of return and the optimization is performed by a genetic algorithm. The results show that the proposed models and method are capable to optimize the grid-connected PV plant and provide reliable results after a 6-7 min calculation time. The method was demonstrated in detail for a Hungarian location, including the losses and cost structure of the optimal plant configuration. The optimization was also performed for 5 additional sites around the world to assess the effect of location and meteorology. The impact of the decreasing PV module prices on the optimal design is calculated to identify the expected future trends in PV plant design. The presented optimization method can be utilized to facilitate the optimal design of commercial PV plants and for research purposes.

关键词： Assembly line balancing   multi-manned workstations   mixed-integer programming   tabu search algorithm   assignment restrictions  

摘要： A multi-manned assembly line is a set of workstations where task operations can be performed on multiple sides of the line. Such assembly lines are important for large products, such as buses, cars and trucks. In this study, a mathematical model for multi-manned assembly lines with assignment restrictions is proposed. The purpose of the mathematical model is to minimize the total number of workers and open multi-manned workstations along the line for a given cycle time simultaneously under various assignment restrictions. The model provides a more realistic situation for multi-manned assembly line problems. The tabu search algorithm (TSA) is also used to solve the problem. The performances of both methods on well-known data-set problems are analysed. Based on the computational experiments, the performance of the proposed TSA is compared with the mathematical model solutions on various problem instances. The experimental results verify the effectiveness and efficiency of the proposed TSA.

关键词： welding flow-shop scheduling problem   non-dominated sorting Genetic Algorithm III   total tardiness   machine interaction effect   setup time  

摘要： This paper addresses a bi-objective welding shop scheduling problem (BWSSP) aiming to minimise the total tardiness and the machine interaction effect. The BWSSP is a special flow-shop scheduling problem (FSP) which is characterised by the fact that more than one machine can process on one job at a certain stage. This study analyses the operation of a structural metal manufacturing plant, and includes various aspects such as job sequence, machine-number-dependent processing time, lifting up time, lifting down time and different delivery time. A novel mixed-integer programming model (MIPM) is established, which can be used to minimise the delayed delivery time and the total machine interaction effect. One machine interaction effect formula is given in this paper. In order to solve this BWSSP, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII), embedded with a restarted strategy (RNSGAIII), is proposed. The restarted strategy, which can increase the diversity of the solutions, will be triggered with a restart probability. Following the iterative process, an effective strategy is applied to reduce the interaction effect penalty, on the premise that the makespan will remain unchanged. Total five algorithms, namely NSGAII, NSGAIII, harmony search algorithm (HSA), strength Pareto evolutionary algorithm (SPEA2), and RNSGAIII are utilised to solve this engineering problem. Numerical simulations show that the improved RNSGAIII outperforms the other methods, and the Pareto solution distribution and diversity, in particular, are significantly improved.

关键词： 区块链技术   社会信用体系   数学算法   社会信用机制   全程追溯   应用场景   公开透明   达成共识  

摘要： 来源:《人民论坛》智慧社会来临对传统社会信用体系提出了挑战,为新型社会信用体系的产生提供了技术基础和应用场景。在此背景下,区块链技术的发展催生了一种新型社会信用机制,即系统信用,它通过构建一种可信的技术系统,保障信息的公开透明、全程追溯和不可篡改,在机器之间建立"信任"网络,通过数学算法为社会成员创造信用和达成共识。

关键词： 高中数学   算法教学   方法  

摘要： 算法在高中数学教学中的引入，对培养学生的逻辑思维能力、创新思维能力和自主探索能力都有着极其重要的教学意义。在高中数学教学中，正视算法在高中数学教学中定位，革新传统教学方法是教研人员应积极探索和研究的重要课题。

关键词： 随机事件   主成分算法   数学化  

摘要： 随机事件,在《概率论与数理统计》课程中,是很重要的基础知识点,但在教学过程中一直没有引起足够的重视。但在现实问题转化为数学问题的过程中,随机事件是首要的第一步。在该文中,将讨论随机事件在实际问题数学化过程中的重要性及其熟练地学习和掌握如何去把现实问题用随机事件这种数学的语言表述出来,并且,还讨论了其在主成分算法中的应用。

关键词： 算法教学   中职数学   人工智能  

摘要： 在人工智能教育日益重要的时代背景下,本文面向中职学校,立足中职数学教学,探析以开展算法教学为第二课堂的中职数学课如何渗透人工智能教育,希望能够为人工智能教育在中职学校的开展提供参考与借鉴,从而提升中职学生的人工智能素养.

关键词： Sequential Monte Carlo   Communication network security   Fuzzy mathematics   Adaptive weighting  

摘要： For the analysis of the current security impact of communication networks, this paper introduces a traditional mathematical model of information security impact. Based on this, further combining the importance of effective implementation of security protection, based on the sequential Monte Carlo localization algorithm, a novel The new positioning method can increase the reliability of the anchor box, optimize the sampling area, and improve the positioning accuracy of the node during the acquisition of the anchor box during the prediction stage by integrating the RSSI principle and the centroid principle. An improved model is for the analysis of the security impact of communication networks based on Monte Carlo algorithm. Although this algorithm increases the positioning complexity to a certain extent, the entire calculation process consumes less energy and the optimization effect is obvious. This model is based on the quantitative analysis of communication network security threats, communication network combat methods, network security attributes, and network security adversarial attributes. It uses fuzzy mathematical theory and adaptive weighting algorithms to effectively communicate in the case of effective security protection The impact of network security was quantitatively analyzed and modeled. The simulation results based on Monte Carlo method prove the validity of the model in this paper. Simulation results show that compared with the traditional MCB positioning algorithm, this algorithm can effectively improve the positioning accuracy.