关键词： 高等数学   复合函数极限运算   教学设计  

摘要： “复合函数极限运算法则”是“函数极限运算法 则”这一节的内容,是全章的重点内容之一,由于其抽象度高和 逻辑性强的特点,使得学生往往不太容易理解和掌握。本文通 过举例来逐步说明定理中假设条件的必要性,同时还举例分析 了极限运算法则中极限等式的逆向运用。通过探讨本节高等 数学课程,可以使学生更好地掌握逆向思维,构建学生的知识 体系,加强学生运用极限法则来解决问题的能力。

关键词： 算法多样化   计算教学   数学课  

摘要： 算法多样化的思想强调的是尊重学生的独立思考,鼓励学生探索不同的方法,并不是让学生掌握多种方法,教师应该在课堂中鼓励、尊重学生思维的结果,引导学生进行讨论和交流,适时点拨,肯定有价值、有创意的方法,从而培养学生良好的思维习惯和探索创新的精神。

关键词： 算法多样化   小学数学   教学探究   认知方式   数学  

摘要： 为了顺应时代的发展,我国的教育制度始终不断地进行调整改革,国家教育部门一直在大力倡导执教者进行教学模式创新,以此来提升教学效率。在上述复杂的背景下,上至国家教育部门,下至基层教育工作者,都在不断地进行教学创新探索。近年来在小学教学中出现了一种'算法多样化'的教学理念,大量的课堂实践表明,其对于多样化教学问题解决有着良好的教学效果。另外这种算法很好的体现了现代教学中倡导学生自主探索学习的理念,其不但能够明显的提升课堂效率,还能够综合的提升学生各项综合能力。本文将结合当代小学数学的现状以及算法多样化的基本特点进行阐述,并在此基础上提出了一系列算法多样化教学的策略方法,希望本文能够对小学数学执教者有所帮助。

关键词： 递归算法   数学   计算机程序设计  

摘要： 数学在计算机程序设计中具有重要地位,通过数学思维、数学计算方法、数学模型的建立等将实际问题不断抽象化,并设计相应的计算机程序获得问题的解,是一个简洁、高效的设计过程,程序员可以将实际问题通过各种科学计算转换为程序,在这一过程中,数学算法的合理应用具有重要意义。文章以递归算法在计算机程序设计中的运用作为基础,探讨数学计算在计算机程序设计中的重要作用。

关键词： 数学算法   计算机编程   优化  

摘要： 数学算法是一种研究型问题的有效解决方式,通过归纳总结的方式进行体现。在编程行为当中大量地应用了数学算法,其中最为重要的原因便在于计算机程序当中包含了极强的逻辑性,这一点与数学算法之间有着非常紧密的联系。本文对数学算法在计算机编程当中对程序的优化作用进行简要分析。

关键词： 遗传算法   机械制造   数学教学  

摘要： 遗传算法在机械制造领域中有着重要的应用价值,不仅能够优化机械制造过程,而且还能帮助机械制造专业数学教师引导学生充分理解并运用遗传算法解决相关问题。详细分析了遗传算法在机械制造专业数学教学中的应用策略,希望能够为相关专业提供可以参考的理论依据。

关键词： Closed-loop supply chain network design   Modified priority-based encoding   Uncertainty   Whale optimization algorithm  

摘要： The closed-loop supply chain (CLSC) management as one of the most significant management issues has been increasingly spotlighted by the government, companies and customers, over the past years. The primary reasons for this growing attention mainly down to the governments-driven and environmental related regulations which has caused the overall supply cost to reduce while enhancing the customer satisfaction. Thereby, in the present study, efforts have been made to propose a facility location/allocation model for a multi-echelon multi-product multi-period CLSC network under shortage, uncertainty, and discount on the purchase of raw materials. To design the network, a mixed-integer nonlinear programming (MINLP) model capable of reducing total costs of network is proposed. Moreover, the model is developed using a robust fuzzy programming (RFP) to investigate the effects of uncertainty parameters including customer demand, fraction of returned products, transportation costs, the price of raw materials, and shortage costs. As the developed model was NP-hard, a novel whale optimization algorithm (WOA) aimed at minimizing the network total costs with application of a modified priority-based encoding procedure is proposed. To validate the model and effectiveness of the proposed algorithm, some quantitative experiments were designed and solved by an optimization solver package and the proposed algorithm. Comparison of the outcomes provided by the proposed algorithm and exact solution is indicative of high quality performance of the applied algorithm to find a near-optimal solution within the reasonable computational time. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Admixture   Neighbor-joining   Phylogenetics   Rogue taxon  

摘要： The neighbor-joining algorithm for phylogenetic inference (NJ) has been seen to have three specific properties when applied to distance matrices that contain an admixed taxon: (1) antecedence of clustering, in which the admixed taxon agglomerates with one of its source taxa before the two source taxa agglomerate with each other;(2) intermediacy of distances, in which the distance on an inferred NJ tree between an admixed taxon and either of its source taxa is smaller than the distance between the two source taxa;and (3) intermediacy of path lengths, in which the number of edges separating the admixed taxon and either of its source taxa is less than or equal to the number of edges between the source taxa. We examine the behavior of neighbor-joining on distance matrices containing an admixed group, investigating the occurrence of antecedence of clustering, intermediacy of distances, and intermediacy of path lengths. We first mathematically predict the frequency with which the properties are satisfied for a labeled unrooted binary tree selected uniformly at random in the absence of admixture. We then introduce a taxon constructed by a linear admixture of distances from two source taxa, examining three admixture scenarios by simulation: a model in which distance matrices are chosen at random, a model in which an admixed taxon is added to a set of taxa that reflect treelike evolution, and a model that introduces a perturbation of the treelike scenario. In contrast to previous conjectures, we observe that the three properties are sometimes violated by distance matrices that include an admixed taxon. However, we also find that they are satisfied more often than is expected by chance when the distance matrix contains an admixed taxon, especially when evolution among the non-admixed taxa is treelike. The results contribute to a deeper understanding of the nature of evolutionary trees constructed from data that do not necessarily reflect a treelike evolutionary process.

关键词： Cobalt oxide   basin-hoping Monte Carlo   DFT  

摘要： The structural, electronic and magnetic properties of the neutral and cationic cobalt oxide clusters (CoO)(n)(q) (n = 3 - 10, q = 0, +1) have been studied using a modified basin-hopping Monte Carlo (BHMC) algorithm refined by spin-polarized DFT. A systematic search of global minimum structures predicts new global minima of (CoO)(9)(0/+) and reproduced other minima that are in excellent agreement with previous works. For most low-spin and high-spin states, the structural transition from planar-like to compact structure occurs at (CoO)(5)(0/+), which is in contrast with the general notion that the structural changes at (CoO)(6)(0/+). Supported by the results of the binding energy, second-order total energy difference, chemical hardness, chemical potential and HOMO-LUMO gap confirms the stability of (CoO)(4). Results of the spin magnetic moments for the global minima show that (CoO)(4) and (CoO)(8) spin configurations exhibit a fully antiferromagnetic (AFM) ordering, while (CoO)(9) spin displays the highest ferromagnetic (FM) ordering. Interestingly, elongation of Co-Co bond in (COO)(4) causes O being polarized by the neighboring Co atoms that accordingly follows the Goodenough-Kanamori-Anderson rule of FM super-exchange coupling for the Co-O-Co structural rearrangement to 90 degrees (D-4h structure) in order to accommodate the spin magnetic ordering changes. This rearrangement is a result of the valence band being shifted away from the Fermi level to lower energy causing high population of the spin-up density of state and leading to the asymmetrical polarization of the whole (CoO)(4)nq structure. As far as the dissociation energy surfaces are concerned, the first ever such surfaces are constructed corresponding to (CoO)(n)(q) -> (CoO)(m)(q) (CoO)((n-m)), which identify a complete dissociation pathway linking the cationic and neutral clusters and finally confirm (CoO)(4)(0/+) as the most stable cluster compared to the rest.