关键词： 数学算法   计算机编程   数据结   C语言  

摘要： 本文针对数学算法和计算机编程基础内容,以及两者之间相关性展开分析,结合数学算法在计算机编程中应用的目的和意义,通过研究数学算法在C语言运用、数据结设计、建立数学模型、对象语言、编程结构中的具体应用,其目的在于提升数学算法应用效果,优化计算机编程内容。

关键词： 多焦点图像   缺失特征填补   离散数学模型   模型参数估计   图像闪烁修复   实验分析  

摘要： 亮度闪烁会造成多焦点图像特征缺失,产生视觉失真效果。为此,提出基于离散数学模型的多焦点图像缺失特征填补算法,修复多焦点图像亮度闪烁问题。根据亮度闪烁离散数学模型展现出的空间域上亮度变化连续性特征,利用位置块估计模型参数。在此基础上,利用亮度闪烁在空间中呈现的连续性特点,检测多焦点图像序列中的运动区域,分别采用基于前向多帧参考、基于运动矢量的闪烁修复算法修复图像静止区域和运动区域,共同实现多焦点图像缺失特征填补。实验结果表明:该算法可有效修复图像亮度闪烁,填补图像的缺失特征,营造良好的视觉效果;该算法可显著改善多焦点图像序列的亮度均值和标准差波动幅度,增强平滑性,且具备较快运行速度。

关键词： 数学图论分析   数据相似度   权重   调整   通信网络  

摘要： 为了提高嵌入式通信网络传输数据的传输质量,提出基于数学图论分析的数据相似度权重调整算法。构建嵌入式通信网络传输数据的模糊信息检测模型,分析数据传输动态模糊特征,采用数学图论分析进行嵌入式通信网络传输数据相似度权重调整过程中的自适应寻优,实现嵌入式通信网络传输数据的优化相似度权重调整。结果表明,在迭代次数分别为100、200、300、400时,采用该方法测试的输出误比特率为0.103、0.043、0、0,远低于对比方法,提高了嵌入式通信网络传输数据的输出质量。

关键词： 国际学术期刊   并行计算机   量子计算机   工程技术研究中心   《科学》杂志   审稿人   数学算法   潘建伟  

摘要： "九章"量子计算机是"一个最先进的实验","一个重大成就"。——中国科学技术大学宣布,该校潘建伟团队与中科院上海微系统所、国家并行计算机工程技术研究中心合作,成功构建76个光子的量子计算原型机"九章",求解数学算法"高斯玻色取样"只需200秒,而目前世界最快的超级计算机要用6亿年。这项研究成果刊发在国际学术期刊《科学》杂志上,审稿人如此评价。

关键词： 算法   多样化   价值思考   实践反思  

摘要： 算法多样化是新课标倡导的基本理念之一。算法多样化有利于促进学生的个性化学习,使得学生经历知识产生的过程,有利于学生核心素养的全面提高。在算法多样化的教学中,要注重汇报前的准备、汇报时的引导和汇报后的择优。

关键词： 路径规划   参数寻优模型   全局最优解   群体智能   灰狼算法  

摘要： 为提供物资配送性能,采用群体智能算法用于物资配送数学模型优化,以降低物资配送成本。首先提出物资配送问题模型,选择物资配送中心所有商品配送至各配送点的成本总和作为优化目标函数,然后采用灰狼算法进行优化,将配送中心与配送点坐标映射至狼群分布坐标,采用配送成本总和的倒数作为适应度函数,选择3个最优个体作为高级狼,剩余为普通狼,普通狼不断的位置更新跟随高级狼,最后获得适应度最高的跟随路径即为物资配送路径。实验证明:通过灰狼优化的物资配送路径,相比于常用的物资配送路径规划算法,能够获得更低的配送成本。

关键词： 65N12   65N15   65N30   65N50   68Q25  

摘要： We consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation interconnecting a finite element discretization, the Banach-Picard linearization, and a contractive linear algebraic solver. In particular, we identify stopping criteria for the algebraic solver that on the one hand do not request an overly tight tolerance but on the other hand are sufficient for the inexact (perturbed) Banach-Picard linearization to remain contractive. Similarly, we identify suitable stopping criteria for the Banach-Picard iteration that leave an amount of linearization error that is not harmful for the residual a posteriori error estimate to steer reliably the adaptive mesh-refinement. For the resulting algorithm, we prove a contraction of the (doubly) inexact iterates after some amount of steps of mesh-refinement/linearization/algebraic solver, leading to its linear convergence. Moreover, for usual mesh-refinement rules, we also prove that the overall error decays at the optimal rate with respect to the number of elements (degrees of freedom) added with respect to the initial mesh. Finally, we prove that our fully adaptive algorithm drives the overall error down with the same optimal rate also with respect to the overall algorithmic cost expressed as the cumulated sum of the number of mesh elements over all mesh-refinement, linearization, and algebraic solver steps. Numerical experiments support these theoretical findings and illustrate the optimal overall algorithmic cost of the fully adaptive algorithm on several test cases.

关键词： Interior-point algorithm   Sufficient linear complementarity problem   Algebraic equivalent transformation   Polynomial complexity  

摘要： We present a short-step interior-point algorithm (IPA) for sufficient linear complementarity problems (LCPs) based on a new search direction. An algebraic equivalent transformation (AET) is used on the centrality equation of the central path system and Newton's method is applied on this modified system. This technique was offered by Zsolt Darvay for linear optimization in 2002. Darvay first used the square root function as AET and in 2012 Darvay et al. applied this technique with an other transformation formed by the difference of the identity map and the square root function. We apply the AET technique with the new function to transform the central path equation of the sufficient LCPs. This technique leads to new search directions for the problem. We introduce an IPA with full Newton steps and prove that the iteration bound of the algorithm coincides with the best known one for sufficient LCPs. We present some numerical results to illustrate performance of the proposed IPA on two significantly different sets of test problems and compare it, with related, quite similar variants of IPAs.

关键词： Process planning   Mixed-integer linear programming model   Hybrid evolutionary algorithm   Benchmark  

摘要： Process planning is an essential part of the manufacturing system linking the designing and practical manufacturing. However, the reported process planning models are too simple to describe all characteristics because of the complexity of process planning. Therefore, a new mixed-integer linear programming (MILP) mathematical model is established based on OR-node of the network graph. In the model, the linear expression of the OR-node controlling function as well as three types of changing costs are first established. Beside, considering the OR-node selection state in the encoding and decoding method, a hybrid evolutionary algorithm (HEA) is designed to combine a genetic algorithm with a simulated annealing algorithm. The tournament selection method is adopted in the proposed HEA, and the discussion on the tournament size is conducted on the open problems to make the algorithm designing more reasonable and scientific. The HEA and the new MILP model are both tested on series of numerical experiments which are carried on the existing benchmarks as well as some randomly generated cases. The behavior of both two methods can verify their effectiveness and superiority successfully.

关键词： Engineering communication   pedagogy   teaching  

摘要： Most textbooks and trade press books on engineering communication are genre based, proscription based, or some are a combination of the two. Henderson takes a different approach to teaching the rules of English grammar and how to apply those rules to craft effective sentences. His approach is mathematics based, presenting the rules of English grammar as sentence equations. This approach makes the book particularly intriguing as a resource for teaching students of engineering and science. Henderson's "A Math-Based Writing System for Engineers: Sentence Algebra & Document Algorithms" presents a distinctive approach and methodology for clear engineering communication, particularly suited to its specific audience. Henderson's methodology, grounded in the "universal language" of mathematics, is unique and refreshing. The book is a welcome addition to available resources for these students and their instructors.