关键词： Geometric algebra   Adaptive filtering   M-estimate   Multidimensional signal processing   Variable step-size  

摘要： In this paper, the transient performance of the geometric algebra based least mean M-estimate (GA-LMM) filtering algorithm is analyzed in detail under some simplifying assumptions. Further, the variable step-size variant VSS-GA-LMM is designed to eliminate the constraint of the constant step size on the per-formance of the GA-LMM and the optimal step size is obtained by maximizing the difference of mean square deviation (MSD) between successive iterations, which effectively balances the contradiction be-tween convergence rate and steady-state error. Finally, numerical simulations are presented to verify the validity of the theoretical analysis of the GA-LMM and the advantages of the GA-LMM and VSS-GA-LMM algorithms. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Preprojective algebra   Deformed preprojective algebra   Self-injective algebra   Periodic algebra   System of equations  

摘要： We construct a numeric algorithm for completing the proof of a conjecture asserting that all deformed preprojective algebras of generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing that non-trivial deformed preprojective algebras of Dynkin types E-7 and E-8 exist only in characteristic 2. As a consequence, we show that deformed preprojective algebras of Dynkin types E-6, E-7 and E-8 are periodic and we obtain an algorithm for a classification of such algebras, up to algebra isomorphism. We do it by a reduction of the conjecture to a solution of a system of equations associated with the problem of the existence of a suitable algebra isomorphism. phi(f): P-f (E-n) -> P(E-n) described in Theorem 2.1. One also shows that our algorithmic approach to the conjecture is also applicable to the classification of the mesh algebras of generalized Dynkin type. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Assembly   Job shop   Branch and bound   Scheduling   Two-stage production system  

摘要： Purpose Two-stage production systems including a processing shop and an assembly stage are widely used in various manufacturing industries. These two stages are usually studied independently which may not lead to ideal results. This paper aims to deal with a two-stage production system including a job shop and an assembly stage. Design/methodology/approach Some exact methods are proposed based on branch and bound (B&B) approach to minimize the total completion time of products. As B&B approaches are usually time-consuming, three efficient lower bounds are developed for the problem and variable neighborhood search is used to provide proper upper bound of the solution in each branch. In addition, to create branches and search new nodes, two strategies are applied including the best-first search and the depth-first search (DFS). Another feature of the proposed algorithms is that the search space is reduced by releasing the precedence constraint. In this case, the problem becomes equivalent to a parallel machine scheduling problem, and the redundant branches that do not consider the precedence constraint are removed. Therefore, the number of nodes and computational time are significantly reduced without eliminating the optimal solution. Findings Some numerical examples are used to evaluate the performance of the proposed methods. Comparison result to mathematical model (mixed-integer linear programming) validates the performance accuracy and efficiency of the proposed methods. In addition, computational results indicate the superiority of the DFS strategy with regard to CPU time. Originality/value Studies about the scheduling problems for two-stage production systems including job shop followed by an assembly stage traditionally present approximate method and metaheuristic algorithms to solve the problem. This is the first study that introduces exact methods based on (B&B) approach.

关键词： 极限   基本初等函数   分类  

摘要： 本文首先提出解决极限问题的首要步骤,接着对极限过程进行具体分类,然后针对不同类型提出了行之有效的解决方法.

关键词： 数学算法   计算机编程   优化策略   高效技术  

摘要： 在对数学算法进行深入研究之后,能够发现其是一种非常严谨精密的计算方法,并在计算机编程中发挥着不可替代的作用。分析数学算法和计算机编程,可知二者具有相辅相成的关系。对于计算机而言,如果想要充分发挥自身高效率计算的优势,就要使数学算法充分发挥自身对计算机编程的优化作用。在计算机编程中应用数学算法模型思想,在满足信息化社会发挥要求的同时,保证计算机编程具有科学合理性。

关键词： 干涉测量   相位解包裹   数学形态学   区域分割  

摘要： 相位解包裹是光学干涉测量的关键环节,要求计算速度快、精度高、适应性强。根据包裹相位不同级次间存在明显边界的特点,本文提出数学形态学区域分割的快速相位解包裹算法。首先,采用数学形态学提取边界并分割相位区域。然后,计算区域之间的相位差异以确定各区域的相位级次和抬升值,判断边界点归属以确定边界各点抬升值。最后,根据抬升值对各区域相位进行整体抬升,最终获得空间上连续分布的相位。仿真和实验表明:基于数学形态学的解包裹算法对于1000×1000 pixels像素的相位处理时间在1 s以内,仅为经典的最小二乘算法用时的1/4,且相位自身边界、无效区域、噪声等因素对解包裹效果并无影响。该算法具有速度快、适用性强、精度较高等优点,在动态光干涉、光全息、光栅条纹投影轮廓测量等对运算速度要求较高的测量场景中有广泛的应用前景。

关键词： 数学模型   网络数据流量   流量特征  

摘要： 由于传统算法统计的异常流量特征存在偏差,使得网络异常数据检测的抗干扰能力有所降低,基于数学模型研究网络数据流量异常的检测算法。在模糊C均值分类异常流量特征集的基础上,应用自适应回归法统计异常流量特征量,计算不同异常流量的向量值,构建数字模型检测异常流量。实验表明:在异常流量检测成功率为100%的前提下,文章算法的抗干扰强度平均能达到19.41dB,比传统算法分别高了10.09dB和10.67dB,说明文章中算法的抗干扰能力更强。

关键词： 阿拉伯世界   吴文俊   著名数学家   两条路线   数学   两条主线  

摘要： 我国著名数学家吴文俊院士首先明确提出:“从历史上来看,数学的发展有两条路线。一条是以希腊为主的路线,通过阿拉伯世界影响到欧洲;还有一条从我们中国起源,通过印度进而影响到世界数学的发展。”这是吴先生第一次明确提出数学发展的两条主线。吴文俊院士在他的第一篇数学史论文中。

关键词： 无人机影像   影像配准   特征点   树冠区域   可见光波段差异植被指数(VDVI)   数学形态学  

摘要： 在无人机影像配准过程中,特征点对提取数量较为庞大,配准效率较低;当特征点位于树冠区域内时,受地形、视角、光照等因素的影响,非常容易产生大量点对的错误匹配。为解决上述问题,文章提出一种基于数学形态学改进的无人机影像配准算法。首先,根据可见光波段差异植被指数(visible-band difference vegetation index,VDVI)与数学形态学原理,对树冠区域内的特征点进行剔除;然后将双向匹配算法与最近邻(k-nearest neighbors,KNN)算法相结合,对特征点进行粗匹配;最后利用渐进一致采样(progressive sample consensus,PROSAC)算法进行精匹配,进一步提高配准精度。实验结果表明,在对有树冠区域覆盖的无人机影像进行配准时,该文提出的算法能有效提高匹配率与配准精度。

关键词： 人工智能算法   船舶航线   约束条件   数学建模   求解  

摘要： 传统的鱼群算法、蚁群算法在对数学建模求解中存在迭代次数过多的问题,针对该问题,对人工智能算法进行优化,设计新的数学建模求解方法。首先,描述船舶航行航线及约束条件;其次,根据约束条件,构建规划数学模型;最后,基于人工智能算法设计此时的求解函数,得出该数学建模的解。实验结果表明:人工智能算法在船舶航线规划的数学建模求解时的迭代次数少,求解性能更佳。