关键词： differential algebraic systems   initial value problems   reproducing kernel algorithm   Gram-Schmidt process  

摘要： The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of differential algebraic systems for ordinary differential equations. The reproducing kernel Hilbert space (circle plus(m)(j=1) W-2(2) [a,b]) circle plus (circle plus(n)(j=m+1) W-2(1) [a,b]) is constructed in which the initial conditions of the systems are satisfied. While, two smooth kernel functions are used throughout the evolution of the algorithm in order to obtain the required grid points. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： Symmetric variable   canonical Reed-Muller algebra system   Boolean function  

摘要： To simplify the process for identifying 12 types of symmetric variables in the canonical Reed-Muller (CRM) algebra system, we propose a new symmetry detection algorithm based on AND-XOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on AND-XOR expansion around two arbitrary logical variables, the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints, the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the complicated process for separating the AND-XOR expansion coefficients into different groups in the Reed-Muller transform methods and solves the problem of completeness in the RM type decomposition map method. The application results show that, compared with traditional methods the new algorithm is an optimal detection method in terms of applicability of the number of logical variables, detection types, and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient.

关键词： Algebra   Algebraic geometry   Algorithms   Applied mathematics   Approximation methods   Bacterial diseases   Biology and life sciences   Curve fitting   Diagnostic medicine   Fatigue   Infectious diseases   Mathematical and statistical techniques   Mathematical functions   Mathematical models   Mathematics   Medicine and health sciences   Muscle contraction   Muscle physiology   Pathology and laboratory medicine   Physical sciences   Physiology   Research and analysis methods   Research Article   Signs and symptoms   Simulation and modeling   Tetanus  

摘要： An unfused tetanus of a motor unit (MU) evoked by a train of pulses at variable interpulse intervals is the sum of non-equal twitch-like responses to these stimuli. A tool for a precise prediction of these successive contractions for MUs of different physiological types with different contractile properties is crucial for modeling the whole muscle behavior during various types of activity. The aim of this paper is to develop such a general mathematical algorithm for the MUs of the medial gastrocnemius muscle of rats. For this purpose, tetanic curves recorded for 30 MUs (10 slow, 10 fast fatigue-resistant and 10 fast fatigable) were mathematically decomposed into twitch-like contractions. Each contraction was modeled by the previously proposed 6-parameter analytical function, and the analysis of these six parameters allowed us to develop a prediction algorithm based on the following input data: parameters of the initial twitch, the maximum force of a MU and the series of pulses. Linear relationship was found between the normalized amplitudes of the successive contractions and the remainder between the actual force levels at which the contraction started and the maximum tetanic force. The normalization was made according to the amplitude of the first decomposed twitch. However, the respective approximation lines had different specific angles with respect to the ordinate. These angles had different and non-overlapping ranges for slow and fast MUs. A sensitivity analysis concerning this slope was performed and the dependence between the angles and the maximal fused tetanic force normalized to the amplitude of the first contraction was approximated by a power function. The normalized MU contraction and half-relaxation times were approximated by linear functions depending on the normalized actual force levels at which each contraction starts. The normalization was made according to the contraction time of the first contraction. The actual force levels were calculated init

关键词： DBSCAN聚类   图像分割   岩石薄片图像   数学形态学  

摘要： 在岩石薄片图像处理中,针对岩屑矿物个数未知、成像多为聚集的点状的特点,提出了一种基于DBSCAN(Density-Based Spatial Clustering of Applications with Noise)算法与数学形态学的矿物分割方法。首先,标记出每个颗粒目标,求得其中心坐标;其次,利用DBSCAN算法对岩屑颗粒目标中心进行聚类,将不同区域的岩屑目标分离出来;最后,利用数学形态学方法对聚类结果做膨胀、填孔、腐蚀等处理,得到颗粒的边界。实验分析表明:该方法聚类效果良好,参数容易控制并有一定的抗噪性能,对岩屑颗粒目标的提取有较好的效果。

关键词： 虹膜特征提取   数学形态学   边缘坐标极值  

摘要： 对于虹膜纹理特征的提取,本文提出了一种基于数学形态学及二维纹理边缘坐标极值的特征提取算法,该算法包括两部分：利用数学形态学检测归一化并增强后的虹膜图像纹理的边缘、分别在横向和纵向提取虹膜纹理边缘的极值点.该算法直接对图像进行操作,简单直观,易于操作,计算量较少,占用存储空间小,提高了系统的运行速度,满足系统实时性要求.

关键词： 模糊权值网络   三角模糊数   最短路问题   模糊结构元   权矩阵法  

摘要： 模糊权值网络的最短路问题是一类重要的网络优化问题.针对边权值为三角模糊数的模糊权值网络的最短路问题,基于模糊数的结构元加权序,将其模糊线性规划模型等价转化为经典的线性规划模型,并提出一种改进的权矩阵算法来求解该问题,算法证明和应用实例表明新算法的正确性和有效性.此外对于边权值为其他形式模糊数的模糊权值网络的最短路问题,文中模型和算法同样有效.

关键词： 数学学习   十指计算法   应用  

摘要： 培养学生的计算能力,历来是小学数学教学的重要任务之一。由于中、重度智障学生的识记和抽象思维能力都很差,这给他们学习加、减计算带来了很大的困难。教学中,教师能把算理讲的很透彻,可是对于我们的学生来说那是根本无法理解的,更不用说去运用算理进行计算了。教学原理,“如果主要通过感觉运动来教,智力落后儿童是能够学习的。”为了避免学生产生厌学情绪,我在教中、重度智障学生学习加减计算时,运用了“十指计算法”,让学生自己的双手十指充分参与学习活动,只要按顺序数数,就能得出计算结果,帮助中重度学生克服学习障碍。