关键词： 数学思想   算理   算法   有效融合  

摘要： 对小学计算教学的目标是让学生在理解算理的基础上掌握算法。在教学过程中，教师要有意识地渗透数学思想，帮助学生理解算理，促进学生将算理与算法有效融合，从而提高学生的数学素养。

关键词： K均值聚类   数学形态学   煤岩微观结构   SEM扫描   图像分割算法  

摘要： 利用SEM扫描观测平煤十矿戊_(10)-20230工作面煤岩的微观形态,针对灰度区域不明显的煤样SEM图像,探究K-means和数学形态学中先开后闭运算相结合分割算法的可行性与有效性,并采用相关分割算法作对比试验。结果表明:本文算法匹配率75.48%,误分率16.96%,相较于其他4种算法匹配率最高,误分率最低,有明显优势,能够较准确地将孔隙从扫描图像中分割出来;本算法TPF值34.79%,TNF值97.18%,正确分割比例最大,而FNF值65.21%,FPF值2.82%,错误分割比例最小,TPF值与FNF值和为1,TNF值与FPF值和也为1,说明评价指标的正确性。

关键词： 数学方法   计算机算法   应用探究  

摘要： 计算机算法可以说是数学方法在现实生活中的实用表现之一,大量的编程设计中的计算机算法以数学方法为参考,教育改革之后针对数学的基础教育也适当地加入了有关逻辑推理的较为简单的方法和思想,本文将针对数学方法自身的特点结合其在计算机算法中的应用进行相关的讨论和探索。

关键词： 数学运算   算法   运算能力   高中数学   计算过程   数据处理   近似计算   数学问题  

摘要： 数学运算能力是高中数学的基本能力，也是高中数学的核心素养之一，它是指会根据法则、公式进行正确运算、变形和数据处理，能根据问题的条件，寻找合理、简捷的运算途径，能根据要求对数据进行估计和近似计算的能力。数学运算需要懂算法，明算理。算法是运算的“处方”，也就是根据数学问题的情境，在将问题分析清楚的基础上，找到解决问题的具体步骤。算理有两方面的含义，一是计算过程中的道理，即计算过程中的思维方式，解决为什么这样算的问题；二是运算的依据，主要指运算性质、法则及方法、技巧等。算理确保每一运算步骤的合理性，整体运算的准确性、深刻性和灵活性。

关键词： 数学算法   计算机编程   优化  

摘要： 随着我国经济的迅速发展,我们已经进入信息化时代,计算机已经逐步走进每家每户,与我们的生活息息相关,第三次科技革命为计算机的出现做了铺垫,计算机的历史并不久远,但却给人类社会的发展带来了巨大的改变,行业的发展依赖于计算机的应用。但是计算机的许多软件都是需要通过编程得以实现,计算机编程的优良影响着软件的工作效率,数学算法是计算机编程的基础,数学算法的充分应用才能优化计算机编程。

关键词： Differential   algebraic equations   implicit integration   constrained dynamical systems   multibody systems   Adams integration methods  

摘要： This paper examines the performance of the 3rd and 4th order implicit Adams methods in the framework of the two-loop implicit sparse matrix numerical integration method in solving the differential/algebraic equations of heavily constrained dynamical systems. The variable-step size two-loop implicit sparse matrix numerical integration/Adams method proposed in this investigation avoids numerical force differentiation, ensures satisfying the nonlinear algebraic constraint equations at the position, velocity, and acceleration levels, and allows using sparse matrix techniques for efficiently solving the dynamical equations. The iterative outer loop of the two-loop implicit sparse matrix numerical integration/Adams method is aimed at achieving the convergence of the implicit integration formulae used to solve the independent differential equations of motion, while the inner loop is used to ensure the convergence of the iterative procedure used to satisfy the algebraic constraint equations. To solve the independent differential equations, two different implicit Adams integration formulae are examined in this investigation;a 3rd order implicit Adams-Moulton formula with a 2nd order explicit predictor Adams Bashforth formula, and a 4th order implicit Adams-Moulton formula with a 3rd order explicit predictor Adams Bashforth formula. A standard Newton-Raphson algorithm is used to satisfy the nonlinear algebraic constraint equations at the position level. The constraint equations at the velocity and acceleration levels are linear, and therefore, there is no need for an iterative procedure to solve for the dependent velocities and accelerations. The algorithm used for the error check and step-size change is described. The performance of the two-loop implicit sparse matrix numerical integration/Adams algorithm developed in this investigation is evaluated by comparison with the explicit predictor-corrector Adams method which has a variable-order and variable-step size. Simple and

关键词： Electrical resistivity Tomography (ERT)   Inverse theory   Numerical modelling   Numerical solutions  

摘要： We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

关键词： Operator algebra   Tensor ring   Integro-differential operators   Linear substitutions   Noncommutative Grobner basis   Reduction systems   Completion   Confluence  

摘要： We propose a general algorithmic approach to noncommutative operator algebras generated by additive operators using quotients of tensor rings that are defined by tensor reduction systems. Skew polynomials are a well-established tool covering many cases arising in applications. However, integro-differential operators over an arbitrary integro-differential algebra do not fit this structure, for example. Instead of using parametrized Grobner bases in free algebras, as has been used so far in the literature, we use Bergman's basis-free analog in tensor rings. Since reduction rules are given by module homomorphisms, the tensor setting often allows for a finite reduction system. A confluent tensor reduction system enables effective computations based on normal forms. Using tensor rings, we can also model integro-differential operators with matrix coefficients, where constants are not commutative. To have smaller reduction systems, we develop a generalization of Bergman's setting. It allows overlapping domains of reduction homomorphisms, which also make the algorithmic verification of the confluence criterion more efficient. Moreover, we discuss a heuristic approach to complete a given reduction system to a confluent one in analogy to Buchberger's algorithm and Knuth-Bendix completion. Integro-differential operators are used to illustrate the tensor setting, verification of confluence, and completion of tensor reduction systems. We also introduce a confluent reduction system and normal forms for integro-differential operators with linear substitutions, which have applications in delay differential equations. Verification of the confluence criterion and completion based on S-polynomial computations is supported by the Mathematica package TenReS. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Information dissemination   gossip   network coding   mobility   random geometric graph (RGG)  

摘要： In this letter, we investigate the performance of algebraic gossip algorithms for information dissemination in mobile ad hoc networks (MANETs). In the gossip algorithms, in each time slot, each node communicates with a neighboring node, which is randomly selected by an Exchange algorithm, to exchange their information. The goal of the algorithm is to efficiently disseminate all the messages to all the nodes as fast as possible. We analyze the convergence time of network coding (NC) based gossip algorithm by taking into account the node mobility in MANETs, and derived a lower bound on the convergence time. It showed that the convergence time of the NC gossip algorithm with node mobility can be reduced by the order of O(n(1/2)/log(3/2)n) over that without considering node mobility. But it is only O(log n) quicker than the gossip algorithm with node mobility but no NC.