关键词： 数学算法   计算机编程   优化   数学模型  

摘要： 计算机编程与数学算法有直接的关系,通过数学理论、数学算法构建合适的数学模型,使不同的类能够转化为统一的数学模型,不断优化该数学模型的算法,设计合理的编程逻辑,通过逻辑继承解决复杂的问题,能够最大限度优化计算机编程,提高编程效率和程序运行效率。文章研究了数学算法对计算机编程的优化。

关键词： Finite-dimensional commutative algebras   Algorithms   Jordan-Chevalley decomposition   Lifting idempotents  

摘要： The algebras considered in this paper are commutative rings of which the additive group is a finite-dimensional vector space over the field of rational numbers. We present deterministic polynomial-time algorithms that, given such an algebra, determine its nilradical, all of its prime ideals, as well as the corresponding localizations and residue class fields, its largest separable subalgebra, and its primitive idempotents. We also solve the discrete logarithm problem in the multiplicative group of the algebra. While deterministic polynomial-time algorithms were known earlier, our approach is different from previous ones. One of our tools is a primitive element algorithm;it decides whether the algebra has a primitive element and, if so, finds one, all in polynomial time. A methodological novelty is the use of derivations to replace a Hensel-Newton iteration. It leads to an explicit formula for lifting idempotents against nilpotents that is valid in any commutative ring.

关键词： Mobile hub location   Dynamic environment   Mobility infrastructure   Genetic algorithm   Greedy local search  

摘要： In this study, a new mobile p-hub location problem in a dynamic environment is proposed, where there are mobile facilities inside hub nodes that can be transferred to other nodes in the next period. Mobile facilities have a mobility feature and can be transferred to other nodes in order to meet demand. Using such facilities will save extra hub establishment and closing costs in networks. This approach can be used in some real-world applications with rapidly changing demand, such as mobile post offices or emergency medical service centers, because designing immobile hub networks may be less efficient. In addition, designing dynamic hub networks entails establishing and closing costs in different periods. The model also considers a mobility infrastructure of hub facilities. The numerical examples confirm that a mobile hub network is more efficient than an immobile hub network in a dynamic environment. The effect of different parameters on the model is analyzed to consider its applicability conditions. A genetic algorithm, along with tuned parameters and a simulated annealing algorithm, are proposed to solve the model in large instances. Proposing of a model considering mobility feature in the hub location networks, proving its efficiency and finally proposing a proper solution algorithm are main contributions of this study. The model and solutions algorithms were analyzed by more numerical instances using Australia post (AP) dataset. (C) 2017 Elsevier Inc. All rights reserved.

关键词： 15A18   15A24   65F15   65F30  

摘要： This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rank formulation, which is a generalization of the Cholesky-factored variant of the Lyapunov ADI method. We discuss important implementation aspects of the algorithm, such as reducing the use of complex arithmetic and shift selection strategies. We show that there is a very tight relation between the new algorithm and three other algorithms for CARE previously known in the literature-all of these seemingly different methods in fact produce exactly the same iterates when used with the same parameters: they are algorithmically different descriptions of the same approximation sequence to the Riccati solution.

关键词： Asynchronous systems   autonomous agents   distributed algorithms   multi-agent systems  

摘要： Two asynchronous distributed algorithms are presented for solving a linear equation of the form Ax = b with at least one solution. The equation is simultaneously and asynchronously solved by m agents assuming that each agent knows only a subset of the rows of the partitioned matrix [A b], the estimates of the equation's solution generated by its neighbors, and nothing more. Neighbor relationships are characterized by a time-dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relationships. Each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by its neighbors which are transmitted with delays. The event time sequences of different agents are not assumed to be synchronized. It is shown that for any matrix-vector pair (A, b) for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents' event times, the algorithms cause all agents' estimates to converge exponentially fast to the same solution to Ax = b. The first algorithm requires a specific initialization step at each agent, and the second algorithm works for arbitrary initializations. Explicit expressions for convergence rates are provided, and a relation between local initializations and limiting consensus solutions is established, which is used to solve the least 2-norm solution.

关键词： Model of tuberculosis transmission   reconstruction of model parameters   system of ordinary differential equations   parameter identification   numerical method   simulated annealing method   gradient descent method  

摘要： A new combined numerical algorithm for solving inverse problems of epidemiology is described in this paper. The combined algorithm consists of optimization and iterative methods, and determines the parameters specific to a particular population by using the statistical information for a few previous years. The coefficients of the epidemiology model describe particular qualities of the population and the development of the disease. The inverse problem of parameter identification in a mathematical model is reduced to the problem of minimizing an objective function characterizing the square deviation of the statistical data from the experimental data. The combination of statistical and optimization algorithms demonstrates the identification of parameters with an appropriate relative accuracy of 30%. The results can be used by public health organizations to predict the infectious disease epidemic in a given region by comparing the data of simulation with historical data.

关键词： Flexible manufacturing   robotic cell   cyclic scheduling   meta-heuristics  

摘要： Flexible robotic cells are used to produce standardized items at a high production speed. In this study, the scheduling problem of a flexible robotic cell is considered. Machines are identical and parallel. In the cell, there is an input and an output buffer, wherein the unprocessed and the finished items are kept, respectively. There is a robot performing the loading/unloading operations of the machines and transporting the items. The system repeats a cycle in its long run. It is assumed that each machine processes one part in each cycle. The cycle time depends on the order of the actions. Therefore, determining the order of the actions to minimize the cycle time is an optimization problem. A new mathematical model is presented to solve the problem, and as an alternative, a simulated annealing algorithm is developed for large-size problems. In the simulated annealing algorithm, the objective function value of a given solution is computed by solving a linear programming model which is the first case in the literature to the best of our knowledge. Several numerical examples are solved using the proposed methods, and their performances are evaluated.

关键词： Algebra   Algorithms   Alternative energy   Applied mathematics   Atmospheric science   Curve fitting   Earth sciences   Energy and power   Engineering and technology   Forecasting   Mathematical and statistical techniques   Mathematical functions   Mathematics   Meteorology   Photovoltaic power   Physical sciences   Polynomials   Research and analysis methods   Research Article   Simulation and modeling   Statistical methods   Statistics (mathematics)   Wind   Wind power  

摘要： The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

关键词： 排课   数学建模   教务管理  

摘要： 本文从排课数学模型和算法的规则以及约束条件出发,给出了具体建立数学模型的过程,并列出了这种排课的数学模型和算法在教务管理系统中的实际应用,供业内人士参考。

关键词： 优化策略   数学算法   计算机编程  

摘要： 数学理论的重点表示式样是数学算法,计算统一化对数学的算法提出了不一样的要求,研究和分析计算中出现的各种问题,最终结果的获取往往采用归纳并总结的方式。在计算机信息技术的广泛普及下,计算机技术影响人们的方方面面,面对这种情况,若要大幅度提高计算机编程软件系统的频率,就必须从根本上解决计算机编程软件的中心问题。笔者从计算机的编程系统角度出发,探索数学算法优化策略,希望为以后相关人员探索数学算法提供借鉴。