Advances in Applied Mathematics

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ISSN / EISSN : 2324-7991 / 2324-8009
Published by: Hans Publishers (10.12677)
Total articles ≅ 1,338
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平闫 军
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 1904-1910; https://doi.org/10.12677/aam.2021.106199

Abstract:
文章分析了Cahn-Hilliard方程的能量不变二次化法的能量稳定性。首先分析了Cahn-Hilliard方程是满足能量耗散,即能量随时间的推移呈衰减趋势,并且这种随时间衰减的性质能得到保持。其次,对定义的自由能被积函数变换成新的二次函数,即能量不变二次化法同样验证了它的能量衰减性质,并给出了Cahn-Hilliard方程能量不变二次化法的能量稳定性。结果表明,该数值格式是无条件稳定,即能量稳定性与时间步长是无关的。最后我们基于有限元方法给出了一个数值算例,来有效的模拟Cahn-Hilliard方程相位变化情况。 The article analyzes the energy stability of the energy-invariant quadratic method of the Cahn-Hilliard equation. Firstly, it is analyzed that the Cahn-Hilliard equation is satisfying energy dissipation, i.e., the energy tends to decay with time, and this decaying property with time can be maintained. Secondly, the defined free energy quadratic function is transformed into a new quadratic function, i.e., the energy-invariant quadratic method is similarly verified for its energy-decaying property, and the energy stability of the energy-invariant quadratic method of the Cahn-Hilliard equation is given. The results show that the numerical format is unconditionally stable, i.e. the energy stability is independent of the time step. Finally we give a numerical example based on the finite element method to effectively simulate the phase variation of the Cahn-Hilliard equation.
男高 胜
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 1937-1944; https://doi.org/10.12677/aam.2021.106204

Abstract:
对DNA序列相似性的比对分析是生物信息学中的重要问题。由于多序列比对(MSA)方法耗时较长,因此非比对方法的应用变得流行起来。DNA序列中的基因突变对序列比对分析的影响是不可忽视的,突变的存在使本应该被匹配的位置丢失。本文在构建环形前缀树以及获得前缀集的基础上,考虑完全匹配与错配两个匹配法则,提取序列中最佳的匹配位置,创建了新的关于位置差的非比对方法,对多序列进行成对比对,并运用邻接(Neighbor-Joining)法构建进化树,从而得到有效的进化关系。 The comparison and analysis of DNA sequence similarity is an important issue in bioinformatics. Because the multiple sequence alignment (MSA) method takes a long time, the application of non- alignment methods has become popular. The influence of genetic mutations in DNA sequences on sequence comparison analysis cannot be ignored. The existence of mutations makes the positions that should have been matched lose. Based on the construction of the ring prefix tree and the acquisition of the prefix set, this paper considers the two matching rules of perfect match and mismatch, extracts the best matching position in the sequence, and creates a new non-alignment method for position difference, which is used for multiple sequences. Perform pairwise comparisons and use the Neighbor-Joining method to construct evolutionary trees to obtain effective evolutionary relationships.
荣 超
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 1988-1999; https://doi.org/10.12677/aam.2021.106209

Abstract:
本文通过灰色预测模型,收集2002~2019年武汉市住宅商品房平均价格作为基础数据,构建了武汉市住宅商品房平均价格变化趋势预测模型,本文运用了GM(1,1)模型、GM(2,1)模型和邓聚龙参数估计模型对武汉市住宅商品房平均价格进行预测,通过对三种预测方式的检验指标和预测值与实际值的比较,发现直接利用Python求解参数的GM(1,1)模型最终的预测结果对现场的参考意义更大;最终运用GM(1,1)模型计算和预测2020~2030年武汉市住宅商品房平均价格走势,从预测的结果来看,武汉市商品房的价格在未来会保持上涨的趋势。 In this paper, the average price of residential commercial housing in Wuhan City from 2002~2019 was collected as the base data through a gray forecasting model, and a forecasting model of the trend of the average price change of residential commercial housing in Wuhan City was constructed. The GM(1,1) model, GM(2,1) model and Deng Jurong parameter estimation model are applied to forecast the average price of residential commodity houses in Wuhan City. By comparing the test indexes and the predicted and actual values of the three forecasting methods, it is found that the final forecasting results of the GM(1,1) model, which directly uses Python to solve the parameters, are more meaningful for realistic reference. The GM(1,1) model was finally applied to calculate and predict the average price trend of residential commercial housing in Wuhan from 2020 to 2030, and from the predicted results, the prices of commercial housing in Wuhan will maintain an upward trend in the future.
云柳 尧
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 2013-2020; https://doi.org/10.12677/aam.2021.106211

Abstract:
本文采用GM(1,1)、GM(2,1)和GM(1,1)邓聚龙灰色预测模型,选取了福建省1995年至2019年的二氧化碳排放量,用以拟合分析我国提出在2030年达到碳达峰前的福建省二氧化碳排放量数据增长趋势,实证分析三种灰色预测模型之间的差异性与一致性,得出GM(2,1)与GM(1,1)邓聚龙模型此次拟合效果具有一致性,均可以采用。并且二氧化碳排放预测结果表明:福建省从2019年开始至2030年,碳排放量呈现一种加速上升的趋势。本文也以此提出我国要在2060年达到碳中和目标的一些举措。 This paper, the GM(1,1), GM(2,1) and GM(1,1) Deng Jurong gray prediction models are used to fit the CO2 emissions in Fujian Province from 1995 to 2019 to analyze the growth trend of CO2 emissions data in Fujian Province before China proposes to reach the carbon peak in 2030, and the differences and consistency between the three gray prediction models are empirically analyzed, and it is concluded that the GM(2,1) and GM(1,1) Deng Jurong models are consistent and can be used, and the prediction results of CO2 emissions show that the carbon emissions in Fujian Province will show an accelerated upward trend from 2019 to 2030. This paper also uses this to propose some initiatives for China to reach the carbon neutrality target in 2060.
李 娜
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 2031-2040; https://doi.org/10.12677/aam.2021.106213

Abstract:
研究保险公司具有模糊厌恶情形下的最优投资问题。在近似扩散风险模型中,金融市场同时存在无风险投资和风险投资。考虑到金融市场具有复杂性的特点以及保险公司对自己的业务熟悉,假设金融市场模型存在模糊性而保险公司模型不存在模糊性,其中保险公司的保费收入通过指数保费原则计算。在最大化保险公司终端财富的期望效用值的目标下,根据动态规划原理方法给出了对应最优控制问题的Hamilton-Jacobi-Bellman (HJB)方程以及目标值函数,求出了值函数的解析解以及相应的最优投资策略的表达式。最后给出了数值算例阐述不同参数对最优投资策略值的影响。 The problem of optimal investment in the case of insurance companies with ambiguity aversion is studied. In the approximate diffusion risk model, there are risk-free investments and risky investments in the financial market. Considering the complexity of the financial market and the familiarity of the insurance company with its own business, it is assumed that there is ambiguity in the financial market model and no ambiguity in the insurance company model, where the premium income of the insurance company is calculated by the exponential premium principle. Under the objective of maximizing the expected utility value of the insurance company’s terminal wealth, the Hamilton-Jacobi-Bellman (HJB) equation and the objective value function corresponding to the optimal control problem are given according to the dynamic programming principle approach, and the analytical solutions of the value function and the expressions of the corresponding optimal investment strategies are derived. Finally, numerical examples are given to illustrate the effect of different parameters on the value of the optimal investment strategy.
甜唐 甜
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 2041-2049; https://doi.org/10.12677/aam.2021.106214

Abstract:
提升整个供应链效益首要解决的任务是牛鞭效应,而提高预测精准度可以有效的抑制牛鞭效应。基于此在深入分析ARIMA模型和BP神经网络特性的基础上,以某商城办公用品的数据为例对需求量进行预测,选取绝对百分比误差MAPE、均方根误差RMSE和平均绝对误差MAE作为模型检验指标,比较相对误差衡量两种预测模型。构建有较高预测精度的模型,为企业应对市场需求变化提供重要的理论依据。 The primary task to be solved to improve the efficiency of the entire supply chain is the bullwhip effect, and improving the accuracy of prediction can effectively suppress the bullwhip effect. Therefore, based on the in-depth analysis of the ARIMA model and the BP neural network characteristics, this paper takes the data of a certain mall office supplies as an example to predict the demand, and selects the absolute percentage error MAPE, the root mean square error RMSE and the average absolute error MAE as the model test indexes that compare the relative errors to measure the two forecasting models. Constructing a model with higher prediction accuracy provides an important theoretical basis for enterprises to respond to changes in market demand.
静徐 晓
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 2151-2154; https://doi.org/10.12677/aam.2021.106224

Abstract:
在数学分析中,构造辅助函数是一种极为重要的研究方法。要对辅助函数进行有效的使用,就要熟练的掌握一些相关定理的条件和结论,如罗尔中值定理、泰勒公式,罗马定理,积分第一中值定理等。基于以上定理在本文中我总结了一些特定类型的辅助函数的构造方法。 In mathematical analysis, the construction of auxiliary function is a very important research method. In order to make effective use of auxiliary functions, it is necessary to master the conditions and conclusions of some related theorems, such as Rolle’s mean value theorem, Taylor’s formula, Roman theorem, integral integral first mean value theorem, etc. Based on the above theorem in this paper I summarized some specific types of auxiliary function construction methods.
奎胡 协
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 2105-2112; https://doi.org/10.12677/aam.2021.106220

Abstract:
本文采用求解的平面动力系统方法研究Newell-Whiehead方程的精确解孤立波解和振荡解的解析近似解。文中对该方程有界行波解对应的平面动力系统做了详细的定性分析,并结合平面动力系统的理论知识作出了全局相图,依据全局相图,得到了该方程有界行波解的个数和大致性态方面的结论;并运用适当的方法求出了该方程在波速为时的两个精确扭状孤立波解,进一步求出了在波速较小时该方程振荡解的解析近似解。 In this paper, the exact solitary wave solution and the analytical approximate solution of the Newell-Whiehead equation are studied by the plane dynamic system method for solving. In this paper, a detailed qualitative analysis of the plane dynamic system corresponding to the bounded traveling wave solution of the equation is made, and combined with the plane. The theoretical knowledge of the dynamic system has made a global phase diagram. According to the global phase diagram, the conclusions on the number of bounded traveling wave solutions and the approximate behavior of the equation are obtained. Using appropriate methods, the two exact twisted solitary wave solutions of the equation at wave speed are obtained, and the analytical approximate solution of the oscillatory solution of the equation when the wave speed is small, is further obtained.
陈 鹏
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 2186-2193; https://doi.org/10.12677/aam.2021.106228

Abstract:
本文针对多元正态总体均值向量偏移问题,将双抽样策略与可变样本容量控制图相结合,构建了双抽样可变样本容量T2控制图(DSVSS T2图)。根据过程的实际运行状态,构建了马尔可夫链转移概率矩阵。综合考虑过程正常和异常两种状态下的运行成本、误报警损失、抽样成本及维修费用,结合Lorenzen-Vance经济模型,提出DSVSS T2控制图的经济设计模型并分析了均值向量变化对决策变量的影响。 Aiming at the problem of mean vector shift of multivariate normal population, this paper combines double sampling strategy with variable sample size control chart, and constructs double sampling variable sample size control chart (DSVSS T2 chart). According to the actual running state of the process, the Markov chain transition probability matrix is constructed. Considering the operation cost, false alarm loss, sampling cost and maintenance cost of normal and abnormal process, based on Lorenzen-Vance economic model, an economic design model of DSVSS T2 control chart is proposed, and the influence of mean vector change on decision variables is analyzed.
娟党 婵
Published: 1 January 2021
Advances in Applied Mathematics, Volume 10, pp 2206-2216; https://doi.org/10.12677/aam.2021.106230

Abstract:
本文主要研究对称随机矩阵的逆特征值问题。通过将该问题转化为求两个集合交点的可行性问题,提出用交替投影法进行求解。因为其中一个集合不是凸集,关于凸可行性问题的收敛性结果不能用来分析算法的收敛性。对于算法的收敛性,本文在已有关于两个黎曼流形的交替投影算法收敛性的研究结果上,建立了交替投影算法在一定条件下的线性收敛性。最后数值例子也表明了算法的有效性。 The symmetric stochastic inverse eigenvalue problem (StIEP) is considered. By reformulating it into a feasibility problem of two sets, the alternating method is proposed for solving it. Since one of the sets is not convex, the convergence analysis technique for the convex cases does not work. For the convergence of the algorithm, this paper establishes the linear convergence of the alternating projection algorithm under certain conditions on the existing results on the convergence of the alternating projection algorithms for two Riemannian manifolds. At last, some numerical experiments are provided to illustrate the efficiency of the method.
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