“同心协力”策略研究

针对"同心协力"拓展项目中队员的协同控制问题,建立了在理想条件下的最优策略模型,以及在非精确控制条件下的鼓面倾斜模型,讨论了稳定性要求对最优策略的影响,给出当球跳动方向偏离竖直方向后,鼓的控制方法及效果.最后对2019年"高教社杯"全国大学生数学建模竞赛B题的参赛论文予以简要评述.     

Heston模型下的方差互换定价研究

通过实证分析论证了波动率具有均值回复性质的合理性.在Heston模型下,利用Ito积分推导出了方差互换在其存续期内任意时刻的价格与公平执行价格的定价公式.得到公平执行价格是波动率的平方的初始水平与长期均值水平的线性组合的性质,并利用该性质对Heston模型参数的敏感性进行了分析.     

基于灰色系统理论的多元线性回归分析

运用灰色系统理论剔除了自变量观察数据中的噪声污染,对传统的多元线性回归分析方法进行了改进,建立了灰色多元线性回归分析模型.将模型应用于陕西省就业问题的研究,取得了满意的预测效果.     

半导体问题的向后差分配置法及误差分析

Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.     

基于Alkire-Foster模型的多维贫困测度影响因素敏感性研究——基于粤北山区农村家庭的调查数据

贫困测度是贫困研究的基础.论文以Alkire-Foster多维贫困测度模型为基础,构建多维贫困影响因素敏感性分析模型,并运用该模型对粤北山区农村家庭进行实证分析,发现:在厨房燃料和教育两个维度贫困发生率高;贫困发生率对教育和居住条件两个指标贫困线的变化较为敏感;权重的改变对测度结果的影响比较大,特别是当被剥夺的临界值k较小时,多维贫困发生率对权重变化更为敏感.     

欧式看涨期权价格折现值的研究

在金融活动中 ,投资者对资金流的现值的了解是很重要的 .为此本文引入期权价格折现值的概念 .讨论了当利率是常数时 ,欧式看涨期权价格折现值所满足的微分方程 .     

随机变量和模型及其实证研究

对于敏感性问题,无法采用直接问答的方式进行调查。本文研究了随机变量和模型,并将该模型应用到药店利润率调查中;在具体操作上,为节约经费与提高精度,对每个个体采集两次数据;为进一步满足被调查者对药店利润率的保密心理,对由指数分布生成的随机数,统一加上一个较大的数,以使被调查者看到的随机数远大于药店的毛利百分数。最后根据调查数据,利用随机和模型给出了药店毛利百分数的均值、方差以及分位点。     

非标准分析及其应用

本文简要介绍非标准分析基础及其在其他数学分支中的应用,特别是在组合数论中的应用.所介绍的基础包含数理逻辑常识、非标准模型构造以及非标准分析常用原理和性质.所介绍的应用包含随机微分方程强解的存在性、关于局部群的Hilbert第五问题、精确大数定律及其在经济学中的应用、组合数论中的和集现象、关于密度的Pl¨unnecke类型不等式和Freiman逆问题.     

产品服务能力与定价联合优化策略机制研究——基于动态性和非线性视角

为了快速响应客户需求的动态变化和提高产品服务能力的管理效率,运用状态相关需求率函数和成本收益率函数,建立用以解决产品服务需求动态性和非线性难题的排队优化模型。通过考虑产品服务化过程中客户需求变化特征,从服务能力和价格两个维度将客户划分为实惠型、经济型、专业型和品质型四个不同类别。依据客户产品服务需求动态演变阶段,针对服务能力与价格的内在关联性,运用排队优化模型分别构建了成本领先策略、服务能力领先策略、价格领先策略和产品服务能力定价联合策略。最后,借助南阳泵业企业运营实例,验证了产品服务能力定价联合策略的优越性,并给出产品服务能力定价联合策略演化路径及其实施对策。     

二元热传导方程的Phragmén-Lindel?f型二择一结果

考虑了二元热传导方程在半无穷区域上解的渐近性质,其中在柱体的侧面上施加局部非齐次Neumann条件.这种条件模拟了柱体侧面上的绝热材料受到局部破坏的情形.利用微分不等式技术和能量分析的方法,得到了热传导模型的Phragmén-Lindel?f型二择一结果.     

n阶常系数非齐次线性微分方程的降阶解法

给出一阶线性非齐次微分方程的积分因子解法,避免了常数变易法带来的不便和不自然;给出,n阶常系数非齐次线性微分方程的降阶解法,可以看出,高阶常系数线性非齐次微分方程最终都可以归结为求解一阶线性微分方程,从而避免了待定系数法求非齐次方程特解的繁琐,并最终说明了一般微积分教材中只给出两种类型常系数非齐次线性微分方程的待定系数解法的原因．     

Propagation of nonlinear thermoelastic waves in porous media within the theory of heat conduction with memory: physical derivation and exact solutions

In this paper, we study a mathematical model of nonlinear thermoelastic wave propagation in fluid‐saturated porous media, considering memory effect in the heat propagation. In particular, we derive the governing equations in one dimension by using the Gurtin–Pipkin theory of heat flux history model and specializing the relaxation function in such a way to obtain a fractional Erdélyi–Kober integral. In this way, we obtain a nonlinear model in the framework of time‐fractional thermoelasticity, and we find an explicit analytical solution by means of the invariant subspace method. A second memory effect that can play a significant role in this class of models is parametrized by a generalized time‐fractional Darcy law. We study the equations obtained also in this case and find an explicit traveling wave type solution. Copyright © 2016 John Wiley & Sons, Ltd.     

常系数线性方程组的一种新解法

对于常系数线性微分方程组:dx/dt=Ax(A是n阶实常数矩阵)通过特征根λ和对应的特征行向量K:K~T(A-λE)=0将微分方程组化为线性方程组:1°当有n个互异的特征根λ_1,λ_2,…,λ_n,对应的线性无关的特征行向量为K_1,K_2,…,K_n,若记K_i=(k_1,k_2,…,k_n)(i=1,2,…,n),则有方程组:(n∑i=1 k_ix_i)′=λ_j(n∑i=1 k_ix_I)(j=1,2,…,n);2°当有不同的特征根λ_1,λ_2,…,λ_m其重数分别为n_1,n_2,…,n_m,n_1+n_2+…+n_m=n,对应的线性无关的特征行向量为K_i=(k_1,K_2,…,k_n)(i=1,2,…,m),则有方程组:(n∑i=1 k_rx_r)′=λ_k(n∑i=1 k_rx_r)((A-λ_jE)x_(n_i)=0;i=1),(n∑i=1 k_rx_r)′=λ_j(n∑i=1k_rx_r)+c_(n_i)e~(λ_jt)((A-λ_kE)x_(i-1)=Ex_i,i=2,…,n_i).     

Sufficient Conditions for the Oscillation of Bounded Solutions of a Class of Impulsive Differential Equations of Second Order with a Constant Delay

Sufficient conditions are found for oscillation of bounded solutions of a class of impulsive differential equations of second order with a constant delay. Some asymptotic properties are studied for the bounded solutions.     

On the Convergence Rate of Euler Scheme for SDE with Lipschitz Drift and Constant Diffusion

It is well known that the weak Euler approximation of a stochastic differential equation has order one, provided the coefficients of the equation are sufficiently smooth. We prove that the order of the approximation is still one in the case where the drift coefficient is a Lipschitz function and the diffusion coefficient is constant.     

Peng g- 期望下的大数定律

Peng 于1997 年通过倒向随机微分方程引入了一类性质很好的非线性数学期望, 即g- 期望. 本文中, 我们将给出Peng g- 期望下的弱大数定律与强大数定律.     

Equilibrium and sensitivity analysis of a spatio-temporal host-vector epidemic model

Insect-borne diseases are diseases carried by insects affecting humans, animals or plants. They have the potential to generate massive outbreaks such as the Zika epidemic in 2015–2016 mostly distributed in the Americas, the Pacific and Southeast Asia, and the multi-foci outbreak caused by the bacterium Xylella fastidiosa in Europe in the 2010s. In this article, we propose and analyze the behavior of a spatially-explicit compartmental model adapted to pathosystems with fixed hosts and mobile vectors disseminating the disease. The behavior of this model based on a system of partial differential equations is complementarily characterized via a theoretical study of its equilibrium states and a numerical study of its transient phase using global sensitivity analysis. The results are discussed in terms of implications concerning the surveillance and control of the disease over a medium-to-long temporal horizon.     

Asymptotic estimates for the solution of stochastic differential equations driven By G-Brownian motion

In this paper, we give four results of asymptotic estimates for the solution of stochastic differential equations driven by G-Brownian motion, which have different convergence rates under different assumptions. One of them can be considered as a Law of the Iterated Logarithm of the solution of G-SDEs under nonlinear conditions.     

常系数线性微分方程组的基解矩阵的一种新求法

在求解常系数线性微分方程组时,关键是基解矩阵的计算.给出了利用哈密顿—凯莱定理计算基解矩阵的一种方法,并通过实例说明了这种方法的特点和在简化计算方面的有效性.