疫苗接种、媒体报道和治疗措施对传染病传播影响的数学模型研究

为了探讨疫苗接种、媒体报道和治疗措施对麻疹传播影响,首先建立了具有非线性发生率的SIR传染病模型,证明了无病平衡点和地方病平衡点的全局渐近稳定性.其次,建立了具有三种控制策略新的传染病模型,得到新的基本再生数R_1.最后,为了获得更好的控制效果,对这三种控制措施进行了最优化设计,得到了相应最优控制策略.数值模拟结果显示媒体报道和疫苗接种策略在抑制麻疹的传播方面比治疗措施具有更好的控制效果.     

具有反馈性能的传染病传播模型

传染病是人类社会面对的严重威胁之一,也是困扰世界医学界的长期难题.文中首先对传染病的传播机理进行了分析研究,将其传播分为自然传播和人为控制两种状态,然后以微分方程理论为基础,运用反馈控制理论分别建立了自然传播状态的闭环自激正反馈微分方程模型和有人为控制时的闭环负反馈微分方程模型,并引入控制度概念把上述两种反馈模型结合起来以反映人为控制因素对传染病传播系统的影响,最后以2003年爆发的SARS为例采用计算机编程仿真,结果与实际比较吻合,并提出了应对传染病的若干对策,为传染病的传播预测、有效预防和控制提供了一定的理论依据.     

考虑部分免疫和环境传播的麻疹传染病模型的全局稳定性

该文考虑一个具有部分免疫和环境传播的麻疹传染病模型,得到基本再生数R_0,并通过构造Lyapunov函数,研究了该模型的无病平衡点和地方病平衡点的全局稳定性.当R_01时,无病平衡点是全局渐近稳定的,即麻疹不会传播开;当R_01时,模型存在唯一的地方病平衡点,且是全局渐近稳定的,即麻疹的传播保持在一个稳定的状态.最后,通过数值分析说明了这些结果的合理性.该文工作对于预防和控制麻疹病毒的传播具有实际意义.     

机动目标的跟踪与反跟踪建模研究

针对机动目标跟踪建模及目标机动规律分析问题,首先建立了基于Kalman滤波的Singer模型和修正的当前模型并利用MATLAB对其进行了求解,然后给出了两种模型下的目标的机动规律.针对飞行目标的航迹关联问题,首先建立了基于直观法的航迹起始模型,然后分别建立基于特征判决的最近邻域航迹关联模型和基于Kalman滤波的航迹关联模型并求解,结果显示,两种航迹关联模型都能较好实现航迹的分离.最后,针对高速机动目标跟踪与航迹预测问题,提出了一种基于初值的Singer模型并分析了高速机动目标的机动规律,然后分别建立了基于空间曲线拟合和基于Kalman滤波的航迹预测模型,并对两种模型进行求解与分析.     

两个城市人口相互流动的流感模型研究

研究了两个城市之间人口相互流动的具有出生死亡的SIR流感模型,获得了该模型基本再生数,并对基本再生数与移出率之间的关系作了敏感度分析.结果显示,人口的适当迁移可以有效控制流感爆发.     

变循环发动机模型的求解算法研究

采用部件法建立了变循环发动机的多维非线性隐式方程组模型,模型具有隐式性,因而求解过程复杂,收敛困难.针对上述问题,采用遗传算法和牛顿-拉夫逊法进行模型求解,提出了算法的有效性评价指标:初值敏感性、收敛性和稳定性.对两种算法进行有效性评价.针对发动机工作性能最优化问题,建立了多目标模型,用遗传算法进行求解,并分析了相关变量随马赫数变化的规律.结果可为变循环发动机模型求解算法的选择与设计提供参考.     

甲流病毒传播的年龄结构模型的稳定性

研究甲型H1N1流感病毒的传播规律,建立年龄结构具有接种措施的SEIR流行病模型,给出了疾病流行的阈值并证明了地方病平衡点的稳定性问题.最后根据一些实际数据,进行数值模拟进而对模型的合理性加以完善,借助模型预测下一阶段甲流爆发的可能性并提出相关应对措施.     

基于小波神经网络与ARIMA组合模型在股票预测中的应用

为了实现对股票价格变化的短期预测,提出了一种基于小波神经网络(WNN)与自回归积分滑动平均模型(ARIMA)的组合预测模型.将股票的收盘价序列数据划分为线性以及非线性(误差项)两个部分,分别利用统计学中ARIMA模型和小波神经网络分别对两部分数据进行预测并得到结果,将两部分结果组合相加合成为整个股票价格的预测结果.实验结果表明该组合模型在预测精度方面有提高,是一种比较有效的预测模型.     

库存计划的稳定性和公司激励机制

文章讨论了在制造生产管理中库存计划的稳定性和公司激励机制 .公司通过工资制度激励工人 .构造了一个以公司和工人为目标的双目标规划模型 ,同时模型中考虑了库存计划的稳定性 .最后讨论了模型分别在制造加工速度由市场外部条件决定和由公司内部决策两种情况下的应用 .     

基于市场债券报价的利率模型参数估计与比较

分别基于短期利率期限结构延拓Vasicek与CIR模型,提出了一种有效的正则化参数估计计算方法.方法将通过当前交易市场中不同期限的零息债券市场报价来实现对于时间函数的参数估计.数值试验表明了参数估计方法的稳定性.     

Border bases and kernels of homomorphisms and of derivations

Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.     

Extension and Lifting of Operators and Polynomials

We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of ${\mathcal{L}_1}$ and ${\mathcal{L}_\infty}$ -spaces that includes and extends those of Lindenstrauss-Rosenthal [32] using compact operators and González-Gutiérrez [23] using compact polynomials. We display several examples to show the difference between extending and lifting compact (resp. weakly compact, unconditionally convergent, separable and Rosenthal) operators to operators of the same type. Finally, we show the previous results in a homological perspective, which helps the interested reader to understand the motivations and nature of the results presented.     

On some results of Strichartz and of Rallis and Schiffman

Let (i, H, E) and (j, K, F) be abstract Wiener spaces and let α be a reasonable norm on E ? F. We are interested in the following problem: is ($\text{i ? j, H}\text{}\text{?}\text{bo}{}_2\text{K, E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha F}}$) an abstract Wiener space ? The first thing we do is to prove that the setting of the problem is meaningfull: namely, i ? j is always a continuous one to one map from $\text{H}\text{}\text{?}\text{bo}{}_2\text{K}$ into $\text{E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha }}\text{F}$. Then we exhibit an example which shows that the answer cannot be positive in full generality. Finally we prove that if F=L^p(X,$\text{X}$,λ) for some σ-finite measure λ ? 0 then $\text{(i?j, H}\text{?}{}_2\text{K,L}{}^{\mathrm{p}}$(X,$\text{X}$,λ) is an abstract Wiener space. By-products are some new results on γ-radonifying operators, and new examples of Banach spaces and cross norms for which the answer is affirmative (in particular α = π the projective norm, and F=L¹(X,$\text{X}$,λ)).     

Shellability and homology of q-complexes and q-matroids

Journal of Algebraic Combinatorics - We consider a q-analogue of abstract simplicial complexes, called q-complexes, and discuss the notion of shellability for such complexes. It is shown that...     

Crossings and nestings of matchings and partitions

We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal block elements and maximal block elements, the crossing number and the nesting number of partitions have a symmetric joint distribution. It follows that the crossing numbers and the nesting numbers are distributed symmetrically over all partitions of , as well as over all matchings on . As a corollary, the number of -noncrossing partitions is equal to the number of -nonnesting partitions. The same is also true for matchings. An application is given to the enumeration of matchings with no -crossing (or with no -nesting).