二维热传导型半导体器件的特征有限体积元方法和H1模分析

将特征线方法与有限体积元方法相结合,采用分片线性函数和分片常数函数分别作为有限体积元方法的试探函数和检验函数空间,构造了热传导型半导体器件的全离散特征有限体积元格式.并进行收敛性分析,在一般的条件下得到了最优阶H1模误差估计结果.     

热传导型半导体器件的二次元特征有限体积元方法及分析：H^1模估计

该文构造了热传导型半导体器件的全离散特征有限体积元格式,将特征线方法与有限体积元方法相结合,采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间,并进行误差分析,得到了最优阶 H1模误差估计结果.     

抛物方程的一种广义差分法(有限体积法)

广义差分法自1982年被提出,至今已获得很大发展（见[1]或[10],这种方法在国际上被称为有限体积（元）法（见[8],[9]）,它的主要优点是保持物理量的局部守恒性.文[3],[5]分别将三角形网格上的椭圆型方程的广义差分法（有限体积法）（见[2],[4]）推广到抛物型方程.我们知道三角形网格与四边形网格是两种基本的分割空间区域的方法,实践上使用哪一种网格,要根据空间区域的几何形状而定.文[7],[6]讨论了一般四边形网上椭圆型方程的广义差分法.本文以抛物方程为模型,取试探函数空间为一般四边形剖分上的等参双线性元,检验函数空间为对偶剖分上的分片常数,导出了一种新的有效的广义差分算法（有限体积算法）,证明了半离散与全离散格式的最佳H1误差估计.遇到的主要困难是双线性形式a（uh,Πh＊uh）     

二维热传导型半导体瞬态问题的二次元特征有限体积元方法

将特征线方法与有限体积元方法相结合,采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间构造了二维热传导型半导体瞬态问题的全离散二次元特征有限体积元格式,并进行误差分析,得到了次优阶L^2模误差估计结果．     

热传导型半导体器件的二次元特征有限体积元方法及分析:H1模估计

该文构造了热传导型半导体器件的全离散特征有限体积元格式,将特征线方法与有限体积元方法相结合, 采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间,并进行误差分析,得到了最优阶H¹模误差估计结果.     

Darcy-Stokes问题的统一稳定化有限体积法分析

本文对Darcy-Stokes问题提出了一种统一的稳定化有限体积法.在离散问题中,采用两种剖分,一种为三角形剖分,一种为其对偶四边形剖分.速度及压力分别采用非协调线性元及分片常数元来做逼近.经证明,文中的统一格式,具有稳定性及最优误差估计.最后用数值算例验证了本文的理论结果.     

解Stokes方程的一种无散稳定二次有限体积法格式

在三角形网格上构造了一种求解Stokes方程的Lagrange二次有限体积法格式.取连续的二次有限元空间与间断的线性有限元空间分别作为Stokes方程的速度项与压力项的试探空间,从而保证了离散方程的速度解在宏元三角形单元上满足局部质量守恒性,且有限元空间对自然满足所谓的inf-sup条件.采用特殊的有限体积法映射与对偶剖分,求解Stokes方程的Lagrange二次有限体积法格式等价于相对应的有限元法格式,因此确保了有限体积法格式的无条件(无需约束三角形网格的几何形状)稳定性和关于速度项的最优阶H1范数的误差估计.最后,数值实验展示了理论结果的正确性以及有限体积法的数值模拟在计算流体力学中的有效性.     

有限体积法定价美式期权

讨论美式期权定价的有限体积法.采用投影超松弛迭代法求解隐式欧拉和CrankNicolson有限体积格式离散Black-Scholes偏微分方程得到的线性互补问题.数值实验结果表明,两种有限体积格式都是有效的,而Crank-Nicolson格式的数值效果要优于隐式欧拉格式.     

非线性抛物型方程组的二次有限体积元方法及其误差估计

讨论基于三角形网格的二维非线性抛物型方程组的有限体积元方法,其中试探函数空间为二次Lagrange元,检验函数空间为分片常数函数空间,对问题的全离散格式证明了最优的能量模误差估计。最后给出一个相关数值算例以验证格式的有效性。     

二维土壤溶质输运方程的有限体积元格式

本文导出二维的土壤溶质输运方程的有限体积元格式, 并分析其误差.通过数值例子说明, 有限体积元格式比有限元格式稳定.     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

Chaotic synchronization with filter based on wavelet transformation

A kind of chaotic synchronization method is presented in the paper. In the transmitter, part signals are transformed by wavelet and the detail information is removed. In the receiver, the component with low frequency is reconstructed and discrete feedback is used, we show that synchronization of two identical structure chaotic systems is attained. The effect of feedback on chaotic synchronization is discussed. Using the synchronous method, the transmitting signal is transported in compressible way, system resource is saved, the component with high frequency is filtered and the effect of disturbance on synchronization is reduced. The synchronization method is illustrated by numerical simulation experiment.     

一类具有垂直传染和预防接种的SEIR传染病模型的定性分析

建立并分析了一类对出生时没有被染病母体垂直传染的染病者的新生儿进行免疫接种的SEIR传染病模型.得到了疾病是否灭绝的阈值R0,当R0<1时,无病平衡点全局渐近稳定的.当R0>1时,地方病平衡点局部渐近稳定的,且疾病一致持续生存.     

Optimal damping ratio for linear second-order systems

In this paper, it is shown that the optimal damping ratio for linear second-order systems that results in minimum-time no-overshoot response to step inputs is of bang-bang type. The optimal damping ratio is zero at the outset and is switched to some maximum value at an appropriate instant of time. The switching time is shown to be a function of the maximum damping ratio and the system natural frequency. Furthermore, it is shown that the larger the maximum damping ratio is, the shorter it takes for the system to reach the desired set point. Finally, it is shown that, if the optimal damping ratio is switched as a function of the system state, then the minimum-time no-overshoot criterion is satisfied, irrespective of the magnitude of the uncertainty in the value of the system natural frequency.     

覆盖下近似算子的拓扑性质

在不限制U为有限论域的情况下,研究了覆盖下近似算子XL和CL的拓扑性质。证明了覆盖下近似算子XL是内部算子,而且由XL生成的拓扑TXL为包含由覆盖C本身作为子基生成的拓扑TC的最小Alexandrov拓扑。特别地,当U为有限论域时,TXL=TC.然而,覆盖下近似算子CL不是内部算子。当覆盖C为某拓扑的基时,CL是内部算子,且此时由CL生成的拓扑TCL与TC是同一个拓扑。若进一步要求U为有限论域,则TCL=TXL=TC,进而CL=XL.     

“正项级数收敛性的一种新的判别法”的注记

给出了标题中所述文章的一个注记.首先否定了该文中的一个断语,其次指出了该文中的"新的判别法"的适用范围并没有超过Cauchy根值判别法.     

Maximal and Minimal Semilattices on Ordered Sets

The map which takes an element of an ordered set to its principal ideal is a natural embedding of that ordered set into its powerset, a semilattice. If attention is restricted to all finite intersections of the principal ideals of the original ordered set, then an embedding into a much smaller semilattice is obtained. In this paper the question is answered of when this construction is, in a certain arrow-theoretic sense, minimal. Specifically, a characterisation is given, in terms of ideals and filters, of those ordered sets which admit a so-called minimal embedding into a semilattice. Similarly, a candidate maximal semilattice on an ordered set can be constructed from the principal filters of its elements. A characterisation of those ordered sets that extend to a maximal semilattice is given. Finally, the notion of a free semilattice on an ordered set is given, and it is shown that the candidate maximal semilattice in the embedding-theoretic sense is the free object.     

沪深股市收益的相关性

以概率作为相关度量指标,分整体相关性和尾部相关性对沪深两市收益进行考察。整体相关性采用概率方法中的变化协调形成的相关性作为度量,结果表明沪深两市收益在整体上具有一定的正相关性。对于尾部相关性,先用t分布分别拟事两市收益底分布,然后用蒙特卡洛模拟确定尾部的最优门限,进而求得尾部相关性,结果显示当市场剧烈波动时两市收益具有正的相关性,且比整体相关性强,尤其在暴跌的时候,两市具有很强的正相关性。     

AR（p）模型中的缺失数据估计

运用EM算法,对含有缺失数据的AR（p）模型进行参数估计,通过最大似然准则就非左端缺失的情况进行插补.最后,用蒙特卡洛方法给出实验分析,表明如下结果：（i）误差与AR模型的阶数正相关,与缺失比例正相关;（ii）当AR模型的特征根模长相对较小时,误差与数据长度负相关,且误差被控制在了标准差的30％以内;（iii）当模长中等时,误差基本控制在1个标准差左右;（iv）当模长较大时,误差与数据长度正相关,而且误差也相对较大.     

Waves in an Inhomogeneous Tube with a Flowing Two-Phase Fluid

Results of theoretical and mathematical justification of the problem on a pulsating flow of a two-phase barotropic bubbly fluid enclosed in an elastic semi-infinite cylindrical tube inhomogeneous along its length are presented. Linear one-dimensional equations are used. It is assumed that the tube is rigidly attached to the surrounding medium and therefore its displacement in the axial direction is absent. At infinity, the tube material is assumed to be homogeneous. To describe the pressure, flow rate, and displacement of the fluid, a pulsating pressure is given at the tube end. The problem stated is reduced to a singular Sturm-Liouville boundary-value problem, which in turn is reduced to a Volterra-type integral equation. This equation is solved by the method of successive approximations. By assuming that the corresponding potential is integrable, it is proved that these approximations converge to the exact solution of the problem. It is shown that this assumption also covers the very important practical case of piecewise inhomogeneity. For numerical realization, we consider a homogeneous tube with flowing water containing a small amount of bubbles. The effect of the volume content of bubbles on wave characteristics is revealed. In particular, it is stated that, for the oscillation regime selected, an increased bubble volume content decreases the wave velocity and considerably increases the flow speed (rate).