HIV与免疫响应动力学的时间-空间模型(英文)

致力于通过使用偏微分方程来描述及刻画HIV病毒、易感染细胞、免疫细胞三者之间的动态免疫响应的时间-空间模型.该模型由3个反应-扩散方程来描述,利用微分不等式技巧以及嵌入定理证明了全局解的存在惟一性,利用常微分方程中解的稳定性理论方法证明了常数稳态解的稳定性,并且通过严格的数学分析证明了非常数稳态解的不存在性,并得出了该模型可以由常微分方程的方法来刻画的结论.     

3-维肿瘤模型解的非对称稳定性

肿瘤的非对称不稳定性,通常暗含肿瘤会浸润周围正常组织.为了研究一个考虑了细胞黏附力的未血管化3-维肿瘤的非对称稳定性,首先对该肿瘤模型球对称静止解增加了非对称扰动,应用Taylor展开,考虑了非对称扰动的线性化问题,即一个关于扰动的偏微分方程初值问题.然后利用球调和函数展开,研究了有关扰动的偏微分方程的变量分离形式的解,最后根据微分方程稳定性定理,在肿瘤静止半径没有限制或肿瘤静止半径小于1的情况下,得到了非对称扰动的稳定和不稳定的条件.     

一类四阶时滞微分方程的无条件稳定性

利用定性分析方法、代数方程根的性质及对数范数,研究了一类四阶时滞微分方程的无条件稳定性及实例的振动性,得到了该时滞微分方程无条件稳定性的充要条件,四次多项式函数在[-1,1]上无零点的充要条件.举出实例并用Matlab绘出了模型数值解的拟合图像.     

Zero-Coupon bond pricing模型的最优系统与群不变解(英文)

将李群理论用于金融问题中出现的数学模型的微分方程,研究了Zero-Coupon bond pricing模型.求出了该模型的单参数李点对称及它相应的群伴随表达式,由此求得该模型允许的一维李群的子代数的最优系统并且利用最优系统构造该模型相应的微分方程的一些特殊的不同类的闭解.     

常利率下有阈红利边界的复合Poisson风险模型

考虑了常利率下有阈红利边界的复合Poisson风险模型,给出了罚金折现期望函数满足的积分-微分方程及带干扰的情况下罚金折现函数所满足的积分-微分方程.利用全概率公式得到了相应积分-微分方程的解、破产概率及破产前瞬时盈余和破产赤字的联合分布的具体表达式.该模型有利于降低公司最终破产的概率.     

盈余过程服从跳扩模型下的破产概率

为了更真实地反映市场随机变化趋势,将经典的扩散模型推广到跳跃-扩散模型.用布朗运动和复合泊松过程共同驱动保险公司的盈余过程,并考虑盈余过程的系数受马尔可夫链干扰的情况.采用鞅方法和微积分方法研究保险公司的破产概率,得到破产概率所满足的偏微分方程.     

二维变系数偏微分方程的小波数值方法

针对两类变系数偏微分方程,提出了小波配点法.该方法选取区间拟shannon尺度函数为权函数,利用配点法对空间域离散得到对时间的常微分方程组,然后用高效数值方法——精细积分法求解,得到了求解变系数偏微分方程的一个有效的数值方法.最后进行了数值实验,实验表明了该方法的有效性.     

盈余过程服从跳扩模型下的破产概率

为了更真实地反映市场随机变化趋势,将经典的扩散模型推广到跳跃-扩散模型.用布朗运动和复合泊松过程共同驱动保险公司的盈余过程,并考虑盈余过程的系数受马尔可夫链干扰的情况.采用鞅方法和微积分方法研究保险公司的破产概率,得到破产概率所满足的偏微分方程.     

基于机器视觉的预包装食品检测

基于机器视觉设计了一种缺陷检测系统,该图像处理采用基于偏微分方程的去噪模型实现了图像去噪;利用双阈值分割方法实现了缺陷区域的分割;并采用BP神经网络根据周长、面积和圆形度实现了缺陷分类。结果表明:试验系统的整体漏检率为0.17%,检测精度比较高;每个包装的检测耗时大约为70ms,检测效率比较高;该系统能很好地满足食品包装实时、快速、准确、稳定的检测要求。     

分数型欧式期权定价模型

运用偏微分方程的方法对欧式期权定价进行了推广.在假定无风险利率、股票波动率以及股票红利率都为时间t的函数,利用金融市场复制策略及分数布朗运动的Ito公式,得到欧式未定权益的一般Black-Scholes偏微分方程,并通过求解偏微分方程获得欧式期权定价公式.     

Inclusion of partial lactations in the genetic analysis of yield traits by differential weighting of records

Mixed model equations are constructed using the convention of regression on dummy variables that are given values of either unity (presence of the effect) or zero (absence of the effect). In the proposed method, incomplete records were included by computing regression coefficients of sire effects as the regression of the effect on the partial record on the same effect on the complete record. Partial and complete records were treated equally for other effects. Regression and the error components of variance were estimated as simple functions of the length of the partial records. The only additional computation required in sire evaluation was the differential weighting of records in the construction of the mixed model equations. This method was tested on field data and was slightly more accurate than evaluations including partial records without differential weighting and significantly more accurate than evaluations obtained with partial records deleted.     

基于近红外光谱技术的老陈醋可溶性固形物定量分析

可溶性固形物含量(SSC)是食品行业的重要技术参数之一。利用近红外光谱技术对不同醋龄的老陈醋SSC进行分析。在不同光谱预处理下,分别采用主成分回归(PCR)和偏最小二乘法(PLS)建立SSC的定量分析模型。结果表明,采用5点平滑预处理后,利用PLS建立的老陈醋SSC的定量分析模型最优,其校正集的相关系数R为0.999 9,校正标准偏差(RMSEC)为0.038 3,预测标准偏差(RMSEP)和交叉验证标准偏差(RMSECV)分别为0.082 1,0.096 4。表明采用近红外光谱技术对不同醋龄的老陈醋SSC进行定量分析建模是可行的。     

A mathematical model of the Torry fish drying kiln

Summary. Proposed developments of the Torry fish drying kiln have led to a need for a closer understanding of commercial fish drying processes. In order to investigate the effects on fish drying of air velocity, air temperature and humidity, and fish packing density, a mathematical model of the kiln has been proposed. This model establishes partial differential equations for fish weight, air temperature and humidity. the model is applicable to the drying of other materials. A solution is obtained numerically by standard finite difference techniques.     

Design and development of an innovative hybrid powder based on a computer simulation and its application to foundation makeup products

An innovative hybrid powder prepared using computer simulation allowed development of a new foundation having a fine, smooth texture that has never been achieved before. The optical structure/design of the powder was based on the results of measurements and analyses conducted on the optical characteristics of a baby's delicate skin, which is the envy of many women. To obtain the optimal optical characteristics, the finite differential time domain (FDTD) method for solving Maxwell's differential equation by difference and time domain was applied to the computer simulation method. For synthesis of the hybrid powder based on the optical model, a proprietary shape regulation coating technology was used in which flaky substrates were coated with microspherical forms of barium sulfate crystals. The hybrid powder developed exhibited optical characteristics that showed a significant diffusion characteristic in the visible light region. The foundation containing this powder could conceal pores, small wrinkles, freckles, and age spots and owing to its microscopic reflection characteristics provided a fine, smooth texture that has never before been available with a conventional foundation.     

线性偏微分方程组Cauchy问题一致适定性的代数判据

从n阶逆正性矩阵的4个充要条件(引理1-4)入手,在文[4]的基础上,给出了线性偏微分方程组大系统的Cauchy问题一致适定性的几个充分条件(定理1-3)和抛物型方程组的判别条件(定理5-6)。     

依赖于2个状态变量的衍生证券的数值解法

对依赖于2个变量的衍生证券所满足的二维Black-Scholes模型，用偏微分方程差分方法求解，建立差分格式，并证明差分格式的稳定性、收敛性．     

连续蒸煮过程的正交配置建模方法

针对具有分布参数系统特性的制浆生产中的连续蒸煮过程，提出了一种通过运用多项式正交配置对模型进行简化的方法。这种方法可使蒸煮过程模型维数显降低，并且既包括了许多影响蒸煮结果的重要物理现象，又适合黑箱辨识。通过蒸煮模型动态特性的计算机仿真．证明了该方法的优越性。