一类Schrodinger算子逆谱问题的惟一性

考虑边值条件中含谱参数的一类Schrodinger算子逆谱的惟一性问题．由Sturm-Liouville问题逆谱理论中的惟一性定理及整函数的性质证明了基于一定条件下,特征值（包括重数）和一个相关的参数γ能惟一确定势函数．     

非均质地基的地震随机反应

基于改进的一维剪切梁模型,利用随机振动理论,并基于基岩输入地震加速度的功率谱密度函数--白噪声谱和过滤白噪声谱,研究了非均质地基对地震的随机动力反应问题.计算结果表明：（1） 在基岩输入地震加速度的功率谱为白噪声谱的情况下,地基的最大期望反应,均有别于过滤白噪声谱时的相应值;（2） 平稳输入与输出过高地估计了地基的随机反应.     

基于共享逆近邻与指数核的密度峰聚类算法

针对密度峰聚类算法中局部密度定义和聚类分配策略的不足,提出了一种基于共享逆近邻与指数核的密度峰聚类算法。该算法利用样本的共享逆近邻点和指数核函数构造一种相似度,得到一种新的密度并将其应用在密度峰聚类算法中生成初始簇,然后将这些簇与凝聚层次聚类算法结合形成最终的类簇。数值实验证明:提出的基于共享逆近邻与指数核的密度峰聚类算法在真实数据集上的聚类结果要优于其他密度聚类算法,并能有效解决密度峰聚类算法中局部密度定义问题和聚类分配策略问题。     

两组谱数据之间势函数的关系

研究由谱数据等相关信息所建立的Sturm-Liouville逆问题.根据谱数据相关信息,建立积分方程K(x,s)+F(x,s)+∫0xK(x,t)F(t,s)dt=0,通过此方程得出2个势函数差距的具体表达式,即(x)-q(x)=2d/dx∑n=0 N 1/cn[φ(x,n)φ~(x,n)-φ(x,λn)φ~(x,λn)].     

极大熵谱估计在轨距不平顺激励研究中的应用

用时间序列分析的极大熵谱估计,根据用地面方法测得的我国铁路轨道轨距不平顺数据,求出了我国铁路一级干线的轨距不平顺功率谱密度函数,并与以往由"FFT"方法得到的谱密度进行了对比.     

Lie-Poisson结构下的约束WKI系统

由一个3×3谱问题得出与之对应的Loop孤子方程,通过将其非线性化,产生一个Lie-Poisson结构下的Hamiltonian系统,并运用母函数法证明此Hamiltonian系统是可积的.     

函数与构建方程模型的不等式解析

对函数与构建方程的不等式可积性的研究有助于对相应物理现象的科学解释和工程应用,也是研究重点,同时也是理论研究的热点。近年来,许多学者提出了研究构建方程精确解的办法。给出函数方程的定义及求解函数方程的基本方法,探索通过构造函数方程求解其它问题的方法,以获得新的解题思路。     

一维可压Navier—Stokes方程自由边值问题的自模解

研究黏性系数μ（ρ）=1＋θρ^θ时一维可压Navier-Stokes方程自模解的非存在性．首先通过建立能量估计式,熵估计式得到密度函数ρ的正的下界,然后对能量函数进行定量分析,利用能量爆破理论证明了θ〉0时一维可压Navier-Stokes方程不存在具有有限总能量的自模解．最后将常黏性系数Navier-Stokes方程自模解的方法推广到黏性系数依赖于密度的情形,并且把θ的范围扩展到θ〉0．     

带跳的具有卖空限制的证券投资组合选择问题

研究了股票价格服从跳跃扩散过程的具有限制卖空约束的均值-方差投资组合选择问题.首先建立一个最优随机LQ问题,由于此问题具有限制卖空约束,因此传统的Riccati方程理论就不再适用,另外与之相关的HJB方程也不存在光滑解.通过2个Riccati方程构建一个连续函数,并证明这个函数就是HJB方程的粘性解.最后通过解Riccati方程得到原始均值-方差问题的有效边界和最优投资策略.     

功率谱分析在机织物组织纹理识别中的应用

将功率谱应用到织物组织识别中,用功率谱及相关函数对织物图像进行处理,得到织物图像的功率谱曲线,从曲线的峰值中提取织物表面的方向性信息,得到织物经纬密度,并进一步确定织物组织的经纬纱特数、飞数和经纬纱循环数,最后得出织物的组织点属性.实验证明这种方法实际可行,对织物组织的计算机分析、识别及进一步的应用研究有重要的理论和实际意义.     

用演化方法反演抛物型方程系数的数值算法

给出了一种利用演化计算方法求解抛物型方程中的一次项参数反问题的方法．该方法把参数识别问题转化为泛函的优化问题,用演化算法求解,用演化计算（Genetic Algorithms）演化待求参数的最优估计值,并将该方法运用于一类方程反问题的数值模拟中．数值结果显示数值解与理论解吻合很好．     

非连续Sturm-Liouville问题的重构

本文考虑非连续Sturm-Liouville的重构问题.通过一组谱及半区间上的势函数,运用拉格朗日插值公式,将已知区间上的势函数转化成未知区间上的两组谱问题.若间断点在前半区间采用解Marchenko方程的方法,若间断点在后半区间采用谱映射的方法,从而给出了整个区间上的势函数的重构公式和实数H2.     

Modelling of UV absorption in a plane photoreactor for solutions with high-patulin concentration

In this paper, the spectral radiant power absorbed by a solution of patulin was calculated as a function of the concentration of the light absorbing substance when it was irradiated with a UV multi-wavelength lamp. Two equations are presented. The first one contains a simplification and, consequently, is only applicable for solutions with low light absorber concentrations. The second equation does not include the simplification, so its calculation is more difficult, but it is applicable in all cases. A comparison between the data obtained with both equations is presented, showing that both models coincide for patulin concentrations below 50 mg/L and diverge substantially for higher concentrations.Both equations are obtained considering the linear spherical emission model and are calculated using the Simpson integration method. The incident spectral radiant power at the surface and the bottom of the reactor was also calculated.The data obtained with the non-simplified equation reach an asymptote for high-patulin concentration values that coincides with the incident spectral radiant power at the surface of the reactor, meaning that for high concentration values, all the radiation that reaches the surface of the reactor is absorbed by the whole volume of the solution.The ratio between the spectral radiant power absorbed and the incident spectral radiant power at the surface was evaluated as a function of the depth of the reactor and the absorbance coefficient, concluding that for a specific absorption coefficient, the absorbed radiation increases asymptotically with the depth of the reactor. The higher the absorption coefficient values, the faster the ratio values increase. The asymptotic value increases if the absorbance coefficient also does because the greater the absorption coefficient, the fewer the beams that exit the solution. For the known values of the absorbance coefficient for fruit juices, it was concluded that almost all the radiation entering the solution is absorbed for depths of much less than 1 mm.     

结合粒子群算法的一类双层纺织材料厚度设计反问题

本文基于低温环境下纺织材料热湿传递稳态模型,研究了一类双层纺织材料厚度设计反问题。本文首先给出了一个双层纺织材料热湿传递稳态模型,该模型是关于温度和湿度的常微分方程组,通过解耦化为两点初边值问题并采用有限差分法求解。然后,本文根据服装热湿舒适性要求,将纺织材料内层厚度看成一个未知量,提出了一类双层纺织材料厚度设计反问题,将该反问题归结为一个具有最小二乘解的优化问题,并采用粒子群算法求解反问题。数值结果显示：双层纺织材料厚度设计反问题是合理的,粒子群算法能有效的解决该反问题,该算法具有鲁棒性。     

Estimation of apparent thermal conductivity of carrot purée during freezing using inverse problem

This article presents an inverse problem to determine the apparent thermal conductivity of carrot purée during the freezing process. The heat diffusion equation with the enthalpy model is solved to estimate the thermal conductivity. A modern meta-heuristic of evolutionary computation field called Differential Evolution (DE) is applied for the solution of inverse problem. Experiments were performed to estimate the thermal conductivity of the carrot purée as a function of temperature, using two piecewise functions. A best least square fitting between the experimental and predicted temperature curves during freezing conditions is obtained using DE. Statistical analysis are considered with Gaussian error of 0.05 and zero mean showing than the results for one piecewise function are more stable than with another piecewise function. Good agreement between the reported and estimated temperature curves was obtained. The apparent thermal conductivity was observed to decrease asymptotically with temperature in the range [−40 °C, 0 °C] and stay approximately a constant value for temperatures bigger than 0 °C.     

Near Infrared Spectrophotometric Determination of Individual Sugars in Aqueous Mixtures

Near infrared region (NIR) spectrophotometry was used to determine concentrations of glucose, fructose and sucrose in aqueous mixtures at 10, 25, and 40% total sugars. Calibration equations and predicted individual concentrations in each total sugar level are reported. The standard errors of prediction varied between 0.35 and 0.69 and confidence limits ranged from ± 0.7 to ± 1.1%. In developing a single equation for predicting individual sugars in solutions, suitable for use over a range of total sugar concentrations, spectral data needed correction for sample density differences. However, at total sugar concentrations above 25%, accompanying wavelength shifts were of sufficient magnitude that a satisfactory single equation could not be developed. Equations for predicting individual sugars in solutions ranging from 10–25% total sugar concentrations were developed. For higher values of total sugars, appropriate calibrations were necessary.