Probability densities for conditional statistics in the cubic sensor problem

This paper applies the techniques of Malliavin’s stochastic calculus of variations to Zakai’s equation for the one-dimensional cubic sensor problem in order to study the existence of densities of conditional statistics. Let {X _t} be a Brownian motion observed by a cubic sensor corrupted by white noise, and let denote the unnormalized conditional estimate of φ(X _i ). If φ₁,...,φ _n are linearly independent, and if , it is shown that the probability distribution of admits a density with respect to Lebesgue measure for anyn. This implies that, at any fixed time, the unnormalized conditional density cannot be characterized by a finite set of sufficient statistics. Research supported in part by NSF Grant No. MCS-8301880 and by the Institute for Mathematics and It Applications, Minneapolis, Minnesota.     

Two new characteristic parameters for runoff computation

A method capable of estimating the hydrograph from a prescribed storm for a practical mild slope upstream catchment is proposed. This method makes use of two new characteristic parameters, andS, in conjunction with the kinematic wave equation to compute lateral inflows of the main stream of the catchment. The depth profile of overland flow at any instant within the catchment and hydrograph at any location can be easily found. Lag times for individual lateral inflows are then considered and are linearly combined to obtain the hydrograph at the outlet of the catchment or depth profile of the main stream at any instant. The validity of the excess rainfall-surface runoff linear relationship in this study has also been verified with Tatsunokuchiyama catchment, and it shows good results for this computed runoff.     

保持边缘特征和增强对比度的图像缩放算法

图像的边缘信息和对比度是影响人体视觉的最主要因素。提出一种能够同时保持边缘特征和增强对比度的图像缩放新方法。通过边缘检测算法、边缘梯度增强以及梯度图的低通滤波算法,得到新的梯度图,再通过求解泊松方程得到重建的图像。由于对图像边缘作了特殊处理,从而避免在图像缩放过程中丢失边缘信息。该方法可以同时保持特征以及增加图像的对比度,从而更好地展现图像的细节。实验结果表明,本文方法能应用于一般图像和医学图像的缩放和增强等应用中。     

线性矩阵方程异类约束最小二乘解的迭代算法

多矩阵变量线性矩阵方程(LME)约束解的计算问题在参数识别、结构设计、振动理论、自动控制理论等领域都有广泛应用。本文借鉴求线性矩阵方程(LME)同类约束最小二乘解的迭代算法,通过构造等价的线性矩阵方程组,建立了求多矩阵变量LME的一种异类约束最小二乘解的迭代算法,并证明了该算法的收敛性。在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LME的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LME的极小范数异类约束最小二乘解。另外,还可求得指定矩阵在该LME的异类约束最小二乘解集合中的最佳逼近解。算例表明,该算法是有效的。     

基于偏微分的图像放大算法研究

在研究图片放大算法中,分析了现有的运用偏微分算法在图像法大中的不足,利用图像放大过程中的边缘信息可预知性,本文提出一种新的基于偏微分方程的图像放大算法,这种算法通过将图像边缘检测、平滑处理,然后采用三次样条插值算法对边缘进行相应倍数的放大,并通过对可能出现的锯齿边缘进行细化处理;将处理过的边缘作为放大图像的边缘,从而可以将源图像的边缘很好的保持下来,避免了偏微分方程放大过程中出现的边缘模糊现象。实验结果显示,该方法是一种能够很好的保存图像的边缘信息的图像放大算法。     

Water table fluctuation with a random initial condition

The nonlinear Boussinesq equation is used to understand water table fluctuations in various ditch drainage problems. An approximate solution of this equation with a random initial condition and deterministic boundary conditions, recharge rate and aquifer parameters has been developed to predict a transient water table in a ditch-drainage system. The effects of uncertainty in the initial condition on the water table are illustrated with the help of a synthetic example. These results would find applications in ditch-drainage design.Notation A / tanh t - a lower value of the random variable representing the initial water table height at the mid point - a+b Upper value of the random variable representing the initial water table height at the midpoint - B tanh t - C 4/ - h variable water table height - h mean of the variable water table height - h _m variable water table height at the mid point - h _m mean of the variable water table height at the mid point - K hydraulic conductivity - L half spacing between the ditches - m ₀ initial water table height at the mid point - N Uniform rate of recharge - S specific yield - t time of observation - x distance measured from the ditch boundary - (4/SL)(NK)^1/2 - (L/4)(N/K)^1/2 - dummy integral variable     

一类负模量Kirchhoff - Carrier方程的解

利用变分方法和反证法研究了一类含有非线性项的Kirchhoff - Carrier方程,证明了当0<λ1时,该方程至少存在一对非平凡解,且当λ≥a λ₁时该方程不存在同号解.     

强度传输方程和神经网络融合的三维重构算法

针对原有强度传输方程法所恢复的相位精度不够精确的缺点,提出强度传输方程和神经网络融合的三维重构算法. 利用强度传输方程求解出物体不同角度的初始相位,利用神经网络算法进行优化,根据不同角度的最终恢复相位结合乘法技术重构出三维体信息. 该算法具有精度高的特点,可以为三维成像技术的应用提供参考. 对于实验中的示例图像,该算法将强度传输方程得到的相位误差从21.40%降低为5.26%,重构三维物体与模拟真实物体的相关程度为显著相关.     

On certain aspects of strain rate sensitivity of sheet metals

The formability of a material depends upon the strain hardening and strain rate hardening of the material. In this study, constitutive parameters using the power law constitutive equation are determined for six different strength steels and two aluminum alloys over different strain ranges, including approximations of the postuniform elongation range. Constitutive parameters are found to be different at different strain ranges. The strain hardening of steels increases with strain at low strain levels (less than 5%) and decreases at high strain levels (greater than 10%). Strain rate hardening decreases with strain for all steels and aluminum alloys. Uniform elongation depends only on strain hardening, and postuniform elongation depends only on strain rate hardening. However, the total elongation depends on both strain hardening and strain rate hardening.     

TA15合金的热变形行为及加工图

研究了TA15合金的热模拟压缩实验。结果表明：变形温度的升高和应变速率的减小使峰值应力和稳态应力显著降低，变形温度会影响进入稳态流动所需变形量。以热模拟压缩实验为基础，建立的加工图表明：TA15合金高温变形时存在2个非稳定区域，一个是变形温度1300K以上和应变速率10．0s^-1以上的区域，另一个是变形温度1200K以下和应变速率0．006s^-1～1．995s^-1之间的区域。同时，建立的TA15合金高温变形时的流动应力模型表征了变形温度、应变速率和变形程度对流动应力的影响，模型的计算精度较高。