一个高精度收敛的变系数微分方程精确解析法*

文[1]给出精确解析法,可用于求解任意变系数微分方程,所得到的解具有二阶收敛精度.在此基础上,本文以变截面梁弯曲为例,给出一个高精度的算法.不增加工作量的情况下可达到四阶收敛精度.具有计算快,简单等特点,文末给出算例,仅用很少的单元即可获得高的收敛精度,表明了本文理论的正确性.     

具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式

本文利用非均匀网格和指数型拟合差分方法给出了具有非光滑边界层函数的线性抛物型方程关于小参数ε一致收敛的差分格式.文章还给出了误差估计和数值结果.     

双轴晶体会聚偏光干涉的理论与实验研究

晶体会聚偏光干涉图包含了晶体特性的许多信息,建立偏光干涉图的定量分析方法可以使这些信息得到充分利用。基于双轴晶体折射时满足的波矢关系,导出了两折射光波相位差的精确计算公式。分析了光波在各界面折射时偏振态的变化,提出了会聚偏光干涉合成振幅的计算方法。针对任意取向的双轴晶体,计算了完整的偏光干涉图,反映了相位分布决定等色线、振幅分布决定消光影的规律。用数字图像模似了干涉图,并讨论了干涉图的变化情况。对4块不同取向的KTP晶片进行实验,实验干涉图与理论干涉图的特征完全一致,两者仔细对比可判断现有KTP晶体色散方程的优劣。     

Dynamic mortality factor model with conditional heteroskedasticity

In most methods for modeling mortality rates, the idiosyncratic shocks are assumed to be homoskedastic. This study investigates the conditional heteroskedasticity of mortality in terms of statistical time series. We start from testing the conditional heteroskedasticity of the period effect in the naïve Lee-Carter model for some mortality data. Then we introduce the Generalized Dynamic Factor method and the multivariate BEKK GARCH model to describe mortality dynamics and the conditional heteroskedasticity of mortality. After specifying the number of static factors and dynamic factors by several variants of information criterion, we compare our model with other two models, namely, the Lee-Carter model and the state space model. Based on several error-based measures of performance, our results indicate that if the number of static factors and dynamic factors is properly determined, the method proposed dominates other methods. Finally, we use our method combined with Kalman filter to forecast the mortality rates of Iceland and period life expectancies of Denmark, Finland, Italy and Netherlands.     

OXIRIS project: Development of a new XRF device for the simultaneous detection and treatment of cancer

A novel and suitable energy-dispersive X-ray fluorescent (EDXRF) device, currently at the prototype stage, the Project OXIRIS (Orthovoltage X-Ray–Induced Radiation System), is presented for the simultaneous detection and treatment of cancer diseases. Monte Carlo simulation and experimental results of EDXRF signals from a small deep artificial tumor consisting of a solution of gold nanoparticles bio-targeted and immersed in a tissue-bioequivalent matrix are presented and compared. Briefly, the device consists of a dynamic orthovoltage X-ray fluence concentration coupled to confocal with an EDXRF system along with a sample holder for 3D scanning; all integrated and controlled by a dedicated software capable of controlling the whole operation functionalities: the X-ray source, the rotating arm, the sample holder, and the detection system. The software also includes dedicated subroutines for X-ray fluorescent spectra processing to correlate K-lines signal at each acquisition position with the corresponding high atomic number elements' concentration to produce a 3D distribution according to the user-defined grid. The confocal configuration ensures that the detected signal comes exclusively from the excited volume as defined by the bulk of the focal spot. Hence, the 3D image is achieved by scanning the sample holder through the movement of the sample-carrier stretcher moved by step motors in the 3 coordinated axes. The feasibility of the proposed methodology and the design of the prototype have been successfully demonstrated experimentally, targeting gold nanoparticles in water-equivalent phantoms.     

Matrix summability and uniform convergence of series

Some classical results about uniform convergence of unconditionally convergent series are generalized to weakly unconditionally Cauchy series by means of the matrix summability method for regular matrices.

     

Orlicz序列空间的弱收敛序列系数

本文给出了Orlicz序列空间的弱收敛序列系数的表达式.     

Recurrence of the integral of a smooth conditionally periodic function

We prove that the integral of a smooth multifrequency conditionally periodic function with zero mean oscillates. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 737–748, May, 1998. The author wishes to express his deep gratitude to S. V. Konyagin for fruitful discussions, verification of the results, and the correction of some misprints. This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00378 and No. 96-15-96072 and by the EFAKOD Foundation.