T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise

The paper deals with the T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise. A difference equation is obtained by applying the numerical method to a linear test equation, in which the Wiener increment is approximated by a discrete random variable with two-point distribution. The conditions under which the method is T-stable are considered and the numerical experiments are given.     

The gerber-shiu expected discounted penalty function for Lévy insurance risk processes

In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.     

The dual geometry of Hermitian two-point codes

In this paper, we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases.     

Random polarizations

We derive conditions under which random sequences of polarizations (two-point symmetrizations) on S^d${\mathbb{S}}^d$, R^d${\mathbb{R}}^d$, or H^d${\mathbb{H}}^d$ converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose distributions need not be uniform. The proof of convergence hinges on an estimate for the expected distance from the limit that yields a bound on the rate of convergence. In the special case of i.i.d. sequences, almost sure convergence holds even for polarizations chosen at random from suitable small sets. As corollaries, we find bounds on the rate of convergence of Steiner symmetrizations that require no convexity assumptions, and show that full rotational symmetry can be achieved by randomly alternating Steiner symmetrizations in a finite number of directions that satisfy an explicit non-degeneracy condition. We also present some negative results on the rate of convergence and give examples where convergence fails.     

Microscopic Approach to Random Walks

In the present paper the microscopic approach to random walk models is introduced. For any particular model it provides a rigorous way to derive the transport equations for the macroscopic density of walking particles. Although it is not more complicated than the standard random walk framework it has virtually no limitations with respect to the initial distribution of particles. As a consequence, the transport equations derived with this method almost automatically give answers to such important problems as aging and two point probability distribution.     

一种非本征光纤法布里-珀罗传感器的信号解调算法

给出了一种基于均方误差估计的非本征光纤法布里-珀罗(EFPI)传感器的腔长解调算法。在参量估计方面, 均方误差将估计子的方差和偏差结合在一起, 具有更高的估计精度和准确度。如果给出某一个真值的一系列估计子, 则具有最小均方误差的估计子比其他估计子更为有效。在非本征光纤法-珀传感器的腔长解调方面, 则实际腔长对应于腔长均方误差估计取最小值时的腔长估计子。对一个非本征光纤法-珀压力传感器的测试结果表明, 腔长解调分辨率为0.18 nm, 对应的压力分辨率可达2.99 kPa。与传统的解调算法相比, 通过该算法可在较宽的动态范围内获得高的解调分辨率, 并实现绝对腔长的解调。     

用157 nm激光制作的光子晶体光纤法布里-珀罗传感器

157nm准分子激光用于微加工具有单光子能量高,峰值功率高,材料吸收系数高,分辨率高等优点。利用157nm激光微加工的方法,在光子晶体光纤上融切出微小矩形孔,从而构成腔长为45.6μm的微光纤法布里-珀罗干涉腔,得到的干涉条纹平滑,衬比度约为26dB,并从激光与石英材料的相互作用上分析了形成较好干涉条纹的原因。把这种微腔应用于应变测量,在550μm范围内,腔长增量相对于应变的灵敏度为0.32nm/μm,线形度达0.9994。实验证明该微腔对温度不敏感,800℃范围内腔长变化仅20nm。157nm准分子激光加工光纤法布里-珀罗腔方法简单,一次成型,具有较高的加工效率和精度,有望实现光纤法布里-珀罗腔的规模化批量制造,具有较好的应用前景。     

宽截止窄带高反射滤光膜设计

窄带高反射滤光膜在光通讯、光学探测仪器等领域有着重要应用.探讨了"基片|H(LH)m1aL(HL)m2βCr,M|空气"膜系结构的窄带高反射滤光膜系,讨论了金属Cr层厚度,以及两种不同的匹配膜系对滤光膜特性的影响,计算了Cr层内部的电场分布.结果表明,较厚的金属层可实现更宽的截止带宽,匹配层的加入有效地实现了宽截止带的深截止,使中心波长处导纳为较大值的匹配膜系可以更好地实现滤光膜宽截止、窄带高反射特性;匹配膜层使中心波长处Cr层内部的电场强度趋于零,有效地降低了整个膜系的吸收,提高了反射率.     

快速傅里叶变换与线性调频Z变换联合算法在光纤法布里-珀罗传感器解调中的应用

将快速傅里叶变换(FFT)与线性调频Z变换(CZT)联合变换的方法应用到法布里-珀罗(F-P)腔传感器的解调中,从理论上分析了该方法的解调原理及误差.模拟计算得出,该联合算法解调出的腔长的相对误差达到0.01%,腔长的最大绝对误差小于0.05 μm.在对测量范围为O～3 MPa的F-P腔微机电系统(MEMS)压力传感器进行的解调试验中,该算法可以辨别0.01 MPa的压力,腔长与压力数据的拟合度为0.99316,测量压力与实际压力的标准偏差小于0.005 MPa.实验结果表明,FFT与CZT联合解调的方法可以在较少计算量的基础上达到较高的精度,满足实际需求.