由Lévy过程驱动的反射型倒向随机微分方程

证明了由Lévy过程驱动的反射型倒向随机微分方程在局部Lipschitz系数下的解的存在唯一性,并且研究了解的稳定性质.此外,当系数满足Lipschitz条件以及反射壁正则时,证明了过程K的正则性.     

基于光传输矩阵方法对EFFP传感器的参数优化研究

为研究光纤法珀传感器中法珀腔结构参数对其条纹对比度的影响,基于光传输矩阵方法,建立了描述非本征型光纤法珀干涉结构中光束传播特性的理论模型。以基于化学腐蚀渐变多模折射率光纤方法制作而成的光纤法珀传感器为例,进行了数值模拟。由模拟结果可以得出,腔长为40μm、曲率半径在85～115μm范围内可以获得较高的条纹对比度。其结果表明,通过优化法珀腔的腔长和形状可以改善光纤法珀传感器反射光谱的条纹对比度。     

JT-60U ��JT-60SA ���������¸��������Ӽ�������ɢ�����ұ���ģ

运用线性回旋动力学与磁流体力学的混合模拟程序,研究了JT-60U和JT-60SA装置中高能量粒子对离散阿尔芬本征模的共振激发.发现了丰富的αTAE动力学不稳定模式,研究了它的不稳定特性对高能量粒子速度的依赖关系.发现在JT-60U高βp ELMy H模运行中有grassy ELM的放电比有gaint ELM的放电更容易被高能量粒子激发成不稳定模式,在有边缘L模存在的负剪切运行下的各个势阱中都存在高能量粒子激发的αTAE不稳定模式.另外在JT-60SA中高βp全非感应电流驱动下的模拟实验放电下也发现了丰富的αTAE不稳定模式,观察了αTAE在该装置中沿磁场线和径向两个方向的二维广域本征模特性.     

Bernstein-Sikkema-Bézier算子的点态逼近

讨论了Bernstein-Sikkema-Bézier算子点态逼近的等价定理,首先利用插项的的方法证明了正定理,然后应用讨论算子逼近的常规方法给出了其逼近的逆定理.     

带投资的时依更新风险模型中破产概率的一致渐近估计

本文考虑索赔额过程与索赔时间过程具有相依性的更新风险模型.假定保险公司将其盈余投资到金融市场中,该投资的价格过程服从几何L′evy过程.当索赔额分布属于L∩D时,本文得到有限时间总索赔额现值尾概率的一致渐近估计,同时也得到有限时间破产概率的一致渐近估计.     

An ergodic theorem of a parabolic Anderson model driven by L��vy noise

In this paper, we study an ergodic theorem of a parabolic Andersen model driven by Lévy noise. Under the assumption that A = (a(i, j)) _i,j∈S is symmetric with respect to a σ-finite measure gp, we obtain the long-time convergence to an invariant probability measure ν _h starting from a bounded nonnegative A-harmonic function h based on self-duality property. Furthermore, under some mild conditions, we obtain the one to one correspondence between the bounded nonnegative A-harmonic functions and the extremal invariant probability measures with finite second moment of the nonnegative solution of the parabolic Anderson model driven by Lévy noise, which is an extension of the result of Y. Liu and F. X. Yang.     

三角形上的分片二阶光滑有理插值

给出三角形上一种C2插值格式,插值函数由偏插值函数加权求和而成.偏插值函数对应于每一个顶点：构造三角形的一种分割,在其上定义一个分片5次多项式,只插值该顶点及其相邻两边上的插值条件.对应于每一个顶点有一个权函数,它由重心坐标定义,是一个有理函数.所得的插值函数是一个分片有理函数,只需被插函数在三角形顶点处的直至2阶导数值,利用多项式的Bernstein-Bézier表示,该插值函数易于表达和计算.     

Intrinsic contractivity properties of Feynman-Kac semigroups for symmetric jump processes with infinite range jumps

Let (X_t)_t≥0 be a symmetric strong Markov process generated by non-local regular Dirichlet form (D, D(D)) as follows: D(f,g)=∫?d∫?d(f(x)-f(y))(g(x)-g(y))J(x,y)dxdy,?f,g∈D(D), where J(x, y) is a strictly positive and symmetric measurable function on ?d×?d. We study the intrinsic hypercontractivity, intrinsic supercontractivity, and intrinsic ultracontractivity for the Feynman-Kac semigroup TtV(f)(x)=Ex(exp?(-∫0tV(Xs)ds)f(Xt)),?x∈?d,f∈L2(?d;dx). In particular, we prove that for J(x,y)≈|x-y|-d-al{|x-y|≤1}+e-|x-y|l{|x-y|>1} with α ∈(0, 2) and V(x)=|x|λ with λ>0, (TtV)t≥0 is intrinsically ultracontractive if and only if λ>1; and that for symmetric α-stable process (X_t)_t≥0 with α ∈(0, 2) and V(x)=log?λ(1+|x|) with some λ>0, (TtV)t≥0 is intrinsically ultracontractive (or intrinsically supercontractive) if and only if λ>1, and (TtV)t≥0 is intrinsically hypercontractive if and only if λ≥1. Besides, we also investigate intrinsic contractivity properties of (TtV)t≥0 for the case that lim inf?|x|→+∞V(x)<+∞     

Branching particle systems in spectrally one-sided Lévy processes

We investigate the branching structure coded by the excursion above zero of a spectrally positive Lévy process. The main idea is to identify the level of the Lévy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump- Mode-Jagers (CMJ) branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Lévy process is established by a time reversal approach. Properties of the measurevalued processes can be studied via the excursions for the corresponding Lévy processes.     

铁的氢氧化合物稳定相α, β-FeOOH的表征及光谱分析

铁的氢氧化合物稳定相针铁矿(α-FeOOH)及四方纤铁矿(β-FeOOH)的合成材料因具有纳米颗粒粒径、较高比表面积,在工业生产和环境治理中被广泛应用。α,β-FeOOH作为重金属等污染物的吸附材料尤受关注。但其合成过程中溶液pH值和反应条件(如不同温度下加热或室温磁力搅拌等)对α,β-FeOOH矿物材料晶型、颗粒形貌、尺寸和界面特性的影响及其与矿物环境功能的相关性报道较少。故本工作基于Fe(NO₃)₃和FeCl₃溶液在一定pH值范围内分别易于形成α-FeOOH和β-FeOOH稳定相,利用X射线衍射仪、透射/扫描电子显微镜和激光粒度分析仪对加热(40和70 ℃)和磁力搅拌(25 ℃)条件下形成的矿物α, β-FeOOH的晶型和颗粒形貌结构进行了鉴定与表征,同时利用红外光谱仪测定了矿物表面的特征结构基团。研究结果表明,40和70 ℃反应温度下形成的矿物Aka-T40, Aka-T70, Gth-T70具有颗粒均一、结晶型较好、比表面积较大等特性,是良好的去除环境污染物的吸附剂材料。