Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

Q过程的不变分布(Ⅱ)

设E为一个可数集,Q=（qi,j;i,j∈E）为E×E上的矩阵,满足m为E上的概率分布满足何时存在Q过程,使得m是它的不变分布? 这个问题由Williams（1979）作为一个开问题提出.文[15]对全稳定情形,解决了这个问题;本文对单瞬时情形,完整地解决了该问题.     

Nonsensitiveness Regions for Threshold Ellipsoids

The problem is to determine nonsensitiveness regions for threshold ellipsoids within a regular mixed linear model.     

平面分拆的矢量控制方法：列严格梯形平面分拆

作为移位平面分拆的自然拓广,本文引入了梯形平面分拆的概念.应用矢量控制技巧,建立了给定形状和行(列)分部约束的列严格梯形平面分拆集合之枚举函数的初等对称函数行列式表达式.其中之一的重要特例构成了关于循环对称平面分拆的Macdonald猜想的证明基础.     

Anisotropy of two-photon absorption in gallium selenide at 1064 nm

The Bridgman method is used to grow single crystals of ε-GaSe. The two-photon absorption (TPA) coefficient β was measured for especially un-doped crystals at room temperature for the ordinary o-ray (β_⊥) and extraordinary e-ray (β_∥) using single-wavelength excitation by a Nd:YVO₄ laser at 1.064 μm with a pulse duration of 10 ps and a repetition rate of 81 MHz. No large anisotropy was observed for the TPA coefficients between the two geometries. The TPA coefficients were found to be β_⊥ = 1.07 × 10⁻⁹ cm/W and β_∥ = 1.88 × 10⁻⁹ cm/W. It was found that doping slightly increases the TPA coefficient. The value of the TPA for crystals doped with 0.5 at.% of Tl is β_⊥ = 7.56 × 10⁻⁹ cm/W.     

变系数非线性方程的Jacobi椭圆函数展开解

把Jacobi椭圆函数展开法扩展并应用到求解变系数的非线性演化方程,比较方便地得到新的解析解 关键词： Jacobi椭圆函数 变系数非线性方程 类椭圆余弦波解 类孤子解     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

红外热像仪参数的双黑体测量装置

对红外热像仪参数双黑体测量装置的工作原理进行了介绍。装置采用双黑体及反射型靶标为温差辐射源，可实现黑体温度温差准直辐射的定期校准和红外热像仪参数测量量值的溯源，也可实现红外热像仪参数的可控性，以及对它进行稳定的、可复现的精确测量。推导出利用红外热像仪参数双黑体测量装置测量信号传递函数SiTF数学模型，分析了红外热像仪参数测量装置的客观因素——仪器常数，针对仪器常数对SiTF测量的影响进行了试验。试验结果表明，仪器常数对红外热像仪SiTF参数测量精度影响较大，并同时影响时域与空域NETD及3D噪声的准确测量。     

Clifford分析中无界域上正则函数的边值问题

在引入修正Cauchy核的基础上,讨论了无界域上正则函数的带共轭值的边值问题：a(t)Φ (t) b(t)Φ (t) c(t)Φ-(t) d(t)Φ=g(t)．首先给出了无界域上正则函数的Plemelj公式,然后利用积分方程方法和压缩不动点原理证明了问题解的存在唯一性．     

Parametric estimation of discretely sampled Gamma-OU processes

The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.