Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

On the approximation of convex functions by Bernstein-type operators

As a consequence of Jensen's inequality, centered operators of probabilistic type (also called Bernstein-type operators) approximate convex functions from above. Starting from this fact, we consider several pairs of classical operators and determine, in each case, which one is better to approximate convex functions. In almost all the discussed examples, the conclusion follows from a simple argument concerning composition of operators. However, when comparing Szász-Mirakyan operators with Bernstein operators over the positive semi-axis, the result is derived from the convex ordering of the involved probability distributions. Analogous results for non-centered operators are also considered.     

酰胺修饰杂化硅胶整体柱的制备及其在莱克多巴胺检测中的应用

以氧化琼脂糖（AG）和四甲氧基硅烷（TMOS）为前驱体,通过溶胶－凝胶法制备 AG/SiO2整体柱,利 用酰胺化反应对整体柱进行酰胺基团修饰。通过X射线光电子能谱（XPS）、傅里叶变换红外光谱（FTIR）、N2 吸附－脱附和扫描电镜（SEM）等表征手段对所制备材料的结构和形貌进行分析。结果显示酰胺基团被成功修 饰至整体柱,该材料具有良好的通透性及较大的比表面积。以其为固相微萃取介质对羊肉中的莱克多巴胺进 行萃取富集,在优化的样品前处理条件下,采用基质添加标准曲线法,结合高效液相色谱－紫外（HPLC－ UV）检测,建立了羊肉中痕量莱克多巴胺的分析方法。该方法在 1. 94～1 170 ng/g范围内线性良好,相关系 数（r 2 ）为 0. 993 1,检出限（LOD）和定量下限（LOQ）分别为0. 618、1. 94 ng/g,3个不同加标水平下样品的平均回 收率为86. 6%～103%,相对标准偏差（RSD,n = 5）为4. 8%～7. 3%。该方法具有检出限低、回收率高、样品用 量少等特点,可用于羊肉中痕量莱克多巴胺的灵敏检测。     

获取超短波长电磁辐射的新途径

在系统研究运动电子对迎面而来的圆偏振激光脉冲的汤姆逊散射的基础上，讨论了获取超短波长电磁辐射的两种新方案。其一是利用超强圆偏振激光在具有特定速度的电子的非线性散射所伴随的谐波频率上称，其二是利用激光在相对论电子反向散射所伴随的多普勒频移。     

Fréchet spaces with unconditional base

A nonnormable ?-space possessing an unconditional basis is not necessarily isomorphic to a generalized Köthe space.     

A Generalization Of Reifenberg’s Theorem In {\mathbb{R}}^3

In 1960 Reifenberg proved the topological disc property. He showed that a subset of which is well approximated by m-dimensional affine spaces at each point and at each (small) scale is locally a bi-H?lder image of the unit ball in . In this paper we prove that a subset of which is well approximated in the Hausdorff distance sense by one of the three standard area-minimizing cones at each point and at each (small) scale is locally a bi-H?lder deformation of a minimal cone. We also prove an analogous result for more general cones in . Received: July 2006, Revised: August 2007, Accepted: January 2008     

Exact solutions to three-dimensional time-dependent Schrödinger equation

With a view to obtain exact analytic solutions to the time-dependent Schrödinger equation for a few potentials of physical interest in three dimensions, transformation-group method is used. Interestingly, the integrals of motion in the new coordinates turn out to be the desired invariants of the systems.     

The Mössbauer spectrum of synthetic hureaulite: Fe5 2+(H2O)4(PO4H)2(PO4)2

The crystal structure of synthetic ferrous hureaulite, Fe₅ ²⁺ (H₂O)₄(PO₄H)₂(PO₄)₂, was refined from single-crystal X-ray data. It is monoclinic, space group C2/c, with a=17.487(4), b=9.017(2), c=9.338(2) Å, β=96.27(3)°, V=1463.6(6) Å³, Z=4 and D _calc=3.327 g/cm³. This end member of the hureaulite series was crystallized under distinctly acidic conditions, by a method that gives perfect crystals, large enough for X-ray single crystal studies. The main feature of the hureaulite structure is that it has an equal number of normal (PO₄)³⁺ and acid (PO₄H)²⁺ tetradentate groups. These are centered on Fe²⁺ atoms and share corners with edge-linked octahedra, forming pentamer units. The five Fe²⁺ atoms are distributed on three distinct sites in these units. This can be directly observed in the Mössbauer spectrum at 295 K, which contains three doublets whose relative intensities correspond to the 1:2:2 distributions of crystallographic sites.