Effect of the initial estimator on the asymptotic behavior of one-step M-estimator

For a general (real) parameter, let M _nbe the M-estimator and M _n ⁽¹⁾ be its one-step version (based on a suitable initial estimator M _n ⁽⁰⁾). It is known that, under certain regularity conditions, n(M _n ⁽¹⁾-M _n)=O _p(1). The asymptotic distribution of n(M _n ⁽¹⁾-M _n) is studied; it is typically non-normal and it reveals the role of the initial estimator M _n ⁽⁰⁾.Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0387     

p—型有限元方法的L^2模误差估计的一个补充

本文讨论Kenneth Erikssion提出的模型问题的p-型有限元方法,解决了文[1]定理2后提出的问题,并给出提高误差收敛阶的一个方法。     

A Density Turán Theorem

Let F be a graph that contains an edge whose deletion reduces its chromatic number. For such a graph F , a classical result of Simonovits from 1966 shows that every graph on vertices with more than edges contains a copy of F . In this article we derive a similar theorem for multipartite graphs. For a graph H and an integer , let be the minimum real number such that every ?‐partite graph whose edge density between any two parts is greater than contains a copy of H . Our main contribution in this article is to show that for all sufficiently large if and only if H admits a vertex‐coloring with colors such that all color classes but one are independent sets, and the exceptional class induces just a matching. When H is a complete graph, this recovers a result of Pfender (Combinatorica 32 (2012), 483–495). We also consider several extensions of Pfender's result.     

Quantitative version of the joint distribution of eigenvalues of the Hecke operators

Recently, Murty and Sinha proved an effective/quantitative version of Serre?s equidistribution theorem for eigenvalues of Hecke operators on the space of primitive holomorphic cusp forms. In the context of primitive Maass forms, Sarnak figured out an analogous joint distribution. In this paper, we prove a quantitative version of Sarnak?s theorem that gives explicitly estimate on the rate of convergence. The same result also holds for the case of holomorphic cusp forms.     

Convergence of an adaptive hp finite element strategy in higher space-dimensions

We show convergence in the energy norm for an automatic hp-adaptive refinement strategy for finite elements on the elliptic boundary value problem. The result is a generalization of a marking strategy, which was proposed in one space-dimension, to problems in two- and three-dimensional spaces.     

Natural hp‐BEM for the electric field integral equation with singular solutions

We apply the hp ‐version of the boundary element method (BEM) for the numerical solution of the electric field integral equation (EFIE) on a Lipschitz polyhedral surface Γ. The underlying meshes are supposed to be quasi‐uniform triangulations of Γ, and the approximations are based on either Raviart‐Thomas or Brezzi‐Douglas‐Marini families of surface elements. Nonsmoothness of Γ leads to singularities in the solution of the EFIE, severely affecting convergence rates of the BEM. However, the singular behavior of the solution can be explicitly specified using a finite set of functions (vertex‐, edge‐, and vertex‐edge singularities), which are the products of power functions and poly‐logarithmic terms. In this article, we use this fact to perform an a priori error analysis of the hp ‐BEM on quasi‐uniform meshes. We prove precise error estimates in terms of the polynomial degree p, the mesh size h, and the singularity exponents. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012     

Er3+/Yb3+/Tm3+共掺杂氟化物中红色上转换发光研究

氧化铒的质量增加到原来的10倍左右时发现两种配方的发光性质有明显不同。根据情况作研究了Er^3 ／Tm^3,Er^3 ／Er^3-和Er^3 ／Yb^3 /Tm^3 发光系统在980nm抽运下的荧光光谱和上转换发光的性质,以及在声子能量较低的氟化物中,3个发光系统建立的优先性和Er^3 离子浓度的关系。根据实验发现当Er^3 离子浓度由小逐渐变大时,绿光和红光的强弱比例也有明显的变化。其中作认为起决定性作用的是Er^3 离子浓度。因为在均匀体系中每个稀土离子的和另一个稀土离子的结合形成发光系统的机会是平等的,组成发光系统的稀土离子间的距离变化,即其中一种起决定作用的离子浓度变化时,那么它所组成的发光系统也就相应发生变化(稀土离子的优先结合性也会在此得到体现),从而发出的主色的光也就跟着变化。     

Formal total synthesis of (-)- and (+)-balanol: two complementary enantiodivergent routes from vinyloxiranes and vinylaziridines

Formal total syntheses of both enantiomers of balanol have been achieved by the preparation of the protected hexahydroazepine core 2. Two complementary routes have been investigated. The first relied on the regioselective opening of 1,2-epoxycyclohex-3-ene with a chiral-auxiliary version of the Burgess reagent to provide a diastereomeric pair of cis-fused cyclic sulfamidates. The sulfamidates were transformed to trans-amino benzoates with ammonium benzoate and, after separation, converted to (−)-2 and (+)-2 by oxidative cleavage and reductive amination. The second approach utilized vinylaziridines derived from 1-bromo-2,3-dihydroxycyclohexa-4,6-diene obtained by the whole-cell fermentation of bromobenzene with Escherichia coli JM109(pDTG601). Stereoselective opening of the aziridines generated the requisite trans-amino alcohol derivatives, which after saturation of the vinyl bromide moieties were converted to (−)-2 and (+)-2 by oxidative cleavage of the cis-diol and reductive amination. Experimental and spectral data are provided for all new compounds.