The Berry–Esseen bounds of the weighted estimator in a nonparametric regression model

Consider the following nonparametric model: \(Y_{ni}=g(x_{ni})+ \varepsilon _{ni},1\le i\le n,\) where \(x_{ni}\in {\mathbb {A}}\) are the nonrandom design points and \({\mathbb {A}}\) is a compact set of \({\mathbb {R}}^{m}\) for some \(m\ge 1\), \(g(\cdot )\) is a real valued function defined on \({\mathbb {A}}\), and \(\varepsilon _{n1},\ldots ,\varepsilon _{nn}\) are \(\rho ^{-}\)-mixing random errors with zero mean and finite variance. We obtain the Berry–Esseen bounds of the weighted estimator of \(g(\cdot )\). The rate can achieve nearly \(O(n^{-1/4})\) when the moment condition is appropriate. Moreover, we carry out some simulations to verify the validity of our results.

     

Temperature Dependence of the Refractive Indices of Doped K2SO4 Crystals

Journal of Applied Spectroscopy - The temperature dependence of the refractive indices of K2SO4 with copper impurity was investigated. It was found that introduction of the copper impurity leads to...     

Novel halogenated cyclopentasilylene-2,4-dienes via DFT

In view of immense importance of silylenes and the fact that their properties undergo significant changes on substitution with halogens, here, we have used B3LYP/6-311++G** level of theory to access the effects of 1–4 halogens (X = F, Cl, Br, and I) on four unprecedented sets of cyclopentasilylene-2,4-dienes; with the following formulas: SiC₄H₃X ( 1 _X ), SiC₄H₂X₂ ( 2 _X ), SiC₄HX₃ ( 3 _X ), and SiC₄X₄ ( 4 _X ). In going down from F to I, the singlet (s)-triplet (t) energy gap (ΔE_s-t, a possible indication of stability), and band gap (ΔE_H-L) decrease while nucleophilicity (N), chemical potential (μ), and proton affinity (PA) increase. The overall order of N, μ, and PA for each X is 2 _X > 1 _X > 3 _X > 4 _X . Precedence of 2 _X over 1 _X is attributed to the symmetric cross conjugation in the former. The highest and lowest N are shown by 2 _I and 4 _F . The trend of divalent angle () for each X is 4 _X > 1 _X > 3 _X > 2 _X . The results show that in going from electron withdrawing groups (EWGs) to electron donating groups (EDGs), the ΔE_s-t and ΔE_H-L decrease while N, μ, and PA increase. Also, rather high N of our scrutinized silylenes may suggest new promising ligands in organometallic chemistry.     

<Emphasis Type="Italic">FCC/BCC</Emphasis> competition and enhancement of saturation magnetization in nanocrystalline Co-Ni-Fe films

The structure, chemical composition, and magnetic properties of electrochemically deposited nanocrystalline Co-Ni-Fe films were investigated using a number of techniques. A high saturation magnetic induction up to B _s = 21 kG was attained. An enhancement of the saturation magnetization compared to the ideal anticipated one was revealed, which correlated with the nonlinear behavior of the structural phase composition and lattice parameters with the change of the composition. The text was submitted by the authors in English.     

Phase state stabilization of ammonium nitrate for creating an oxidizing agent for smokeless gas-generating formulations yielding no toxic combustion products

Methods for phase stabilization of ammonium nitrate were sought for in order to considerably expand the application area of this oxidizing agent in various-purpose self-combustible formulations, including that in a new generation of gas-generating formulations for automobile air bags. New methods for stabilization of ammonium nitrate were studied and, in particular, a search was made for organic compounds that can stabilize ammonium nitrate even at their low content. The mechanism of phase state stabilization of ammonium nitrate by compounds of this kind was examined.     

Carbon adsorbents for the sorpting and concentrating nobel metals

Kinetic, sorption and selectivity properties of commercial adsorbents are improved by adding petroleum residues (tar asphaltene concentrates) 13% of whole mass. Obtained adsorbents can be used for selective extraction of nobel metals from multicomponent polymetallic solutions of heavy metals and fro sewages purification for removing arsenic.     

Rigidity and flexibility of virtual polytopes

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.     

双掺(Tm3+,Tb3+)LiYF4激光器1.5 μm波长激光阈值分析

由速率方程推出了双掺（Tm^3 ,Tb^3 ）离子准四能级系统的激光阈值解析式，讨论了Tm^3 和Tb^3 离子之间的相互作用。分析了1.5μm波长附近的激光阈值和Tm^3 、Tb^3 离子的掺杂原子数分数及晶体长度的关系。结果表明，对于对应Tm^3 离子^3H4→^3F4跃迁的约1.5μm波长的激光，激活离子Tm^3 的掺杂原子数分数过大时，交叉弛豫作用将使系统阈值迅速增加。Tb^3 离子的加入，一方面能抽空激光下能级，起到降低阈值的作用；另一方面亦减少了激光上能级的寿命，使阈值升高。故Tb^3 离子有最佳掺杂原子数分数。对于Tm原子数分数为y=0.01的Tm:LiYF4晶体，Tb^3 离子的最佳掺杂原子数分数为0.002左右，同时表明，激光阈值与晶体长度有关。最佳晶体长度与Tm^3 、Tb^3 离子的掺杂原子数分数以及晶体的衍射损耗和吸收损耗有关。     

YBa2Cu1-xCox(Cu1-yZny)2Oz体系的Co,Zn共同掺杂效应

本文报道通过对YBa₂Cu_1-xCo_x(Cu_1-yZn_y)₂O_z(0≤x,y≤0.1)体系晶体结构、氧含量、正常态电阻-温度关系、Hall效应以及超导临界温度等的综合测量,发现随着Co和Zn含量的增加,体系经历了从正交结构的超导金属向四方结构的非超导半导体的转变,超导临界温度T_c和载流子浓度n_h均迅速下降,Co 关键词：