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.

     

Unlocking the Drug Potential of the Bryostatin Family: Recent Advances in Product Synthesis and Biomedical Applications

Bryostatins are a class of naturally occurring macrocyclic lactones with a unique fast developing portfolio of clinical applications, including treatment of AIDS, Alzheimer's disease, and cancer. This comprehensive account summarizes the recent progress (2014–present) in the development of bryostatins, including their total synthesis and biomedical applications. An emphasis is placed on the discussion of bryostatin 1 , the most-studied analogue to date. This review highlights the synthetic and biological challenges of bryostatins and provides an outlook on their future development.     

Measurement of Residual Dipolar Couplings of Organic Molecules in Multiple Solvent Systems Using a Liquid-Crystalline-Based Medium

Residual dipolar coupling (RDC), a robust anisotropic NMR parameter for structural elucidation of organic molecules, is only accessible in an anisotropic environment. Herein, we introduce a novel alignment medium based on the molecular self-assembly of oligopeptide amphiphile (OPA). This medium is compatible with different intermediate and polar solvent systems, such as CD₃OD, [D₆]DMSO, and D₂O. The preparation of the OPA-based medium is simple and rapid, while only very weak background signals were observed from OPAs. Furthermore, we show that the purity of OPA has only a minor influence on the quality of the RDC data. These advantages allow RDC measurements of organic molecules with different polarities and solubilities with high efficiency and accuracy.     

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：