L1-optimal estimates for a regression type function in R

Let X₁, X₂, …, X_n be random vectors that take values in a compact set in R^d, d ≥ 1. Let Y₁, Y₂, …, Y_n be random variables (“the responses”) which conditionally on X₁ = x₁, …, X_n = x_n are independent with densities f(y | x_i, θ(x_i)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θ_q,d of real valued functions, an optimal L₁-consistent estimator of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θ_q,d.     

关于多项式系数微分方程复振荡理论的两个结果

本文证明了：如果ａ_ｋ－ｊ（ｊ＝１，…，ｋ）为多项式，ｄｅｇａ_ｋ－ｊ＝ｎ_ｋ－ｊ，存在某个ａ_ｋ－s（１≤ｓ≤ｋ）满足：当１≤ｊ＜ｓ时，ｎ_ｋ－ｊ／ｊ≤ｎ_ｋ－s／ｓ；当ｓ＜ｊ≤ｋ时，ｎ_ｋ－ｊ＜ｎ_ｋ－s－（ｊ－ｓ）．如果Ｆ≠０是整函数且满足σ（Ｆ）＝β＜（ｎ_ｋ－s＋ｓ）／ｓ，那么微分方程ｆ^（ｋ）＋ａ     

Spherically symmetric static inhomogeneous cosmological models

Spherically symmetric static cosmological models filled with black-body radiation are considered. The models are isotropic about a central observer but inhomogeneous. It is suggested that the energy density of the free gravitational field, which is coupled to the isotropic radiation energy density, might play an important role in generating sufficient field (vacuum) energy (when converted into thermal energy) and initiate processes like inflation. On the central world line the energy density of the free gravitational field vanishes whereas the proper pressure and density of the isotropic black-body radiation are constants. Further, it is shown that the cosmological constant is no more arbitrary but given in terms of the central pressure and density. Also, at its maximum value the energy density of the free gravitational field is proved to be equal to one third of the combined value of radiation pressure and density.     

B（X）上保点谱的可加映射和初等算子

记Ｘ为复数域上无限维Ｂａｎａｃｈ空间，Ｈ为无限维复可分Ｈｉｌｅｒｔ空间。本文给出Ｂ（Ｘ）上保持点谱的满射可加射具有的形式，以及Ｂ（Ｈ）上某些初等算子保点谱的充要条件。     

优化路问题的代数方法—论动态规划（Ⅱ）

本文用同一思路求解多阶段有向图中三种优化路问题:最优路、N阶最优路及多指标Pareto优化路问题,它们都服从嘉量原理,都用同一个代数公式表达它们的嘉量,并可在同一种表格中进行计算,只是所在半域不同,以本文的方法讨论动态规划中一些离散决定型典型应用问题,其提法、建模思路以及求解过程都有可观的扩大与改善。     

F－L模型的状态方程与退禁闭相变图象

用温度场论方法计算了Ｆ－Ｌ模型在有限温度和密度下的状态方程，分析了压强对净重子数密度的等温线．结果表明，在平均场近似下，Ｆ－Ｌ模型所给出的退禁闭相变为一级相变．     

激光沉积超导薄膜过程中出射粒子速度的飞行时间谱分析

采用飞行时间谱技术,测量了准分子激光烧蚀沉积高温超导薄膜过程中,由靶面出射粒子的飞行速度。研究了粒子速度与充氧压及其激光能量密度的关系。讨论了高能粒子在薄膜原位低温外延生长中的作用。     

氢化丁苯共聚物结构的核磁共振波谱表征Ⅰ.13C谱带的归属

本文分别用JEOL FX-90Q和Bruker AM-300波谱仪测定了氢化聚丁二烯和氢化丁苯共聚物的¹H,¹³C-NMR谱,得到了分辨率较高的谱图和新的结构信息。借助DEPT技术确定了各谱带的CH或CH₂类型。利用Grant-Paul和Lindeman-Adams介绍的化学位移经验计算公式,考虑苯基对α、β和γ碳原子的影响,计算了各种三单元序列中有关碳原子的化学位移。对脂肪碳部分的28组谱带重新进行了归属。化学位移计算值与实测值基本相符,并得到了不同组成的模型聚合物¹³C-NMR谱的各谱带强度变化规律的验证。     

一种实现光源与光纤耦合的方法

本文介绍了一种用显微镜筒与透镜构成的光学系统来实现光源与光纤耦合的方法。该方法具有光路系统小巧方便、耐用、耦合效率高等优点。     

Mechanism of the thermal decomposition of nitrates from graphite furnace mass spectrometry studies

A basically new mechanism of the thermal decomposition of solids is proposed to explain the mass spectral observations of gaseous molecules of CoO, CuO, Cu₂O, NiO, PbO and Mg(OH)₂ during the low-temperature decomposition of the anhydrous and hydrated nitrates of these metals. The mechanism consists of two stages: congruent gasification of all reaction products irrespective of their saturated vapor pressure and subsequent condensation of the low-volatility species (oxides and hydroxides). The partial pressures of these species at the appearance temperatures calculated from this theory for the first stage of the process (1–50 mPa) are in agreement with the detection limits of the quadrupole mass spectrometers used in these experiments. The proposed mechanism is supported by other available data obtained by thermal analysis.