关于《L_p范数下凸约束最佳逼近的特征》中一个引理的注记

最近．许树声［１］撰文给出了对Ｌ_ｐ范数下凸约束最佳逼近的特征定理．并研究了该定理的苦干应用．然而，文［１］引理１证明中部分地方有误．本文给予了纠正，予以重新证明     

Maximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances

To analyze the isotonic regression problem for normal means, it is usual to assume that all variances are known or unknown but equal. This paper then studies this problem in the case that there are no conditions imposed on the variances. Suppose that we have data drawn fromkindependent normal populations with unknown meansμ_i's and unknown variancesσ²_i's, in which the means are restricted by a given partial ordering. This paper discusses some properties of the maximum likelihood estimates ofμ_i's andσ²_i's under the restriction and proposes an algorithm for obtaining the estimates.     

人类认识和利用能源的历史

能源,是人类利用的自然界能量资源的总称。人类在不断征服自然、改造社会的斗争中,逐步加深、扩大对能源的认识和利用;而对自然界能源的利用越发展,就越增强了人类改造世界的物质力量。因此,能源发展史和人类社会的发展史总是紧密联系在一起的。在阶级社会里,人类对自然力的认识和利用,总是受一定的阶级关系支配的。因此,从原     

Core/shell quantum-dot-photosensitized nano-TiO2 films: fabrication and application to the damage of cells and DNA

Through the use of monodisperse core/shell quantum dots (QDs) as photosensitizers for the first time, a novel strategy for the fabrication of QD-photosensitized nano-TiO2 films was demonstrated. Core/shell QDs were self-assembled on nano-TiO2 films through carboxyls as anchoring groups to metal oxides. Atomic force microscopy and some other experiments showed the fabrication strategy is successful. Reactive oxygen species detection experiments indicated that such films have photosensitization ability. The results of bactericidal and DNA damage experiments demonstrate that such films have excellent photoactivity.     

Fluorescence study of aggregation in water of PEO-grafted polydiphenylamine

Fluorescence spectra of water-soluble conducting poly(ethylene oxide)-grafted polydiphenylamines (PDPA-g-PEOs with the M(n)s of PEO 350, 750, and 2000) in water were determined and interpreted. The emissions of the PDPA-g-PEOs occurred in the range from 360 to 700 nm and were dependent on their concentrations, PEO chain length, extent of oxidation, pH, and temperature. An optimum concentration, above which the fluorescence intensity decreased dramatically because of quenching, was observed. This quenching was a result of the aggregation of PDPA-g-PEO macromolecules in water. The doped PDPA-g-PEO molecules provided a lower optimum concentration than the corresponding reduced-state macromolecules. A rod-shaped microstructure of nanoscale size was generated through the aggregation of the PDPA-g-PEO macromolecules. This microstructure was also confirmed by dynamic light scattering, atomic force microscopy, and surface elemental analysis.     

An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1]

Let I = [0, 1], c ₁, c ₂ ∈ (0, 1) with c ₁ < c ₂ and f : I⊸I be a continuous map satisfying: are both strictly increasing and is strictly decreasing. Let A = {x ∈ [0, c ₁]∣f(x) = x}, a=max A, a ₁ =max(A\{a}), and B = {x ∈ [c ₂, 1]∣f(x) = x}, b=minB, b ₁ =min(B\{b}). Then the inverse limit (I, f) is an arc if and only if one of the following three conditions holds: (1) If c ₁ < f (c ₁) ≤ c ₂ (resp. c ₁ ≤ f (c ₂) < c ₂), then f has a single fixed point, a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods, furthermore, if A≠φ and B≠φ, then f (c ₂) > a (resp. f (c ₁) < b). (2) If f (c ₁) ≤ c ₁ (resp. f (c ₂) ≥ c ₂), then f has more than one fixed point, furthermore, if B≠φ and A\ {a} ≠φ, f (c ₂) ≥ a or if a ₁ < f (c ₂) < a, f ² (c ₂) > f (c ₂), (resp. f has more than one fixed point, furthermore, if A≠φ and B\{b}≠φ, f (c ₁) ≤ b or if b < f (c ₂) < b ₁, f ² (c ₁) < f (c ₁)). (3) If f (c ₁) > c ₂ and f (c ₂) < c ₁, then f has a single fixed point, a single period two orbit lying in I\(u, v) but no points of period greater than two, where u, v ∈ [c ₁, c ₂] such that f (u) = c ₂ and f (v) = c ₁. Supported by the National Natural Science Foundation of China (No. 19961001, No. 60334020) and Outstanding Young Scientist Research Fund. (No. 60125310)     

Freeze-drying of mononuclear cells and whole blood of human cord blood

The research on haematopoietic stem cells of human cord blood has become more important recently. People have concentrated on the preservation of cord blood stem cells. At present, cord blood can be preserved at ultra-low temperatures. In this study, we try to preserve cord blood and its constituents by freeze-drying. The experiments on both the mononuclear cell content and the whole blood of human cord blood were carried out respectively. The samples were frozen firstly by different cooling protocols in the presence of PVP, sucrose, and mannitol. Afterwards, they were vacuum-dried at a selected shelf temperature of -30 degree C for the main drying stage, and then vacuum-dried at 15 degree C for the second drying stage. The entire time of the freeze drying was 52 hours. Samples were stored at room temperature for 2 days prior to evaluation. Subsequently, the dried samples were suspended in an isotonic phosphate-buffered saline solution. The recovery of the cells were tested by a haemacytometer, and the highest cell numerical count recovery of MNC was 75.0 percent (SD = 4.1 percent) (P = 0.01), obtained in the protocol of 40 percent PVP + 20 percent sucrose + 10 percent Mannitol. The viability of the nucleated cells measured by PI staining and the ratio of the number of CD34+ to the number of lymphocytes (by the FITC anti-human CD34+ conjugated antibody method) were measured using a flow cytometer (FCM). The protocol of 40 percent PVP + 20 percent sucrose + 10 percent fetal bovine serum had the highest viability of 98.6 percent (SD = 0.7 percent) (P = 0.01). The highest ratio of CD34+ to lymphocytes was 1.2%, and the highest recovery of CD34+ was 68.4 percent (SD = 39.5 percent) (P = 0.05). Comparing the results of the lyophilized MNC subfraction with that of the whole blood, the lyophilization of the isolated MNC was more successful than that of whole blood.     

A QM/MM study of a nucleophilic aromatic substitution reaction catalyzed by 4-chlorobenzoyl-CoA dehalogenase

Calculated using a QM/MM method, the free energy profile for the conversion of 4-chlorobenzoate to 4-hydroxybenzoate catalyzed by 4-chlorobenzoyl-CoA dehalogenase indicates the existence of a stable Meisenheimer complex.