更正

<正>本刊2014年77卷第2期172页上的图1有部分曲线未能显示出来,正确的图请见该期图文摘要部分97页最下方的插图。对于由此给作者和广大读者带来的不便,特表歉意。     

部分还原二氧化钛的NMR和EPR研究

Partially reduced TiO₂ nanomaterials have attracted significant interest because of their visible-light activity for catalysis and photodegradation. Herein, we prepared a partially reduced anatase TiO₂ (Re-A-TiO₂) nanoparticle material using a fast combustion method, demonstrating good activity toward decomposing methyl orange under visible light irradiation. The surface structure of the prepared material, after being surface-selectively ¹⁷O-labeled with H₂¹⁷O (¹⁷O-enriched water), was studied via ¹⁷O and ¹H solid-state magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy and electron paramagnetic resonance (EPR) spectroscopy, and the obtained results were compared to those of non-reduced anatase TiO₂ (A-TiO₂). The EPR results showed that the concentrations of paramagnetic species (i.e., oxygen vacancies (OV) and Ti³⁺) in Re-A-TiO₂ were much higher than that in A-TiO₂, while the former was associated with a higher OV/Ti³⁺ ratio. The intensities of the EPR signals were significantly affected by the adsorbed water, and this phenomenon was explored in combination with ¹H NMR spectroscopy. The ¹H species on Re-A-TiO₂ appeared at larger chemical shifts, denoting the increased acidity of the sample, and these ¹H species on Re-A-TiO₂ were more difficult to remove than those on A-TiO₂. On the other hand, different features were observed for the signals arising from the two-coordinated oxygen atoms (μ₂-O) in ¹⁷O NMR, suggesting a typical anatase TiO₂(101) surface on A-TiO₂, but a more complex surface environment for Re-A-TiO₂. Furthermore, a larger amount of hydroxyl groups (OH) were observed on Re-A-TiO₂ compared to that on A-TiO₂, indicating a larger proportion of exposed (001) facets on Re-A-TiO₂. However, the μ₂-O signals broadened and became similar when the drying temperature was increased to 100 ℃, indicating a non-faceted anatase TiO₂ surface in such conditions. Based on the EPR and NMR results, a significant fraction of the OH species is believed to be formed from the reaction of the paramagnetic centers and adsorbed water molecules. The ¹H→¹⁷O cross polarization (CP) MAS and two-dimensional heteronuclear correlation (2D HETCOR) NMR spectra were used to verify the spatial proximity of the hydrogen and oxygen species, confirming the spectral assignments of a strongly adsorbed water and one type of surface OH species. In particular, the ¹H NMR signals at approximately 11 ppm were ascribed to the hydrogen species in the intramolecular hydrogen bond. In summary, this study investigated the paramagnetic species and surface structure of anatase TiO₂ materials by combining EPR along with ¹H and ¹⁷O solid-state NMR spectroscopy. The differences in the surface structures of Re-A-TiO₂ and A-TiO₂ should be closely related to their different properties toward the photodegradation of methyl orange.     

双动点中的分类思想

分类是一种重要的数学思想方法,平面图形中双点运动时,常有某个元素不能确定,需作分类处理.     

Design of phase plates for shaping partially coherent beams by simulated annealing

Taking the Gaussian Schell-model beam as a typical example of partially coherent beams, this paper applies the simulated annealing （SA） algorithm to the design of phase plates for shaping partially coherent beams. A flow diagram is presented to illustrate the procedure of phase optimization by the SA algorithm. Numerical examples demonstrate the advantages of the SA algorithm in shaping partially coherent beams. An uniform flat-topped beam profile with maximum reconstruction error RE 〈 1.74% is achieved. A further extension of the approach is discussed.     

部分线性模型中估计的收敛速度

考虑回归模型（Ⅰ）：其中（ｘ＿ｉ，ｔ＿ｉ）是固定非随机设计点列，ｘ＿ｉ＝（ｘ＿（ｉｌ），…，ｘ＿（ｉｐ））＇β＝（β＿１，…，β＿ｐ）＇（ｐ＞１），ｇ是定义在［０，１］上的未知函数，β是未知待估参数，０＜ｔ＿ｉ＜１，ｅ＿ｉ是ｉ．ｉ．ｄ．随机误差，且Ｅｅ＿ｉ＝０，Ｅｅ＝σ￣２＜∞。基于ｇ的估计取一类非参数权估计（包括常见的核估计和近邻估计），我们讨论了β的最小二乘估计及ｇ的估计的最优强弱收敛速度。     

On Weak Regular ^＊-semigroups

In this paper, a special kind of partial algebras called projective partial groupoids is defined.It is proved that the inverse image of all projections of a fundamental weak regular ^*-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular ^*-semigroup has a projective partial groupoid structure. Moreover, a weak regular ^*-product which connects a fundamental weak regular ^*-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular ^*-product is in fact a weak regular ^*-semigroup and any weak regular ^*-semigroup is constructed in this way.     

储存环高频剔除系统

 介绍了用于电子储存环部分填充和非均匀填充的一种实验装置,它利用储存环中电子运动所具有的横向自由振荡和束团脉冲的时间结构这一特性,采用外加激励的方法使其产生共振,从而使得储存环中部分束团中的电子丢失,形成储存环的部分填充和非均匀填充。还扼要介绍了用高频剔除系统在储存环上实现不同填充方式时的束流积累结果。     

物光的偏振性对全息记录质量的影响

通过对菲涅耳三维漫反射全息记录光路中物光与参考光偏振状态的实验检测，发现线偏振的激光被不同表面材料的物体散射和漫反射后变成“部分偏振光”，几乎所有目标物都有显著的消偏振现象，全息干板上实际记录的是线偏振的参考光与“部分偏振”的物光形成的相干度较低的干涉条纹。物光偏振度的大幅度下降影响干涉条纹的衬比度，并增加全息图的噪声。给出实验方案和检测光路，采用在参考光路中插入1/4波片的方法，可充分利用非偏振物光各个振动方向的光能，提高条纹的衬比度。     

高功率激光系统随机相位屏的特性研究

 高功率激光系统中随机相位屏的统计模型出发，分析了其相位噪声及梯度的一阶和二阶统计性质。研究了完全相干光与部分相干光通过随机相位屏后的传输性质，推导得出部分相干光在经过随机相位屏后，其交叉谱密度的期望等于随机相位屏透过率函数的期望与入射光交叉谱密度的乘积。对该模型下的远场分布进行了数值模拟。结果显示，能量对称分布的完全相干光通过相位干屏后,只有通过随机相位屏透过率函数期望的远场分布是对称的；部分相干光在传输通过随机相位屏后，其谢尔模光束性质不会改变，但光强分布不再具有对称性，且强度明显降低。     

二层信用策略下部分延期付款的库存模型

当前二层信用期相关文献考虑的都是零售商提供给其顾客相同的信用期,但现实中零售商往往会根据物品的种类不同提供给顾客不同的信用期.为研究此问题,建立了优化供货周期使零售商平均相关成本最小的库存模型,证明了最优供货周期的存在性,并给出实例加以说明.