Rank equalities related to outer inverses of matrices and applications

A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin inverses and weighted Moore-Penrose inverses of matrices.     

具有三个公共值的亚纯函数(Ⅱ)

本文研究了具有三个公共值的亚纯函数的唯一性问题，改进了Ueda，H．,叶寿桢和仪洪勋的有关定理，并且纠正了Gross和Yang的一个结果．     

Z型复合催化剂g-C3N4/Vo-ZnO光催化活性的研究

随着科学技术的不断进步和经济的快速发展,人类对自然资源的需求量越来越大,在开发利用自然资源的同时,大量的有机污染物也随之进入自然环境.这些物质不仅污染环境、破坏生态,更对人类的生活和健康带来了巨大的威胁.研究证实,半导体光催化剂在光照条件下可以破坏有机污染物的分子结构,最终将其氧化降解成CO2、H2O或其它不会对环境产生二次污染的小分子,从而净化水质.近年来,有关光催化降解有机污染物的报道日益增多. ZnO作为一种广泛研究的光催化降解材料,因其无毒、低成本和高效等特点而具有一定的应用前景.但是ZnO较大的禁带宽度(3.24 eV)导致其只能吸收紫外光部分,而对可见光的吸收效率很小,极大地制约了其实际应用.除此之外, ZnO受光激发产生的电子-空穴分离效率较低、光催化过程中的光腐蚀严重也是制约其实际应用的重要因素.为了提高ZnO的光催化活性和稳定性,本文合成了用g-C3N4修饰的氧空位型ZnO(g-C3N4/Vo-ZnO)复合催化剂,在有效调控ZnO半导体能带结构的同时,通过负载一定量的g-C3N4以降低光生电子-空穴对的复合速率和反应过程中ZnO的光腐蚀,增强催化剂的光催化活性和稳定性.本文首先合成前驱体Zn(OH)F,然后焙烧三聚氰胺和Zn(OH)F的混合物得到g-C3N4/Vo-ZnO复合催化剂,并采用电子顺磁共振波谱(EPR)、紫外-可见光谱(UV-vis)、高分辨透射电镜(HRTEM)和傅里叶变换红外光谱(FT-IR)等表征了它们的结构及其性质. EPR结果表明,ZnO焙烧后具有一定浓度的氧空位,导致其禁带宽度由3.24 eV降至3.09 eV,因而提高了ZnO对可见光的吸收效率. UV-vis结果显示, Vo-ZnO复合g-C3N4后对可见光的吸收显著增强. HRTEM和FT-IR结果均表明, g-C3N4纳米片和Vo-ZnO颗粒之间通过共价键形成了强耦合,这对g-C3N4/Vo-ZnO复合催化剂中光生载流子的传送和光生电子-空穴对的有效分离起到重要作用.可见光催化降解甲基橙(MO)和腐殖酸(HA)的实验进一步证明, g-C3N4/Vo-ZnO复合材料具有较好的光催化活性,优于单一的g-C3N4或Vo-ZnO材料.同时还发现, g-C3N4的负载量对光催化活性有显著影响,当氮化碳的负载量为1 wt%时,所制材料具有最高的光催化活性：可见光照射60 min后,MO降解率可达到93%, HA降解率为80%.复合材料光催化活性的增强一方面是因为氧空位的形成减小了ZnO的禁带宽度,使得ZnO对可见光的吸收能力大大增强;另一方面, g-C3N4和Vo-ZnO的能带符合了Z型催化机理所需的有效能带匹配,使得光生电子-空穴对得到了有效的分离,从而提高了光催化活性.降解MO的循环实验表明, g-C3N4/Vo-ZnO催化剂具有很好的稳定性且不容易发生光腐蚀.与此同时,我们对比了用不同方法制备的g-C3N4/ZnO材料的催化性能.结果显示,本文制备的g-C3N4/Vo-ZnO复合材料具有更好的降解效率.总体而言,对于降解有机污染物, g-C3N4/Vo-ZnO可能是一个更为有效可行的催化体系.此外,本文也为设计与制备其他新型光催化剂提供了一条新的思路.     

An axially chiral, electron-deficient borane: synthesis, coordination chemistry, Lewis acidity, and reactivity

An axially chiral dihydroborepine with a binaphthyl backbone and a C(6)F(5) substituent at the boron atom was prepared by transmetalation from the corresponding tin precursor. This novel motif was structurally characterized by X-ray diffraction analysis as its THF and its PhCN Lewis acid/base complex. (1)H NMR measurements at variable temperatures of the former adduct revealed a remarkable dynamic behavior in solution. Several more Lewis pairs with oxygen, nitrogen, carbon, and phosphorus σ-donors were synthesized and analyzed by multinuclear NMR spectroscopy. The determination of the borane's Lewis acidity with the Gutmann-Beckett method attests its substantial Lewis acidity [85% with Et(3) PO as well as 74% with Ph(3) PO relative to the parent B(C(6)F(5))(3)]. Representative examples of Si-H bond activation (carbonyl reduction and dehydrogenative Si-O coupling) are included, demonstrating the chemical stability and the synthetic potential of the new chiral boron-based Lewis acid.     

New inequalities for subspace arrangements

For each positive integer n?4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n=4 we recover Ingleton's inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also presented.     

Random half-integral polytopes

We show that polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as Ω(logn/loglogn) with positive probability—even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank is due to certain obstructions. We determine the exact threshold number, when those cease to exist.     

A rank based particle swarm optimization algorithm with dynamic adaptation

The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. This paper presents a variation on the standard PSO algorithm called the rank based particle swarm optimizer, or PSO_rank, employing cooperative behavior of the particles to significantly improve the performance of the original algorithm. In this method, in order to efficiently control the local search and convergence to global optimum solution, the γ best particles are taken to contribute to the updating of the position of a candidate particle. The contribution of each particle is proportional to its strength. The strength is a function of three parameters: strivness, immediacy and number of contributed particles. All particles are sorted according to their fitness values, and only the γ best particles will be selected. The value of γ decreases linearly as the iteration increases. A time-varying inertia weight decreasing non-linearly is introduced to improve the performance. PSO_rank is tested on a commonly used set of optimization problems and is compared to other variants of the PSO algorithm presented in the literature. As a real application, PSO_rank is used for neural network training. The PSO_rank strategy outperformed all the methods considered in this investigation for most of the functions. Experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness.     

Factors that affect quantification of diode array data in comprehensive two-dimensional liquid chromatography using chemometric data analysis

There has been a tremendous increase in research on comprehensive two dimensional LC (LC×LC); however, to date, the central analytical issue, quantification, has received only minimal attention. It is vital to the further development of LC×LC that a greater understanding of the specific factors affecting peak quantification in LC×LC be attained. This work focuses on the following factors: data complexity, retention time shifting, dynamic range issues, chromatographic and spectral peak overlap and difficulties related to background signal removal. The above mentioned factors that affect peak quantification are investigated using fourteen replicate analyses of a urine sample, representing the effects of such factors when analyzing samples in complex matrices. We demonstrate that quantification of LC×LC data is improved following implementation of chemometric techniques that minimized the deleterious effects on quantification due to chromatographically overlapped peaks, retention time shifting and background signal interference. The chemometrically resolved data shows a 2.5-fold increase in precision of quantification over the quantification of the raw data. It is also demonstrated that the method quantifies sixteen peaks that were not visually evident prior to chemometric analysis. The purpose of this paper is to determine the impact of these issues on the effectiveness of LC×LC as a technique for the quantitative analysis of complex samples.