两类四角系统的匹配数与点独立集数

给出了两类四角系统的完美匹配数、匹配数和点独立集数的计算公式     

Sign or root of unity ambiguities of certain Gauss sums

Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite field with q elements. Recently, the problem of explicit evaluation of Gauss sums in the small index case has been studied in several papers. In the process of the evaluation, it is realized that a sign (or a root of unity) ambiguity unavoidably occurs. These papers determined the ambiguities by the congruences modulo L, where L is certain divisor of the order of Gauss sum. However, such method is unavailable in some situations. This paper presents a new method to determine the sign (root of unity) ambiguities of Gauss sums in the index 2 case and index 4 case, which is not only suitable for all the situations with q being odd, but also comparatively more efficient and uniform than the previous method.     

四氧化三铁纳米团簇的表面修饰及生物毒性研究

采用微波辅助溶剂热法制备了四氧化三铁(Fe3O4)纳米团簇.为了改善团簇的稳定性,用改进的St(o)ber法,在Fe3O4团簇的表面包覆—层氧化硅(SiO2),成功制备出核-壳结构的Fe3O4@SiO2粒子.用透射电镜(TEM)、X射线衍射仪(XRD)、纳米粒度仪、Zeta电位、振动样品磁强计(VSM)、MTT比色法等测试手段,对样品的形貌、结构、粒径分布、胶体稳定性、磁学性质及生物毒性进行了研究,结果表明:所制备的Fe3O4纳米团簇平均尺寸约为60nm,尺寸均匀,在室温下表现出超顺磁性.包覆后的核-壳结构Fe3O4@SiO2粒子平均尺寸约为150 rn,具有良好的水分散性和胶体稳定性,包覆前后的样品均具有低的生物毒性.     

Stepwise Evolution of Molecular Nanoaggregates Inside the Pores of a Highly Flexible Metal–Organic Framework

The crystalline sponge method (CSM) is primarily used for structural determination by single‐crystal X‐ray diffraction of a single analyte encapsulated inside a porous MOF. As the host–guest systems often show severe disorder, reliable crystallographic determination is demanding; thus the dynamics of the guest entering and the formation of nanoconfined molecular aggregates has not been in the spotlight. Now, the concept is investigated of the CSM for monitoring the structural evolution of nanoconfined supramolecular aggregates of eugenol guests with displacement of DMF inside the cavities of the flexible MOF, PUM168. The interpretation of the electron density provides a series of unique detailed snapshots depicting the supramolecular guest aggregation, thus showing the tight interplay between the host flexible skeleton and the molecular guests through the DMF‐to‐eugenol exchange process.     

Mechanical Control of the Kinetic Propylene/Propane Separation by Zeolitic Imidazolate Framework‐8

One intriguing feature of many porous MOFs is their stimulus‐induced flexibility, which makes them unique compared to standard adsorbents. Here we propose an innovative concept to achieve an efficient kinetic separation of species with similar properties by the mechanical fine‐tuning of the pore architecture of the flexible zeolitic imidazolate framework ZIF‐8. This unprecedented approach was applied to one of the most challenging societally relevant separations: the separation of propylene and propane, which is of vital importance in the petrochemical industry. It was demonstrated that the application of an external pressure creates a gradual enhancement in the propylene/propane diffusion selectivity to more than one order of magnitude at 1 GPa pressure. A detailed analysis of the molecular simulations was further able to unravel the origin of this unusual behavior at the atomistic level.