Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities

This paper is intended mainly to present some generic uniqueness results for a class of vector Ky Fan inequalities. By employing the methods of set-valued analysis, we prove that, in the sense of Baire category, most of the problems in a complete metric space, consisting of vector Ky Fan inequalities satisfying some conditions, have unique solution and that every vector Ky Fan inequality, possessing more than one solution, can be approached arbitrarily by a sequence of vector Ky Fan inequalities each of which has a unique solution. Our discussions are under two different settings. One setting is related to vector Ky Fan inequalities defined on a compact set; the other is related to vector Ky Fan inequalities defined on a noncompact set. The corollaries of our results generalized the corresponding results in the literature.     

Efficient Synthesis of Aryl Hydroxylactams by Reducing Imides With Activated Zinc Dust

A series of aryl hydroxylactams (2a, 2b, 2d–2g, 2i–2k, 2m, and 2n) was synthesized by partially reducing aryl cyclic imides in moderate to excellent yields with activated zinc dust alone in acetic acid. This method was regiospecific and can be employed as an alternative for reported methods to partially reduce aryl cyclic imides.     

Excellent degradation performance of azo dye by metallic glass/titanium dioxide composite powders

The metallic glass/titanium dioxide powders (MG/TiO₂) with enhanced photocatalytic oxidation activity were synthesized, which exhibit a higher efficiency in decolorizing methylene blue solutions (MB). Compared with the pure TiO₂ and crystalline alloy/TiO₂ (CA/TiO₂) under the same circumstances, its degradation rate was 60 % and 30 % higher, respectively. Furthermore, compared with the CA/TiO₂, the MG/TiO₂ photocatalytic rate was three times faster when decolorizing MB. Considering the excellent intrinsic high-performance photocatalytic degradation under visible light irradiation, these novel powders were proven to have potential applications in water purification industry.     

Fabrication of ZIF‐8@SiO2 Core–Shell Microspheres as the Stationary Phase for High‐Performance Liquid Chromatography

The unique features of high porosity, shape selectivity, and multiple active sites make metal–organic frameworks (MOFs) promising as novel stationary phases for high‐performance liquid chromatography (HPLC). However, the wide particle size distribution and irregular shape of conventional MOFs lead to lower column efficiency of such MOF‐packed columns. Herein, the fabrication of monodisperse MOF@SiO₂ core–shell microspheres as the stationary phase for HPLC to overcome the above‐mentioned problems is reported. Zeolitic imidazolate framework 8 (ZIF‐8) was used as an example of MOFs due to its permanent porosity, uniform pore size, and exceptional chemical stability. Unique carboxyl‐modified silica spheres were used as the support to grow the ZIF‐8 shell. The fabricated monodisperse ZIF‐8@SiO₂ packed columns (5 cm long × 4.6 mm i.d.) show high column efficiency (23 000 plates m^?1 for bisphenol A) for the HPLC separation of endocrine‐disrupting chemicals (bisphenol A, β‐estradiol, and p‐(tert‐octyl)phenol) and pesticides (thiamethoxam, hexaflumuron, chlorantraniliprole, and pymetrozine) within 7 min with good relative standard deviations for 11 replicate separations of the analytes (0.01–0.39, 0.65–1.7, 0.70–1.3, and 0.17–0.91 % for retention time, peak area, peak height, and half peak width, respectively). The ZIF‐8@SiO₂ microspheres combine the advantages of the good column packing properties of the uniform monodisperse silica microspheres and the separation ability of the ZIF‐8 crystals.     

Highly Efficient C?H Oxidative Activation by a Porous MnIII–Porphyrin Metal–Organic Framework under Mild Conditions

A simple strategy to rationally immobilize metalloporphyrin sites into porous mixed‐metal–organic framework (M′MOF) materials by a metalloligand approach has been developed to mimic cytochrome P450 monooxygenases in a biological system. The synthesized porous M′MOF of [Zn₂(MnOH–TCPP)(DPNI)] ? 0.5 DMF ? EtOH ? 5.5 H₂O ( CZJ‐1 ; CZJ=Chemistry Department of Zhejiang University; TCPP=tetrakis(4‐carboxyphenyl)porphyrin); DPNI=N,N′‐di(4‐pyridyl)‐1,4,5,8‐naphthalenetetracarboxydiimide) has the type of doubly interpenetrated cubic α‐Po topology in which the basic Zn₂(COO)₄ paddle‐wheel clusters are bridged by metalloporphyrin to form two‐dimensional sheets that are further bridged by the organic pillar linker DPNI to form a three‐dimensional porous structure. The porosity of CZJ‐1 has been established by both crystallographic studies and gas‐sorption isotherms. CZJ‐1 exhibits significantly high catalytic oxidation of cyclohexane with conversion of 94 % to the mixture of cyclohexanone (K) and cyclohexanol (A) (so‐called K–A oil) at room temperature. We also provided solid experimental evidence to verify the catalytic reaction that occurred in the pores of the M′MOF catalyst.     

New Entangled Coordination Networks Based on Charge‐Tunable Keggin‐Type Polyoxometalates

Investigation into a hydrothermal reaction system with transition‐metal (TM) ions, 1,4‐bis(1,2,4‐triazol‐1‐lmethyl)benzene (BBTZ) and various charge‐tunable Keggin‐type polyoxometalates (POMs) led to the preparation of four new entangled coordination networks, [Co^II(HBBTZ)(BBTZ)_2.5][PMo₁₂O₄₀] ( 1 ), [Cu^I(BBTZ)]₅[BW₁₂O₄₀] ? H₂O ( 2 ), [Cu^II(BBTZ)]₃[AsW^V₃W^VI₉O₄₀] ? 10 H₂O ( 3 ), and [Cu^II₅(BBTZ)₇(H₂O)₆][P₂W₂₂Cu₂O₇₇(OH)₂] ? 6 H₂O ( 4 ). All compounds were characterized by using elemental analysis, IR spectroscopy, thermogravimetric analysis, powder X‐ray diffraction, and single‐crystal X‐ray diffraction. The mixed valence of W centers in compound 3 was further confirmed by using XPS spectroscopy and bond‐valence sum calculations. In the structural analysis, the entangled networks of 1 – 4 demonstrate zipper‐closing packing, 3D polythreading, 3D polycatenation, and 3D self‐penetration, respectively. Moreover, with the enhancement of POM negative charges and the use of different TM types, the number of nodes in the coordination networks of 1 – 4 increased and the basic metal–organic building motifs changed from a 1D zipper‐type chain (in 1 ) to a 2D pseudorotaxane layer (in 2 ) to a 3D diamond‐like framework (in 3 ) and finally to a 3D self‐penetrating framework (in 4 ). The photocatalytic properties of compounds 1 – 4 for the degradation of methylene blue under UV light were also investigated; all compounds showed good catalytic activity and the photocatalytic activity order of Keggin‐type species was initially found to be {XMo₁₂O₄₀}>{XW₁₂O₄₀}>{XW_12?nTM_nO₄₀}.