一类Hermitian鞍点矩阵的特征值估计

本文研究了一类大型稀疏Hermitian鞍点线性系统Az=(B E E* 0)(x y)=(f g)=b系数矩阵的特征值,其中B∈C~(p×p)是Hermitian正定阵矩阵,E∈C~(p×q)是列降秩.本文分别给出了该系数矩阵正特征值与负特征值界的一个估计式,同时通过数值算例验证本文所给出的特征值界的估计是合理且有效的.     

Willmore submanifolds in the unit sphere via isoparametric functions

In this paper, we show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore, hence all focal submanifolds of isoparametric hypersurfaces in the sphere are Willmore.     

Two Coordination Polymers Constructed from 5‐(4‐Pyridyl)‐1H‐tetrazole Ligands with Different Organic Carboxylates: Structure and Luminescence Properties

Two coordination polymers (CPs), namely, [Cu(Hptz)₂(Hhba)₂]_n ( 1 ) [Hptz = 5‐(4‐pyridyl)‐1H‐tetrazole, H₂hba = 2‐hydroxybenzoic acid] and [Zn₃(ptz)₂(hpa)₂]_n ( 2 ) (H2hpa = 2‐hydroxy‐2‐phenylacetic acid), were synthesized by solvothermal reactions. Both complexes were characterized by elemental analysis, infrared spectroscopy, powder X‐ray diffraction, thermogravimetric analysis, and single‐crystal X‐ray diffraction analysis. Compound 1 exhibits a 2D (4,4) network, where each layer connects to four adjacent layers to construct a 3D supramolecular framework. Compound 2 has a 3D framework structure composed of 1D SUBs, which are formed by both carboxyl and tetrazole groups. The complexes represent two rare examples of CPs constructed from Hptz and organic carboxyl acid ligands. Complex 2 exhibits intense, red‐shifted emissions in the visible region at room temperature.     

Three New Coordination Compounds with Neodymium Based on Tetrazole Containing Carboxylic Acid Ligands

Reactions of three tetrazole containing carboxylic acid ligands, namely, Hpztza, Htzpya, and Hpytza [Hpztza = 5‐(2‐pyrazinyl)tetrazole‐2‐acetic acid, Htzpya = 3‐(5‐tetrazolyl)pyridine‐1‐acetic acid, Hpytza = 5‐(3‐pyridyl)tetrazole‐2‐acetic acid] with NdCl₃ · 6H₂O under hydrothermal conditions, afforded the complexes [Nd(pztza)₂(H₂O)₆] · pztza · 3H₂O ( 1 ), [Nd₂(tzpya)₂(H₂O)₁₂]Cl₄ · 2H₂O ( 2 ), and [Nd(pytza)₂Cl(H₂O)₂] ( 3 ). The compounds were structurally characterized by elemental analysis, IR spectroscopy and single‐crystal X‐ray diffraction. X‐ray diffraction analyses revealed that compound 1 displays a mononuclear structure, 2 shows a dinuclear structure, and 3 features a 1D polymeric chain structure via pytza as linker. Furthermore, the luminescent properties investigated at room temperature in the solid state show that compound 2 has an obvious decrease in its luminescence, when compared to the ligand.     

Easily Accessible Auxiliary for Palladium‐Catalyzed Intramolecular Amination of C(sp2)?H and C(sp3)?H Bonds at δ‐ and ε‐Positions

An easily synthesized and accessible N,O‐bidentate auxiliary has been developed for selective C H activation under palladium catalysis. The novel auxiliary showed its first powerful application in C H functionalization of remote positions. Both C(sp²) H and C(sp³) H bonds at δ‐ and ε‐positions were effectively activated, thus giving tetrahydroquinolines, benzomorpholines, pyrrolidines, and indolines in moderate to excellent yields by palladium‐catalyzed intramolecular C H amination.     

A rapid and effective method for silver staining of PCR products separated in polyacrylamide gels

With the development of molecular quantitative genetics, particularly, genetic linkage map construction, quantitative trait loci mapping or genes fine mapping and association analysis etc., more and more PCR products separated in polyacrylamide gels need to be silver‐stained. However, conventional silver‐staining procedures are complicated and time‐consuming as they require a lot of preparation and handling of several solutions prior to use. In this study, a simple and rapid protocol for silver staining of PCR products was developed. The number of steps was reduced compared to conventional protocols, thus achieving detection of PCR products in 7 min, saving time and resources. Fixation and staining solution and developing solution in present staining procedure allowed a reutilization for 12 and 8 times, respectively, reducing the cost greatly. Meanwhile, the sensitivity was significantly improved with the improved method and the minimum of 0.097 ng/μL of DNA amount can be detected in denaturing polyacrylamide gel. The protocol developed in this study will facilitate the development of molecular quantitative genetics.     

Organocatalytic asymmetric one-pot sequential reaction: synthesis of highly substituted spirocyclohexanepyrazolones with six contiguous stereogenic carbons

An atom-economical synthesis of chiral polyfunctionalized spiropyrazolone derivatives based on the development of a new organocatalytic enantioselective one-pot sequential Michael/Michael/Aldol reaction of 1,3-dicarbonyl compounds with unsaturated pyrazolones and α,β-unsaturated aldehydes has been developed. The notable features of this one-pot sequential process include the generation of up to six consecutive stereogenic carbon centers including one quaternary stereocenter and five tertiary stereocenters with high enantioselectivities (up to 95% ee) and excellent diastereoselectivities (>99:1 d.r.).     

Ultraviolet light absorber with low surface energy: synthesis and characterization

Novel fluorine-containing ultraviolet absorbers (FBPs) with low surface energy were successfully synthesized based on 2,4-dihydroxy benzophenone (BP-1), and their structures were characterized by ¹H NMR, ¹³C NMR, FTIR, and HRMS. UV absorption of FBPs was studied in 10⁻⁴ M dichloromethane (CH₂Cl₂), which demonstrated the superior UV absorption capability of FBPs (ca. ?=1.7×10⁴ to 2.2×10⁴ at λ_max) over the matrix (?=1.7×10⁴ at λ_max). Quantum chemistry calculation was performed to investigate the stable structure and UV electronic absorption bands of FBPs. The surface chemistry information of high-chlorinated polyethylene (HCPE) coating films embedded with ultraviolet absorbers (UVAs) was given by X-ray photoelectron spectroscopy (XPS) and contact angle measurement. The results show that the surface enrichment capability of FBPs is remarkably better than traditional UVAs (including BP-1, BP-3, BP-12) because of the low surface energy properties of FBPs.