On perturbation bounds for orthogonal projections

In this paper, we present some new perturbation bounds for the orthogonal projections onto the column and row spaces of a matrix, which improve some existing results. Numerical examples are presented to illustrate our results.     

A 3D Luminescent Metal‐organic Framework Constructed from Cu4I4 Cubane Clusters and Triangular Imidazole Ligand

Abstract . The solvothermal reaction between cuprous iodide and the rigid triangular imidazole ligand in mixed N,N′‐dimethylacetamide (DMA)‐acetonitrile solvent leads to the isolation of the 3D metal‐organic framework [(Cu₄I₄)₃(TIPA)₄] · 7DMA ( 1 ) [TIPA = tri(4‐imidazolylphenyl) amine], which was characterized by elemental analysis, IR spectroscopy, powder X‐ray diffraction, and single‐crystal X‐ray diffraction. Topologically, the structure of 1 is an unprecedented 3,3,4,4‐connected net with a point symbol of {4.8.10}₂{4.8²}₂{4².8².10²}₂{8⁴.12²}. Compound 1 exhibits orange‐red photoluminescence with an emission maximum at 622 nm at room temperature.     

An efficient and facile synthesis of novel substituted pyrimidine derivatives: 4-amino-5-carbonitrile-2-nitroaminopyrimidine

One-pot, multicomponent reaction for the synthesis of novel substituted pyrimidine derivatives: 4-amino-5-carbonitrile-2-nitroaminopyrimidine from aromatic aldehydes, 1-nitroguanidine, and malononitrile under ethanol is described. Because of containing many active functional groups, such as amino, cyan and nitro, these products are important intermediate of organic synthesis. The advantages of this procedure include the short reaction time, mild reaction conditions, and excellent yields.     

Two 2D uranyl coordination complexes showing effective photocatalytic degradation of Rhodamine B and mechanism study

Two new hydrostable two-dimensional(2 D) uranyl coordination complexes [(UO_2)_5(μ_3-O)_2(nbca)_2].7 H_2O(1) and [(UO_2)_3(nbca)_2(H_2O)_3]·2 H_2O(2)(H_3 nbca=5-nitro-1,2,3-benzenetricarboxylic acid) were hydrothermal synthesized.Single-crystal structural refinements reveal that both of the two complexes were formed by the packing of 2D uranyl coordination sheets via the hydrogen bonds.The nbca ligand coordinating to the uranyl polyhedron centers constructed the 2D sheets.There are UO_8 hexagonal bipyramids and UO_7 pentagonal bipyramids in 1 while only U07 pentagonal bipyramids in 2.Photocatalytic degradation of rhodamine B(RhB) in aqueous solution was studied.Complex 2 possesses better performance than 1 with 96.2 % of the RhB was degraded in only 60 min.Mechanism studies reveal that the dissolved oxygens are essential to the RhB degradation.The photocurrent density of 2 is more stable than that of 1,which indicating the stronger ability to separate photoexcited electrons and hole pairs of 2.