Some singular value and unitarily invariant norm inequalities for Hilbert space operators

In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results.     

Fabrication and characterization of highly crystalline mordenite membranes on α-alumina disks via a seeded in situ template-free hydrothermal treatment

A template-free seeded short-time in situ hydrothermal treatment was carried out in a brass autoclave to synthesize crystalline mordenite (MOR) membranes on alumina-silicate disk supports with micro-scale pores. According to XRD analysis, MOR was the only zeolitic material present in the membrane layers on the supports. SEM examination of the membranes showed three different layers of the membrane thickness: (i) support sub-layer, (ii) mix penetrated mid-layer, the MOR crystals filling the pores among the support (about 4–5 μm), and (iii) MOR top-layer (about 4–5 μm). The crystalline bonds between MOR crystals of the membrane top-layer and the crystals of the support were clearly observed within the mid-layer. The continuous top-layer of zeolitic membrane was formed by many large and well-shaped crystals. The seeding treatment significantly enhanced the formation of MOR crystals onto the surface of the supports. EDAX analysis showed a Si/Al ratio of 6.8 for the MOR layer of the membrane. Due to their hydrophilic natures, the polycrystalline MOR membranes were found to be selective for continuous dehydration of different EtOH–water mixtures through an adsorption–diffusion–desorption mechanism. Both total permeation flux and separation factor of the membrane were found to increase by increasing temperature and water concentration of feed. The continuity and high crystallinity of the membrane top-layer led to the fairly high dehydration of EtOH. It was found that there was no pinhole within the layer and the morphology of the membrane was almost defect-free.     

Highly edge-connected factors using given lists on degrees

Let G be a 2k-edge-connected graph with and let for every . A spanning subgraph F of G is called an L-factor, if for every . In this article, we show that if for every , then G has a k-edge-connected L-factor. We also show that if and for every , then G has a k-edge-connected L-factor.     

Strong red emissions induced by Pt–Pt interactions in binuclear cycloplatinated(II) complexes containing bridging diphosphines

A series of dinuclear cycloplatinated(II) complexes with general closed formula of [Pt₂Me₂(C^N)₂(μ‐P^P)] (C^N = 2‐vinylpyridine (Vpy), 2,2′‐bipyridine N‐oxide (O‐bpy), 2‐(2,4‐difluorophenyl)pyridine (dfppy); P^P = 1,1‐bis(diphenylphosphino)methane (dppm), N,N‐bis(diphenylphosphino)amine (dppa)) are reported. The complexes were characterized by means of NMR spectroscopy. Due to the presence of dppm and dppa with short backbones as bridging ligands, two platinum centres are located in front of each other in these complexes so a Pt…Pt interaction is established. Because of this Pt…Pt interaction, the complexes have bright orange colour under ambient light and are able to strongly emit red light under UV light exposure. These strong red emissions originate from a ³MMLCT (metal–metal‐to‐ligand charge transfer) electronic transition. In most of these complexes, the emissions have unstructured bell‐shaped bands, confirming the presence of large amount of ³MMLCT character in the emissive state. Only the complexes bearing dfppy and dppa ligands reveal dual luminescence: a high‐energy structured emission originating from ³ILCT/³MLCT (intra‐ligand charge transfer/metal‐to‐ligand charge transfer) and an unstructured low‐energy band associated with ³MMLCT. In order to describe the nature of the electronic transitions, density functional theory calculations were performed for all the complexes.     

Computational mechanistic investigation of the gas phase C2H4 + CO reaction on the singlet and triplet potential energy surfaces

Reaction pathways of ethylene and carbon monoxide on the singlet and triplet potential energy surfaces (PESs) have been calculated at B3LYP/6-311++G (3df, 3dp), G3B3 and CCSD(T)//B3LYP levels. Reaction mechanisms have been investigated by analysis of various structures. Suggested reaction mechanisms reveal that ³P3(CH₂CHCHO) and ³P4(CH₃CCHO) are thermodynamically stable adducts with the negative value in Gibbs free energies on the triplet PES. In addition, results show that one intersystem crossing exists between triplet and singlet PESs, which are obtained by scanning of the C–C bond length in ¹IN3 and ³IN7 species.