On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

Octanuclear and nonanuclear supramolecular copper(II) complexes with linear "tritopic" ligands: structural and magnetic studies

The structures and magnetic properties of self-assembled copper(II) clusters and grids with the "tritopic" ligands 2poap (a), Cl2poap (b), m2poap (c), Cl2pomp (d), and 2pomp (e) are described [ligands derived by reaction of 4-R-2,6-pyridinedicarboxylic hydrazide (R = H, Cl, MeO) with 2-pyridinemethylimidate (a-c, respectively) or 2-acetylpyridine (d, R = Cl; e, R = H)]. Cl2poap and Cl2pomp self-assemble with Cu(NO(3))(2) to form octanuclear "pinwheel" cluster complexes [Cu(8)(Cl2poap-2H)(4)(NO(3))(8)].20H(2)O (1) and [Cu(8)(Cl2pomp-2H)(4)(NO(3))(8)].15H(2)O (2), built on a square [2 x 2] grid with four pendant copper arms, using "mild" reaction conditions. Similar reactions of Cl2pomp and 2pomp with Cu(ClO(4))(2) produce pinwheel clusters [Cu(8)(Cl2pomp-2H)(4)(H(2)O)(8)](ClO(4))(8).7H(2)O (3) and [Cu(8)(2pomp-2H)(4)(H(2)O)(8)](ClO(4))(8) (4), respectively. Heating a solution of 1 in MeOH/H(2)O produces a [3 x 3] nonanuclear square grid complex, [Cu(9)(Cl2poap-H)(3)(Cl2poap-2H)(3)](NO(3))(9).18H(2)O (5), which is also produced by direct reaction of the ligand and metal salt under similar conditions. Reaction of m2poap with Cu(NO(3))(2) produces only the [3 x 3] grid [Cu(9)(m2poap-H)(2)(m2poap-2H)(4)](NO(3))(8).17H(2)O (6) under similar conditions. Mixing the tritopic ligand 2poap with pyridine-2,6-dicarboxylic acid (picd) in the presence of Cu(NO(3))(2) produces a remarkable mixed ligand, nonanuclear grid complex [Cu(9)(2poap-H)(4)(picd-H)(3)(picd-2H)](NO(3))(9).9H(2)O (7), in which aromatic pi-stacking interactions are important in stabilizing the structure. Complexes 1-3 and 5-7 involve single oxygen atom (alkoxide) bridging connections between adjacent copper centers, while complex 4 has an unprecedented mixed micro-(N-N) and micro-O metal ion connectivity. Compound 1 (C(76)H(92)N(44)Cu(8)O(50)Cl(4)) crystallizes in the tetragonal system, space group I, with a = 21.645(1) A, c = 12.950(1) A, and Z = 2. Compound 2 (C(84)H(88)N(36)O(44)Cl(4)Cu(8)) crystallizes in the tetragonal system, space group I, with a = 21.2562(8) A, c = 12.7583(9) A, and Z = 2. Compound 4 (C(84)H(120)N(28)O(66)Cl(8)Cu(8)) crystallizes in the tetragonal system, space group I4(1)/a, with a = 20.7790(4) A, c = 32.561(1) A, and Z = 4. Compound 7(C(104)H(104)N(46)O(56)Cu(9)) crystallizes in the triclinic system, space group P, with a = 15.473(1) A, b = 19.869(2) A, c = 23.083(2) A, alpha = 88.890(2) degrees, beta = 81.511(2) degrees, gamma = 68.607(1) degrees, and Z = 2. All complexes exhibit dominant intramolecular ferromagnetic exchange coupling, resulting from an orthogonal bridging arrangement within each polynuclear structure.     

Harnack’s inequality for a class of non-divergent equations in the Heisenberg group

We prove an invariant Harnack’s inequality for operators in non-divergence form structured on Heisenberg vector fields when the coe?cient matrix is uniformly positive definite, continuous, and symplectic. The method consists in constructing appropriate barriers to obtain pointwise-to-measure estimates for supersolutions in small balls, and then invoking the axiomatic approach developed by Di Fazio, Gutiérrez, and Lanconelli to obtain Harnack’s inequality.     

Oxotitanium(IV) complexes of some bis‐unsymmetric Schiff bases: Synthesis,structural elucidation and biomedical applications

A number of oxotitanium(IV) complexes of the type TiOL with bis‐unsymmetric dibasic tetradentate Schiff base (LH₂) containing ONNO donor atoms have been synthesized. Mono‐Schiff base (OPD‐HNP) was prepared by the condensation of 1:3 molar ratio of 2‐hydroxy‐1‐naphthaldehyde (HNP) with o‐phenylenediamine (OPD). Dibasic unsymmetric tetradentate diamine Schiff bases were prepared by the reaction of OPD‐HNP with 2‐hydroxyacetophenone, 2‐hydroxypropeophenone, benzoylacetone, acetylacetone and ethylacetoacetate. Further, titanylacetylacetonate was reacted with these ligands to obtain their metal complexes. On the basis of analytical and physiochemical data, the formation of complexes as TiOL was suggested having square pyramidal geometry. Quantum mechanical approach also confirmed this geometry. The assessment of the synthesized ligands and their complexes showed that some behave as good inhibitors of mycelial growth against selected phytopathogic fungi but weak inhibitors against some selected bacteria. A few of them also showed antioxidant properties.     

Electrochemical behavior of aluminum and some of its alloys in chloroaluminate ionic liquids: electrolytic extraction and electrorefining

The electrochemical behaviors of pure Al, Al–6%Si, Al–3%Cu, and Al–3.7%Cu–0.9%Mg–0.8%Pb–0.6%Fe alloys were investigated in the chloroaluminate ionic liquids 1-butyl-3-methylimidazolium chloride [BMIm]Cl/AlCl₃ (40/60 mol%) and 1-ethyl-3-methylimidazolium chloride [EMIm]Cl/AlCl₃ (40/60 mol%). Electrolytic extraction of copper from Al–Cu alloys in the employed ionic liquids was explored. The alloys were anodically dissolved in the ionic liquids and then pure copper was recovered under potentiostatic conditions. Due to the large difference between the deposition potentials of Cu and Al, pure Cu can be obtained without Al contamination. Electrorefining of Al–3%Cu and Al–6%Si alloys was also investigated in [BMIm]Cl/AlCl₃ (40/60 mol%) at room temperature. High purity aluminum deposits were obtained with significantly low energy consumption of about 2 kWh/kg of Al.     

Ionic Liquids Supported on Metal‐Organic Frameworks: Remarkable Adsorbents for Adsorptive Desulfurization

Acidic ionic‐liquids (IL) supported on metal–organic frameworks (MOFs) have been shown to be beneficial for adsorptive desulfurization. A remarkable improvement in the adsorption capacity (ca. 71%) was observed in for ILs supported on MIL‐101 compared with virgin MIL‐101. The improved adsorptive performance might be explained by the acid–base interactions between the acidic ionic liquid and basic benzothiophene (BT). Moreover, from this study, it can be suggested that porous MOFs, supported with ionic liquids, may introduce a new class of highly porous adsorbents for the efficient adsorption of various compounds.     

Self-stabilized passive, harmonically mode-locked stretched-pulse erbium fiber ring laser

We have studied a passive, harmonically mode-locked stretched-pulse erbium fiber ring laser with net positive dispersion that is self-stabilized by gain depletion and electrostriction. Periodic pulses with supermode suppression of >75 dB and picosecond jitter are achieved. The pulses are compressible to 125 fs by external chirp compensation. The repetition rate is 220 MHz, and the average power is as high as 80 mW.     

Unexpected decomposition of the bis (trifluoromethylsulfonyl) amide anion during electrochemical copper oxidation in an ionic liquid

In this letter we report on the decomposition of the bis (trifluoromethylsulfonyl) amide (TFSA) anion under quite mild electrochemical conditions. The results show clearly that the TFSA anion can easily be decomposed during anodic oxidation of copper in the ionic liquid 1-butyl-1-methylpyrrolidinium bis (trifluoromethylsulfonyl) amide [BMP] TFSA at 70 °C leading to the formation of CuF₂. At room temperature, however, no significant decomposition was obtained. Therefore, one has to be very careful in applying ionic liquids based on TFSA anions under anodic conditions at elevated temperature as the TFSA anion might decompose, depending on the anode material.     

Fabrication of gold nanoparticles in water by laser ablation technique and their characterization

A colloidal solution of gold nanoparticles in deionized nanopure water was produced by laser ablation technique without the use of any chemical/surfactant. Spectral characterization and morphological studies of these nanoparticles were carried out by UV-Vis Spectroscopy and Scanning Electron Microscopy, respectively. A number of variables of the ablating laser pulse have been used to control the size of the fabricated nanoparticles. Excellent correlation between ablating laser pulse parameter and optical and morphological parameters of the gold colloids were obtained. The peak of the extinction spectra shows a monotonic blue shift for laser fluence of 410 J/cm² and above. Below this the extinction peak remains fairly constant in wavelength. Blue shifts of the extinction spectra were also observed with increasing re-ablation time of previously ablated gold colloids. Possible explanations of all these observations are discussed.     

Liquid-phase dehydration of sorbitol under microwave irradiation in the presence of acidic resin catalysts

Liquid-phase dehydration of sorbitol has been investigated in wide reaction conditions especially under microwave irradiation in the presence of acidic resin catalysts. From the selectivity for sorbitan and isosorbide, it can be understood that the dehydration is a consecutive reaction (sorbitol to sorbitan, and finally to isosorbide) and that the sorbitan is an intermediate of the dehydration. By using microwave irradiation, the dehydration can be accelerated by around 20?C34 times compared with the rate by conventional electric heating at the same temperature, or the reaction temperature can be decreased by around 40 °C for the comparable conversion in a similar reaction time. However, the microwaves do not have noticeable effects on the selectivity for isosorbide or sorbitan. The accelerated dehydration under microwaves is mainly due to decreased activation energy.