Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations

We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a time-dependent inner product. We apply our general results to obtain possible Hilbert space structures on the solution space of the equation of motion for a classical simple harmonic oscillator, a free Klein-Gordon equation, and the Wheeler-DeWitt equation for the FRW-massive-real-scalar-field models.Comment: 29 pages, slightly revised version, accepted for publication in Class. Quantum Gra

Ag(I) and Zn(II) isonicotinate complexes: Design, characterization, antimicrobial effect and CT–DNA binding studies

<div><p></p><p>Trinuclear Ag(I) (<b>1</b>) and dinuclear and mononuclear Zn(II) isonicotinate (<b>2</b> and <b>3</b>) complexes were prepared and characterized by X–ray crystallography, elemental analysis, IR spectroscopy and thermal analysis. Single crystal analysis of the Ag(I) complex reveals two different monodentate carboxylate coordination modes, protonated and deprotonated, respectively. IR spectra showed correlations between isonicotinate coordination modes and <i>Δ</i>(<i>ν</i>_as–<i>ν</i>_s)_IR values. In addition, the hydrogen bonds significantly influence a position of carboxylate absorption bands. Moreover, IC₅₀ and MIC data for bacteria, yeasts and filamentous fungi were determined and the binding of Ag(I) and Zn(II) complexes to calf thymus DNA was investigated using electronic absorption, fluorescence and CD measurements. Biological tests showed that the Ag(I) complex is more active than commercially used Ag(I) sulfadiazine against <i>E. Coli</i>. The fluorescence spectral results indicate that the complexes can bind to DNA through an intercalative mode. The Stern–Volmer quenching constants for investigated complexes obtained from the linear quenching plot are in the range of 1.67 × 10⁴ to 3.42 × 10⁴ M^–1.</p></div

Mononuclear Fe(III) Schiff Base Complex with Trans-FeO₄N₂ Chromophore of <i>o</i>-Aminophenol Origin: Synthesis, Characterisation, Crystal Structure, and Spin State Investigation

A new iron(III) complex (Et3NH)2[Fe(L)2](ClO4)·MeOH (1) where H2L = 2-{(E)-[2-hydroxyphenyl)imino]methyl}phenol has been synthesised and characterised by single crystal XRD, elemental analysis and DC magnetic susceptibility measurements. The dianionic ligands L2− coordinate in a tridentate fashion with the Fe(III) through their deprotonated phenolic oxygens and azomethine nitrogen atoms, resulting in a trans-FeO4N2 chromophore. Variable-temperature magnetic measurements were performed between 300 and 5 K under an applied field of 0.1 T and show that 1 is in the high spin state (S = 5/2) over the whole measured temperature range. This is confirmed by Mössbauer spectroscopy at 77 and 300 K