Kinetics of the thallic ion oxidation of olefins

The kinetics of oxidation of chalkone (phenyl styryl ketone) and cinnamaldehyde by T1 (III) acetate in aqueous acetic acid is of the first order in olefin and first order with respect to the oxidant. The parameters of the transition state theory have been computed. The rate of the reaction is strongly accelerated by increasing acid concentration. The reaction rate is also retarded by added sodium chloride and sodium acetate. The results have been interpreted in the light of the ionic mechanism considering T1 (OAc)₃ to be the active oxidant in aqueous acetic acid.     

Effect of sintering temperature on mechanical behaviour and bioactivity of sol-gel synthesized bioglass-ceramics using rice husk ash as a silica source

Bioglass-ceramics with SiO₂-Na₂O-CaO composition was prepared by sol-gel method using rice husk ash as a silica source. Material was sintered at different temperatures ranging from 900 to 1050 °C for 2 h. Phase-formation behaviour, densification characteristics, and mechanical strength of glass-ceramics were investigated. The material sintered at 1000 °C showed a good mechanical strength. Mechanical properties were correlated with microstructural features. Both in vitro bioactivity and biodegradability of sintered material were investigated by incubating in simulated body fluid and Tris buffer solution, respectively. Scanning electron microscopy, energy dispersive spectroscopy and X-ray diffraction were used to investigate the surface deposition during body fluid incubation. Both bioactivity and degradability decreased with increase in sintering temperature.     

Iteration of certain exponential-like meromorphic functions

The dynamics of functions \(f_\lambda (z)= \lambda \frac{\mathrm{e}^{z}}{z+1}\ \text{ for }\ z\in \mathbb {C}, \lambda >0\) is studied showing that there exists \(\lambda ^* > 0\) such that the Julia set of \(f_\lambda \) is disconnected for \(0< \lambda < \lambda ^*\) whereas it is the whole Riemann sphere for \(\lambda > \lambda ^*\). Further, for \(0< \lambda < \lambda ^*\), the Julia set is a disjoint union of two topologically and dynamically distinct completely invariant subsets, one of which is totally disconnected. The union of the escaping set and the backward orbit of \(\infty \) is shown to be disconnected for \(0<\lambda < \lambda ^*\) whereas it is connected for \(\lambda > \lambda ^*\). For complex \(\lambda \), it is proved that either all multiply connected Fatou components ultimately land on an attracting or parabolic domain containing the omitted value of the function or the Julia set is connected. In the latter case, the Fatou set can be empty or consists of Siegel disks. All these possibilities are shown to occur for suitable parameters. Meromorphic functions \(E_n(z) =\mathrm{e}^{z}(1+z+\frac{z^2}{2!}+\cdots +\frac{z^n}{n!})^{-1}\), which we call exponential-like, are studied as a generalization of \(f(z)=\frac{\mathrm{e}^{z}}{z+1}\) which is nothing but \(E_1(z)\). This name is justified by showing that \(E_n\) has an omitted value 0 and there are no other finite singular value. In fact, it is shown that there is only one singularity over 0 as well as over \(\infty \) and both are direct. Non-existence of Herman rings are proved for \(\lambda E_n \).     

The Hadamard determinant inequality — Extensions to operators on a Hilbert space

A generalization of classical determinant inequalities like Hadamard's inequality and Fischer's inequality is studied. For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a tracial state, we give a different proof. We also improve and generalize to the setting of finite von Neumann algebras, some ‘Fischer-type’ inequalities by Matic for determinants of perturbed positive-definite matrices. In the process, a conceptual framework is established for viewing these inequalities as manifestations of Jensen's inequality in conjunction with the theory of operator monotone and operator convex functions on $[0,\infty )$. We place emphasis on documenting necessary and sufficient conditions for equality to hold.     

Synthesis and Characterization of Some BODIPY‐based Substituted Salicylaldimine Schiff Bases

Salicylaldimine Schiff bases represent an important class of hetero‐polydentate ligands capable of forming mononuclear, binuclear, and polynuclear complexes with transition and non‐transition metals. In this report, we developed an easy synthesis of BODIPY‐based salicylaldimine Schiff bases and synthesized five new derivatives. These were characterized by elemental analysis, infrared, UV‐Vis, nuclear magnetic resonance spectroscopy, and X‐ray crystallography. Finally, one of the Schiff bases was reacted with BF₃·OEt₂ to synthesize corresponding bis‐BF₂ boron complex. The photophysical and electrochemical properties of the Schiff bases and the boron complex were evaluated and rationalized by theoretical calculations. The bis‐BF₂ boron complex showed excited state charge redistribution, thus could be useful as sensitizers for designing new dye‐sensitized solar cells.