On the Analytic Part of Univalent Harmonic Mappings

In this article we obtain two sharp results concerning the analytic part of harmonic mappings \(f=h+\overline{g}\) from the class \(\mathcal {S}^0_H(\mathcal {S})\) which was recently introduced by Ponnusamy and Sairam Kaliraj. For example, we get the sharp estimate for \(|\arg h'(z)|\) in the case when \(|z| \le 1/\sqrt{2}\) and obtain the sharp radius of convexity for h. Our approach is applicable to a more general situation. Finally, we determine simple condition on the analytic part of univalent harmonic mappings so that it is in \(H_p\) spaces for \(0<p<1/3\).     

An in situ Al K-edge XAS investigation of the local environment of H+- and Cu+-exchanged USY and ZSM-5 zeolites

Aluminum coordination in the framework of USY and ZSM-5 zeolites containing charge-compensating cations (NH4+, H+, or Cu+) was investigated by Al K-edge EXAFS and XANES. This work was performed using a newly developed in-situ cell designed especially for acquiring soft X-ray absorption data. Both tetrahedrally and octahedrally coordinated Al were observed for hydrated H-USY and H-ZSM-5, in good agreement with 27Al NMR analyses. Upon dehydration, water desorbed from the zeolite, and octahedrally coordinated Al was converted progressively to tetrahedrally coordinated Al. These observations confirmed the hypothesis that the interaction of water with Br?nsted acid protons can lead to octahedral coordination of Al without loss of Al from the zeolite lattice. When H+ is replaced with NH4+ or Cu+, charge compensating species that absorb less water, less octahedrally coordinated Al was observed. Analysis of Al K-edge EXAFS data indicates that the Al-O bond distance for tetrahedrally coordinated Al in dehydrated USY and ZSM-5 is 1.67 angstroms. Simulation of k3chi(k) for Cu+ exchanged ZSM-5 leads to an estimated distance between Cu+ and framework Al atoms of 2.79 angstroms.     

The Apollonian inner metric and uniform domains

In this paper we characterize uniform domains in terms of the Apollonian inner metric and the j‐metric, thus providing solutions to two open problems given in [16]. We also discuss the relationships among uniform, A‐uniform, Apollonian quasiconvex and quasi‐isotropic domains (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of entire functions of exponential type defined by convolution

Based on the Borel transformation and the Hadamard multiplication theorem on singularities on the convolution of holomorphic functions, results on the growth of entire functions defined by convolution of an entire function of exponential type with a function holomorphic at the origin are obtained. Received: 29 August 2005     

Recent developments in the metal catalysed cross-coupling reactions for the synthesis of the enone system of chalcones

For the last two decades, chalcones and their derivatives have attracted special interest among researchers due to their pharmaceutical properties. Numerous research works have been still going on to improve the methodologies of chalcone synthesis. Chalcone has displayed a remarkable curative efficiency to cure numerous diseases and it continues to show promise for new drug investigations. This review highlights the metal catalysed cross-coupling reactions for the synthesis of chalcone and its derivatives from 2009 to 2020.     

On the Fekete-Szegö problem for concave univalent functions

We consider the Fekete-Szegö problem with real parameter λ for the class Co(α) of concave univalent functions.     

Growth and characterization of metal ions doped l-serine NLO single crystals for optoelectronic applications

Single crystals of pure and metal ions (K⁺, Na⁺ and Li⁺) doped l-serine have been grown by slow evaporation solution growth technique (SEST). Energy dispersive X-ray analysis (EDAX) and inductively coupled plasma optical emission spectroscopy (ICP-OES) prove the incorporation of metal ions into the doped crystals. The lattice parameters have been obtained from single crystal X-ray diffraction (XRD) studies. The presence of functional groups is identified by Fourier transform infrared (FTIR) and FT-RAMAN analyses. The thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) reveal that the thermal stability of lithium doped l-serine crystal is enhanced. The mechanical properties have been studied by vicker's microhardness test. UV–vis-NIR spectroscopy shows that the percentage of transmission is increased in lithium doped l-serine crystals. Potassium and lithium ions doped l-serine crystals have enhanced second harmonic generation (SHG) efficiency indicating that these crystals are potential candidates for non linear optical (NLO) applications.