Differential subordinations concerning starlike functions

Denote byS ^* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a ₂z²+...+a_nzⁿ+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)^μ−1<h(z) implies f∈S^*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.     

R3Al-R'3SiOTf: novel and powerful reagent system for stereospecific alkylation-silylation reactions of epoxides

[reaction: see text] A novel and powerful reagent system R(3)Al-R'(3)SiOTf for the one-pot alkylation-silylation reaction of epoxides was discovered, and the reactions of various epoxides with the new reagent system have been demonstrated to occur stereospecifically giving rise to the corresponding alkylation-silylation products in excellent yields.     

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $\left|g^{\prime }\left(z\right)\right|\le \left|h^{\prime }\left(z\right)\right|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.     

Synthesis and Characterization of Some Novel Polymaleamides from N,N'-Biphenylbismaleimide and Aliphatic Diamines

New polymaleamides were synthesized by ring-opening polyaddition of N,N'-biphenylbismaleimide (BPBMI) to the aliphatic diamines 1,4-diaminobutane, 1,6-diaminohexane, 1,8-diaminooctane, piperazine, and 2,5-dimethylpiperazine in m-cresol. The appropriate model compound was also prepared. These polymers are completely soluble in concentrated sulfuric acid as well as in m-cresol and are found to be insoluble in common organic solvents. The identities of BPBMI, the model compound, and the polymaleamides were confirmed by elemental analysis and IR spectroscopy. These polymaleamides were found to have inherent viscosities in the range 0.10–0.14 dL/g. Their IR spectra reveal the retention of cis-geometry about the C=C bonds in BPBMI and in the polymaleamides. The thermal degradation behavior of the polymaleamides was studied by thermogravimetric analysis, differential scanning calorimetry, and mass spectrometry. Fragmentation schemes for the polymaleamides are proposed.     

Montmorillonite K-10 Clay Catalysed Glycosidation of 1-O-Acetyl-2,3-dideoxy-dl-pent-2-enopyrano-4-ulose

The O-glycosidation reaction of 1-O-acetyl-2,3-dideoxy-DL-pent-2-enopyran - 4 -ulose catalysed by the environmentally accepted and inexpensive industrial catalyst Montmorillonite K-10 clay with variety of alcohols in high yield is reported.     

Phytofabrication of silver nanoparticles from Limonia acidissima leaf extract and their antimicrobial,antioxidant and its anticancer prophecy

Green synthesis of nanoparticles by eco-friendly methods is a recent technique which draws the attention of researchers because of the reward over many conventional chemical methods. The present work focuses on aqueous Limonia acidissima leaf extract in synthesizing silver nanoparticles and its applications in a simple way. The silver nanoparticles formed were characterized by Infrared, Ultra violet-visible, X-ray diffraction, transmission electron microscopic, and atomic force microscopic techniques. The powder X-ray diffraction studies and transmission electron microscopic images reveal that the silver nanoparticles synthesized were approximately 10–40 nm and have a spherical structure. The nanoparticles were assayed for their antibacterial, antifungal and antioxidant activity. The antimicrobial studies for the silver nanoparticles show a maximum zone of inhibition of 8.8 mm for Bacillus subtilis bacteria and 8.5 mm for Candida albicans fungi at 3 and 1 μg/mL respectively. In-silico ADMET studies reveal that the toxicity, bioactivity, pharmacokinetics and drug-likeness properties of Limonia acidissima leaf extract is good. The molecular docking studies show that the microbial activity is high for Bacillus subtilis and Candida albicans showing the coincidence of the in silico and in vitro studies as expected. The free radical scavenging activity of nanoparticles is 80 for 100 μg/mL. The 50% of inhibition of silver nanoparticles against human breast cancer cell lines is 18 μg/mL. It is evident that silver nanoparticles would be helpful in treating cancer cell lines and have great perspectives in the biomedical sector.     

Keggin-type heteropoly-11-molybdo-1-vanadophosphoric acid supported montmorillonite K-10 clay-catalysed one-pot multi-component synthesis of chromeno[2,3-b]indoles

One-pot three-component synthesis of twelve different chromeno[2,3-b]indole derivatives were achieved by the condensation of β-naphthol, oxindole and various substituted aldehydes. Two more chromeno[2,3-b]indole derivatives were also synthesized through one-pot two-component condensation of salicylaldehyde with oxindole/chlorooxindole. Both the condensations were achieved by using Keggin-type heteropoly-11-molybdo-1-vanadophosphoric acid, H₄[PVMo₁₁O₄₀] supported on montmorillonite K-10 clay for about 10% as catalyst under environmentally benign solvent-free reaction condition. Shorter reaction time, excellent yield of product, sustainability of catalytic material and simple workup procedure under green experimental conditions are the advantages of this protocol.