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.     

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.     

Acceptor tuning effect on TPA-based organic efficient sensitizers for optoelectronic applications—quantum chemical investigation

Structural Chemistry - A new series of triphenylamine (TPA)-based organic dyes (A1-A4) are characterized and implemented as photosensitizers for dye-sensitized solar cells (DSSCs). In the...     

Decomposition and removability properties of John domains

In this paper we characterize John domains in terms of John domain decomposition property. In addition, we also show that a domain D in ℔ ⁿ is a John domain if and only if D\P is a John domain, where P is a subset of D containing finitely many points of D. The best possibility and an application of the second result are also discussed.     

Studies on electron transfer reactions: reduction of heteropoly 10-tungstodivanadophosphate by <Emphasis Type="SmallCaps">l</Emphasis>-cysteine in aqueous acid medium

l-cysteine undergoes facile electron transfer with heteropoly 10-tungstodivanadophosphate, [ \textPV^\textV \textV^\textV \textW _{1 0} \textO _{4 0} ]^{5 -} , \left[ {{\text{PV}}^{\text{V}} {\text{V}}^{\text{V}} {\text{W}}_{ 1 0} {\text{O}}_{ 4 0} } \right]^{5 - } , at ambient temperature in aqueous acid medium. The stoichiometric ratio of [cysteine]/[oxidant] is 2.0. The products of the reaction are cystine and two electron-reduced heteropoly blue, [PV^IVV^IVW₁₀O₄₀]⁷⁻. The rates of the electron transfer reaction were measured spectrophotometrically in acetate–acetic acid buffers at 25 °C. The orders of the reaction with respect to both [cysteine] and [oxidant] are unity, and the reaction exhibits simple second-order kinetics at constant pH. The pH-rate profile indicates the participation of deprotonated cysteine in the reaction. The reaction proceeds through an outer-sphere mechanism. For the dianion ⁻SCH₂CH(NH₃ ⁺)COO⁻, the rate constant for the cross electron transfer reaction is 96 M⁻¹s⁻¹ at 25 °C. The self-exchange rate constant for the ^- \textSCH₂ \textCH( \textNH₃ ⁺ )\textCOO ^- \mathord

On an extreme point conjecture for concave functions

Let CO(A), A ∈ (1; 2], denote the family of concave univalent functions in the unit disk ⅅ with opening angle at infinity bounded by πA. We prove a weak form of a conjecture on the extreme points of clco CO(A) from the paper in Indian J. Math. 50, 339–349 (2008).