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...     

Geometric Properties of Generalized Hypergeometric Functions

Let denote the generalized hypergeometric function where no denominator parameter can be zero or a negative integer and (a,n) denotes the ascending factorial notation. Ponnusamy and Vuorinen raised the problem of finding conditions on the parameters a_j > 0, b_j > 0 so that the function is univalent in . The main aim of this paper is to discuss this problem in detail for the case q = 2.     

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.     

Univalence and starlikeness of nonlinear integral transform of certain class of analytic functions

Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition

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.