Convolution properties of some classes of analytic functions

Let A denote the class of functions which are analytic in |z|<1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A be the class of functions f such thatRe[f′(z)+αzf″(z)]>β,Re α>0, β<1. We determine conditions under which (i) f ∈ R(α₁, β₁), g ∈ R(α₂, β₂) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β₁), g ∈ R(0, β₂) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]^μ-1 ≺ 1 + λz, μ>0, 0<λ<1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α>0, δ>0, is convex or starlike. Bibliography: 16 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 138–154.     

Studies on montmorillonite K10-microwave assisted isomerisation of Baylis-Hillman adduct. Synthesis of E-trisubstituted alkenes and synthetic application to lignan core structures by vinyl radical cyclization

The isomerisation of acetates from the Baylis-Hillman adducts with Mont.K10 clay-microwave combination furnished E-trisubstituted alkenes in high yield. The simple Baylis-Hillman adducts with trimethyl orthoformate and unsaturated alcohols under clay catalytic condition gave densely functionalised-isomerized products under solvent free condition. Application of the propargyl derivatives thus obtained from the isomerisation of the Baylis-Hillman adducts with propargyl alcohol has been demonstrated in the synthesis of lignan core structures by tri-n-butyltin hydride mediated vinyl radical cyclization.     

Radial Length,Radial John Disks and K-quasiconformal Harmonic Mappings

Potential Analysis - In this article, we continue our investigations of the boundary behavior of harmonic mappings. We first discuss the classical problem on the growth of radial length and obtain...     

Synthesis and biological activities of nitro-hydroxy-phenylquinolines; validation of antibiotics effect over DNA gyrase inhibition and antimicrobial activity

A family of 11 nitrophenol 2-nitro-5-(4-substituted phenylquinolin-2-yl)phenol derivatives (4, 4a-j) was effectively synthesized as antimicrobial medications. A mixture of the substituted 3-hydroxy-4-nitrobenzaldehyde substituted aromatic amine and substituted phenylacetylenes were used to synthesis the title compounds 4, 4a-j. Antimicrobialactivity potential of 4, 4a-j was evaluated against Streptococcus pyogenes (MTCC 442), Staphylococcus aureus (MTCC 96), Pseudomonas aeruginosa (MTCC 424), and Escherichia coli (MTCC 443). DNA gyrase inhibition studies carried out to understand the mechanism ofaction of the antimicrobial effect of target compounds. HRBC membrane stabilization (in vitro) property was also assessed as a representative human cellular cytotoxic effect of 4, 4a-j since HRBC alike lysosomal cells and the lysozyme activity leads to inflammation and its adverse effects in cellular systems. Results reveal that compounds 4c and 4h have remarkable antibacterial activity and screened for further preclinical studies.     

Mineralogical role on natural radioactivity content in the intertidal sands of Tamilnadu coast (HBRAs region), India

Activity concentration and mineralogical characterization in the intertidal sand samples of Tamilnadu coast, India have been analyzed. From the gamma spectral analysis, the average value of ²³⁸U, ²³²Th and ⁴⁰K in the intertidal sand samples are 12 ± 4, 59 ± 4 and 197 ± 26 Bq kg⁻¹ respectively. The average value of ²³²Th alone is slightly higher than the world average value. From XRD and FTIR analysis, monazite, zircon, ilmenite, magnetite, hematite, quartz, witherite, calcite, nacrite, microcline feldspar, orthoclase feldspar, gibbsite and organic carbon are identified. Of these minerals, monazite and microcline feldspar are the most associated with the presence of ²³²Th and ⁴⁰K respectively.

     

A first one-pot synthesis, isomerization and synthetic utility of mono- and bis Morita-Baylis-Hillman adducts of 1,1′-ferrocenedialdehyde

A one-pot synthesis of mono- and bis-Morita-Baylis-Hillman adducts of 1,1′-ferrocenedialdehyde has been achieved. These adducts undergo a facile and efficient stereoselective isomerization with a number of saturated, unsaturated, aromatic alcohols, phenols and thiophenol with a montmorillonite K10 clay catalyst to afford highly functionalized trisubstituted alkene derivatives of ferrocene. The synthetic utility of isomerized derivatives has been demonstrated by a ferrocene appended novel macrocycle synthesis, a ferrocenyl bis-triazole synthesis and an evaluation of the liquid crystalline property of a cholesterol derivative of ferrocene.     

Synthesis of functionalized 3-spirocyclopropane-2-indolones from isomerised Baylis-Hillman adducts of isatin

A facile, high yield stereoselective synthesis of functionalized diastereomeric 3-spirocyclopropane-2-indolones (10-17a,b) from the isomerised bromo derivatives of Baylis-Hillman adducts of isatin(2-9a,b) by reductive cyclization with sodium borohydride is reported.     

Polylogarithms in the Theory of Univalent Functions

Let a, b > ?1, p and q be non-zero real numbers such that p + q ≥ 1. In this paper, we study the geometric mapping properties of the (normalized) generalized polylogarithm defined in the unit disc