Coefficient estimates of negative powers and inverse coefficients for certain starlike functions

For ?1≤B<A≤1, let \(\mathcal {S}^{*}(A,B)\) denote the class of normalized analytic functions \(f(z)= z+{\sum }_{n=2}^{\infty }a_{n} z^{n}\) in |z|<1 which satisfy the subordination relation z f ^′(z)/f(z)?(1 + A z)/(1 + B z) and Σ^?(A,B) be the corresponding class of meromorphic functions in |z|>1. For \(f\in \mathcal {S}^{*}(A,B)\) and λ>0, we shall estimate the absolute value of the Taylor coefficients a _n (?λ,f) of the analytic function (f(z)/z)^?λ . Using this we shall determine the coefficient estimate for inverses of functions in the classes \(\mathcal {S}^{*}(A,B)\) and Σ^?(A,B).     

A tandem synthesis of 3-aroylcoumarinoflavones catalyzed by <Emphasis Type="SmallCaps">l</Emphasis>-proline and their antioxidant activity

A facile, convenient, efficient and high-yielding synthesis of 3-aroylcoumarinoflavones has been developed by the condensation of easily synthesized 7-hydroxy-8-formylflavones and benzoyl acetonitriles in the presence of catalytic amount of l-proline in ethanol reflux. All the synthesized compounds were evaluated for their antioxidant activity. Some of the compounds showed very good activity compared to standard BHT.     

Cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of several members of the 1,ω-bis(4-cyanobiphenyl-4′-yl) alkane (CBnCB) and the 1-(4-cyanobiphenyl-4′-yloxy)-ω-(4-cyanobiphenyl-4′-yl) alkane (CBnOCB) homologous series are reported. The new odd members described CB5CB, CB13CB, CB4OCB, CB8OCB and CB10OCB all exhibit twist-bend nematic and nematic phases. The members of these series already reported in literature, CB7CB, CB9CB, CB11CB and CB6OCB, were also prepared in order to allow for a direct comparison of their transitional properties. The properties of these dimers are also compared to those of the corresponding members of the 1,ω-bis(4-cyanobiphenyl-4,-yloxy) alkanes (CBOnOCB). For any given total spacer length, for odd members of these series, the nematic–isotropic transition temperatures and associated entropy changes are greatest for the CBOnOCB dimer and lowest for the CBnCB dimer. These trends are understood in terms of molecular shape. For short spacer lengths, the twist-bend nematic–nematic transition temperature (T_NTBN) is higher for the CBnOCB series than for the CBnCB series but this is reversed as the spacer length increases. Of the CBOnOCB dimers, a virtual value of T_NTBN was estimated for CBO3OCB and T_NTBN was measured for CBO5OCB. These values are considerably lower than those observed for the corresponding members of the CBnCB or CBnOCB series. The dependence of T_NTBN on molecular structure is discussed not only in terms of the molecular curvature but also in the ability of the molecules to pack efficiently. As the temperature range of the preceding nematic phase increases, so the twist-bend nematic–nematic transition entropy change decreases and the transition approaches second order for the longer spacers. For comparative purposes, the transitional behaviour of the even-membered dimers CB6CB, CB5OCB and CBO4OCB is reported and differences accounted for in terms of molecular shape.     

Synthesis and self‐assembly of diblock copolymers composed of poly(3‐hexylthiophene) and poly(fluorooctyl methacrylate) segments

Regioregular poly(3‐hexylthiophene)‐b‐poly(1H,1H‐dihydro perfluorooctyl methacrylate) (P3HT‐b‐PFOMA) diblock copolymers were synthesized by atom transfer radical polymerization of fluorooctyl methacrylate using bromoester terminated poly(3‐hexylthiophene) macroinitiators in order to investigate their morphological properties. The P3HT macroinitiator was previously prepared by chemical modification of hydroxy terminated P3HT. The block copolymers were well characterized by ¹H NMR spectroscopy and gel permeation chromatography. Transmission electron microscopy was used to investigate the nanostructured morphology of the diblock copolymers. The block copolymers are able to undergo microphase separation and self‐assemble into well‐defined and organized nanofibrillar‐like micellar morphology. The development of the morphology of P3HT‐b‐PFOMA block copolymers was investigated after annealing in solvent vapor and also in supercritical CO₂. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Bilateral Mixed Laryngoceles: Simultaneous Strobovideolaryngoscopy and External Video Examination

A music medicine practice affords a unique opportunity to diagnose and treat laryngeal music performers. Strobovideolaryngoscopic (SVL) and external video examination of the voice professional or brass instrument player may focus on the vocal folds, yet abnormalities of the supraglottis, neck, and thorax should be appreciated and documented. Laryngoceles are uncommon laryngeal disorders but may occur in up to 5% of benign laryngeal lesions. While many laryngoceles are asymptomatic, they may cause a cough, hoarseness, stridor, sore throat, pain, snoring, or globus sensation. In particular, musicians who play brass instruments are at high risk for laryngocele development. We highlight two patients with symptomatic laryngoceles to present anatomical, historical, classification, epidemiological, diagnostic, and management considerations.     

APPLICATION OF SHELLAC IN POLYMERS

Abstract

Lac is the only known natural resin of animal origin. It is the secretion of a tiny insect known as Kerriar lacca (formally called Laceifer lacca). The lac-forming tiny insect grows on some types of trees, mostly abundant in tropical countries, including India. The secretion of the lac insect hardens in air and forms a covering on the body of the insect. This covering or the nest forms a continuous incrustation on the branches of the host trees. Lac is collected by scraping the incrustation from the branches of the trees.     

Inversion formulas for the reznitskaya transform and stability of lipschitz type in determination of initial heat distribution

In the Reznitskaya transform combining the solutions of some general linear partial differential equations of hyperbolic type and parabolic type, isometrical identities and inversion formulas are established. Furthermore, stability of Lipschitz type in the determination of initial heat distribution is given as an application.