Coefficient characterizations and sections for some univalent functions

Let (α) denote the class of locally univalent normalized analytic functions f in the unit disk |z| < 1 satisfying the condition $Re\left( {1 + \frac{{zf''(z)}} {{f'(z)}}} \right) < 1 + \frac{\alpha } {2}for|z| < 1 $ and for some 0 < α ≤ 1. We firstly prove sharp coefficient bounds for the moduli of the Taylor coefficients a _n of f ∈ (α). Secondly, we determine the sharp bound for the Fekete-Szegö functional for functions in (α) with complex parameter λ. Thirdly, we present a convolution characterization for functions f belonging to (α) and as a consequence we obtain a number of sufficient coefficient conditions for f to belong to (α). Finally, we discuss the close-to-convexity and starlikeness of partial sums of f ∈ (α). In particular, each partial sum s _n (z) of f ∈ (1) is starlike in the disk |z| ≤ 1/2 for n ≥ 11. Moreover, for f ∈ (1), we also have Re(s′ _n (z)) > 0 in |z| ≤ 1/2 for n ≥ 11.     

Highly efficient organic indolocarbazole dye in different acceptor units for optoelectronic applications—a first principle study

A series of novel organic dyes (ICZA1, ICZA2, ICZA3, ICZA4) with D-π-A structural configuration incorporating indolo[3,2,1-jk]carbazole moiety as donor (D) unit, thiophene as π-linker and 2-cyanoacrylic acid as acceptor unit were investigated using density functional theory (DFT) and time-dependent DFT (TD-DFT) methods. Indolo[3,2,1-jk]carbazole-based D-π-A dyes composed of different acceptor groups were designed. By modulating acceptor unit, the efficiency of D-π-A dye-based dye-sensitized solar cells (DSSCs) can be further improved. In the present work, four novel push-pull organic dyes only differing in electron acceptor, have been designed based on the experimental literature value of IC-2. In order to further improve the light harvesting capability of indolo[3,2,1-jk]carbazole dyes, the acceptor influence on the dye performance were examined. The NLO property of the designed dye molecules can be derived as polarizability and hyperpolarizability. The calculated value of ICZA2 dye is the best candidate for NLO properties. Furthermore, the designed organic dyes exhibit good photovoltaic performance of charge transfer characteristics, driving force of electron injection, dye regeneration, global reactivity, and light harvesting efficiency (LHE). From the calculated value of ICZA4 dye, it has been identified as a good candidate for DSSCs applications. Finally, it is concluded that the both ICZA2 and ICZA4 dyes theoretically agrees well with the experimental value of IC-2 dye. Hence, the dyes ICZA2 and ICZA4 can serve as an excellent electron withdrawing groups for NLO and DSSCs applications.     

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.     

Stereoselective synthesis of 3-spiro-α-methylene-γ-butyrolactone oxindoles from Morita-Baylis-Hillman adducts of isatin

A concise stereoselective synthesis of 3-spiro-α-methylene-γ-butyrolactone oxindoles from Morita-Baylis-Hillman adducts of isatin in excellent yield has been achieved following a three-step reaction sequences viz. (1) Isomerisation of the Morita-Baylis-Hillman adducts of isatin with trimethyl orthoformate and montmorillonite K10 clay catalyst, (2) a second Morita-Baylis-Hillman reaction with formaldehyde, and (3) an acid catalysed lactonization. The structure and stereochemistry of the products were assigned by X-ray crystallographic and NMR spectroscopic studies. Formation and mechanism of the minor product spirofuran oxindoles and a one-pot base promoted second Morita-Baylis-Hillman adduct formation-lactonization reaction have also been achieved.     

A facile and efficient synthesis of highly functionalised 3,3′-dispiropyrrolidine- and 3,3′-dispiropyrrolizidine bisoxindoles via [3+2] cycloaddition

The [3+2] cycloaddition reaction of azomethine ylides with isomerised Morita-Baylis-Hillman adducts, both dipoles and dipolarophiles are derived from isatin, afforded highly functionalised 3,3′-dispiro pyrrolidine- and 3,3′-dispiropyrrolizidine bisoxindoles in high yields.     

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

Concave functions,blaschke products,and polygonal mappings

We consider the class Co(p) of all conformal maps of the unit disk onto the exterior of a bounded convex set. We prove that the triangle mappings, i.e., the functions that map the unit disk onto the exterior of a triangle, are among the extreme points of the closed convex hull of Co(p). Moreover, we prove a conjecture on the closed convex hull of Co(p) for all p ∈ (0, 1) which had partially been proved by the authors for some values of p ∈ (0, 1).     

Growth and characterization of cadmium magnesium tetra thiocyanate crystals

Cadmium Magnesium Tetra Thiocyanate, CdMg(SCN)₄, [CMTC] belongs to bimetallic thiocyanate complexes. CMTC crystals has been grown by solution growth technique at room temperature. The morphologies of the grown crystals are identified by single crystal analysis. Also the Powder X‐ray Diffractogram of the crystal has been recorded and the various planes of reflection are identified. The title compound crystallizes under triclinic structure with lattice parameters a = 10.0976 Å, b = 7.5015 Å, c = 5.7720 Å and β = 90.2135°. The presence of magnesium and cadmium in the grown crystals were confirmed through Atomic Absorption Spectroscopy. The grown crystals are analysed qualitatively by Fourier Transform Infrared (FTIR) and Fourier Transform Raman spectral measurements. The transmittance spectrum of the crystal in the UV‐Visible region has been recorded and analysed. The dielectric measurements for the crystals were carried out in the microwave region. The thermal stabilities of the crystals were studied by using different thermal analyses like Thermo Gravimetric Analysis (TGA), Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC). (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Grindstone Chemistry: Design,One-Pot Synthesis,and Promising Anticancer Activity of Spiro[acridine-9,2′-indoline]-1,3,8-trione Derivatives against the MCF-7 Cancer Cell Line

In this study, the synthesis of one-pot 10-phenyl-3,4,6,7-tetrahydro-1H-spiro [acridine-9,2′-indoline]-1,3,8-trione derivatives was achieved via a four-component cyclocondensation reaction, which was carried out in solvent-free conditions, and using p-toluenesulfonic acid (p-TSA) as a catalyst. The product was confirmed by FT-IR, ¹H-NMR, ¹³C-NMR, mass spectra, and elemental analysis. Furthermore, the anticancer activity was screened for all compounds. Among these compounds, compound 1c was more effective (GI₅₀ 0.01 µm) against MCF-7 cancer cell lines than standard and other compounds. Therefore, the objective of this study was achieved with a few promising molecules having been demonstrated to be potential anticancer agents.