On the Fekete-Szegö problem for concave univalent functions

We consider the Fekete-Szegö problem with real parameter λ for the class Co(α) of concave univalent functions.     

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.     

Near-edge X-ray absorption fine structure study of disordering in Gd2(Ti1-yZry)2O7 pyrochlores

Disorder in Gd2(Ti(1-y)Zry)2O7 pyrochlores, for y = 0.0-1.0, is investigated by Ti 2p and O 1s near-edge X-ray absorption fine structure spectroscopy. Ti(4+) ions are found to occupy octahedral sites in Gd2Ti2O7 with a tetragonal distortion induced by vacant oxygen sites. As Zr substitutes for Ti, the tetragonal distortion decreases, and Zr coordination increases from 6 to 8. The migration of oxygen ions from 48f or 8b sites to vacant 8a sites compensate for the increased Zr coordination, thereby reducing the number of vacant 8a sites, which further reduces the tetragonal distortion and introduces more disorder around Ti. This is evidence for simultaneous cation disorder with anion migration.     

A facile and efficient stereoselective synthesis of highly functionalised trisubstituted alkene derivatives of ferrocenealdehyde

The reaction of the Baylis–Hillman adduct 2 of ferrocenealdehyde with various oxygen and carbon nucleophiles in the presence of montmorillonite K10 clay catalyst furnished highly functionalised trisubstituted alkene derivatives of ferrocenealdehyde in excellent yield. Synthetic use of one of products 7 has been demonstrated with the synthesis of a 1,3-diyne ether derivative of ferrocene 16 via an Eglinton coupling reaction.     

Montmorillonite K10 Clay Catalysed Friedel-Crafts Aralkylation in Room Temperature: Synthesis of Functionalised Linear Aryl-Alkyl-Aryl Systems

The Montmorillonite K10 clay catalysed Friedel-Crafts aralkylation of compound 2 with a number of aromatic hydrocarbons furnished functionalised linear Aryl-Alkyl-Aryl systems in good yield. A comparative study of this reaction was carried out with mont-K10 and Fe³⁺-Mont-K10.     

On the Analytic Part of Univalent Harmonic Mappings

In this article we obtain two sharp results concerning the analytic part of harmonic mappings \(f=h+\overline{g}\) from the class \(\mathcal {S}^0_H(\mathcal {S})\) which was recently introduced by Ponnusamy and Sairam Kaliraj. For example, we get the sharp estimate for \(|\arg h'(z)|\) in the case when \(|z| \le 1/\sqrt{2}\) and obtain the sharp radius of convexity for h. Our approach is applicable to a more general situation. Finally, we determine simple condition on the analytic part of univalent harmonic mappings so that it is in \(H_p\) spaces for \(0<p<1/3\).     

Effect of annealing on natural calcitic crystals—A thermostimulated luminescence (TSL) study

The quality crystals (Calcitic limestone) were selected using the UV–visible methylene blue adsorption method. The thermostimulated luminescence (TSL) glow curve characteristics of six well crystallized limestone samples were analyzed. The glow curves of unannealed sample show only one peak in the range 320–330 °C. The sample irradiated with a gamma dose of 100 Gy shows two additional peaks in the range of 113–125 °C and 242–260 °C when recorded with linear heating rate of 10 °C/s. The annealed sample also shows the same trend as that of irradiated sample. Annealing treatment above 250 °C increases the sensitivity of all TSL peaks except 320 °C. On the other hand, annealing at 750 °C caused a collapse in the TSL sensitivity. The enhancement in TSL sensitivity was found to depend on the annealing temperature and time. Annealing treatment at 650 °C for 4 h followed by quenching in air is the optimum condition for TSL sensitization. The response to gamma irradiation is linear in the range from 0.5 Gy to 10⁴ Gy. The emission spectra of all the samples show an emission at around 610 nm but with different intensities for each TSL peak. With reference to earlier work, it may be assumed that the recombination site always involves Mn²⁺ ions. The observation made through infra-red (IR) and X-ray diffraction (XRD) studies with thermal treatment shows the structural changes of calcite from D_3h to C_s symmetry at 750 °C. The Thermogravimetric-Differential Thermal Analysis (TG-DTA) analysis shows the calcite gets disordered at 760 °C. Hence, the collapse in the TSL sensitivity at 750 °C is due to structural change or structural disorderedness.     

Covering and distortion theorems for planar harmonic univalent mappings

In this paper, we investigate Clunie and Sheil-Small’s covering theorems for sense-preserving planar harmonic univalent mappings defined in the unit disk. Our results significantly improve the earlier known result. Also, we obtain a distortion theorem for fully starlike harmonic mappings in the unit disk.     

Functional inequalities for modified Bessel functions

In this paper, our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kind. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Turán-type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind, we prove that the cumulative distribution function of the gamma–gamma distribution is log-concave. At the end of this paper, several open problems are posed, which may be of interest for further research.