Synthesis and characterization of a new organic nonlinear optical crystal: l-Phenylalaninium maleate

l-Phenylalaninium maleate (abbreviated as LPM) chemical formula C₉H₁₂NO₂⁺·C₄H₃O₄⁻, a new organic nonlinear optical crystal was grown by slow evaporation technique. Transparent needle shaped crystal of dimensions 7 mm × 1 mm × 0.5 mm was obtained. Single crystals of LPM have been subjected to X-ray diffraction analysis to estimate the lattice parameters and the space group. The powder X-ray diffractogram of the crystal has been recorded and the reflections from various planes are identified. The XRD studies confirm the crystalline nature. The qualitative analysis on the crystal has been carried out using Fourier transform infrared (FTIR) and Fourier transform Raman (FTRaman) spectral measurements. The presence of hydrogen and carbon in the grown crystal was confirmed by using proton and carbon nuclear magnetic resonance (NMR) spectral analyses. Optical behaviour of the crystal was investigated using UV–vis spectroscopy. The thermal stability of the crystal was analysed with the aid of thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The nonlinear optical (NLO) property of the crystal was tested by Nd:YAG laser source.     

Growth of entire functions of exponential type defined by convolution

Based on the Borel transformation and the Hadamard multiplication theorem on singularities on the convolution of holomorphic functions, results on the growth of entire functions defined by convolution of an entire function of exponential type with a function holomorphic at the origin are obtained. Received: 29 August 2005     

Chemometrics Assisted Formulation of Glimepiride Nanosuspension for Solubility Enhancement in Diabetic Therapy—A Systematic Approach

Glimepiride (GLM), a third-generation sulfonylurea oral hypoglycemic medication, is used to treat type II diabetes. Admittedly, it has a low bioavailability, a relatively short half-life (t_1/2), and high toxicity. To address the issue, a nanosuspension of poorly soluble GLM is designed using a Quality-by-Design (QbD) method, to enhance its solubility. Prospective risk factors are identified and assessed using Critical Material Attribute (CMAs) and Critical Processing Parameter (CPPs) to evaluate the targets by Taguchi orthogonal array (OA) design and to study the effects of formulation and process variables on dependent variables. The amount of Polyvinylpyrrolidone (PVP) (X2), agitation time (X5), and concentration of Poloxamer (X7) are found as significant parameters (p < 0.05), and are further optimized using the Box Behnken Design as response surface methodology model. The optimized GLM nanosuspension 1) has mean particle size (PS), zeta potential, viscosity (VS), and percentage cumulative drug release (CDR%) of 258.17 nm, −25.2 mV, 1.087cPs, and 98.52%, respectively. The pattern of drug release is fitted to Non-Fickian kinetics. The study results in an economic and efficient nano formulation with enhanced solubility.     

Studies on ultrasonic properties of different series of liquid systems

Fifteen specimens of tetraalkoxysilanes were prepared and their tentative tetrahedral structures proposed. Ultrasonic velocities were measured over the temperature range of 30–80°C using a multifrequency ultrasonic interferometer. Intermolecular free length, free volume and internal pressure of different classes of compounds were evaluated using the experimentally determined ultrasonic velocity, density, specific heat, thermal expansion, viscosity and molecular weight employing different empirical equations and the data obtained were compared.     

Maximal Area Integral Problem for Certain Class of Univalent Analytic Functions

One of the classical problems concerns the class of analytic functions f on the open unit disk |z| < 1 which have finite Dirichlet integral Δ(1, f), where

$$\Delta(r ,f) = \iint_{|z| < r} |f' (z)| ^ 2 \, {\rm d} x {\rm d}y \quad (0 < r \leq 1)$$

The class \({\mathcal{S} ^*(A,B)}\) of normalized functions f analytic in |z| < 1 and satisfies the subordination condition \({zf'(z)/f(z)\prec (1+Az)/(1+Bz)}\) in |z| < 1 and for some \({-1\leq B\leq 0}\) , \({A \in \mathbb{C}}\) with \({A\neq B}\) , has been studied extensively. In this paper, we solve the extremal problem of determining the value of

$$\max_{f\in \mathcal{S}^*(A,B)}\Delta(r,z/f)$$

as a function of r. This settles the question raised by Ponnusamy and Wirths (Ann Acad Sci Fenn Ser AI Math 39:721–731, 2014). One of the particular cases includes solution to a conjecture of Yamashita which was settled recently by Obradovi? et al. (Comput Methods Funct Theory 13:479–492, 2013).

     

Synthesis,structural, DFT investigations and antibacterial activity assessment of pyrazoline-thiocyanatoethanone derivatives as thymidylate kinase inhibitors

Two novel compounds 1-(5-[4-fluorophenyl]-3-phenyl-4,5-dihydro-1H-pyrazol-1-yl)-2-thiocyanatoethanone (FSCN) and 1-(5-[4-chlorophenyl]-3-phenyl-4,5-dihydro-1H-pyrazol-1-yl)-2-thiocyanatoethanone (ClSCN) were synthesized and characterized by SC-XRD, 1H NMR, 13C NMR, FTIR, and UV methods. The X-ray diffraction studies were utilized to prove the 3D crystal structures of FSCN and ClSCN. In both the compounds, the packing is mostly driven by C H⋯N, C H⋯O, and C H⋯π (benzene ring as an acceptor) interactions. In ClSCN, additionally, the π⋯π interaction is observed between the pyrazole ring of one molecule and the benzene ring of the other molecule. The experimental values were compared with the results of DFT/B3LYP/6-311G++(d,p) theoretical computations. The pharmacological screening for FSCN and ClSCN was performed using molinspiration and PreADMET web server. To analyze antibacterial inhibition of the synthesized ligands and Ciprofloxacin (control drug) were interacted with antibacterial protein Thymidylate Kinase (TMK) (PDB ID: 4QGG) with the help of AutoDock Vina tool. The ADMET and docking results of FSCN and ClSCN pointed out the better drug likeness nature and good inhibition behavior with TMK protein. The antibacterial in vitro studies suggested that FSCN compound inhibited well with antibacterial strains than that of ClSCN. The current investigation suggests that with further improvements, our compounds could be preferred as substitute medicine for bacterial diseases.     

WAVE PROPAGATION IN A TRANSVERSELY ISOTROPIC THERMOELASTIC SOLID CYLINDER OF ARBITRARY CROSS-SECTION

The wave propagation in an infinite, homogeneous, transversely isotropic solid cylinder of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-dimensional theory of thermoelasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for elliptic and parabolic cross-sectional zinc cylinders. The computed non-dimensional wave numbers are presented in the form of dispersion curves.     

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.