The Separation of Zeros of Solutions of Higher Order Linear Differential Equations With Entire Coefficients

Suppose that a homogeneous linear differential equation has entire coefficients of finite order and a fundamental set of solutions each having zeros with finite exponent of convergence. Upper bounds are given for the number of zeros of these solutions in small discs in a neighbourhood of infinity.     

Stacked films immobilization of MBTH in nafion/sol-gel silicate and horseradish peroxidase in chitosan for the determination of phenolic compounds

The stacked-film immobilization of 3-methyl-2-benzothiazolinone hydrazone (MBTH) in hybrid nafion/sol-gel silicate film and horseradish peroxidase (HRP) in chitosan, performed in order to allow the determination of phenolic compounds, was investigated via an optical method. The stacked films were deposited onto a microscope glass slide by a spin-coating technique. The quinone or free radical product formed by the enzymatic reactions of phenolic compounds interacts with MBTH to form azo-dye products, which can be measured spectrophotometrically at a wavelength of 500 nm. The color intensity of the product was found to increase in proportion to the phenolic concentration after 5 min of exposure. The response of the biosensor was linear over concentration ranges of 0.025–0.500, 0.010–0.070 and 0.050–0.300 mM for guaiacol, resorcinol and o-cresol, respectively, and gave detection limits of 0.010, 0.005 and 0.012 mM. The sensor exhibited good sensitivity and stability for at least two months.     

Basic gravitational currents and Killing–Yano forms

It has been shown that for each Killing–Yano (KY)-form accepted by an n-dimensional (pseudo)Riemannian manifold of arbitrary signature, two different gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general geometrical facts implied by these conservation laws are also elucidated. In particular, the conservation of the one-form currents implies that the scalar curvature of the manifold is a flow invariant for all of its Killing vector fields. It also directly follows that, while all KY-forms and their Hodge duals on a constant curvature manifold are the eigenforms of the Laplace–Beltrami operator, for an Einstein manifold this is certain only for KY 1-forms, (n − 1)-forms and their Hodge duals.     

Synthesis,Characterization, and In Vitro Antibacterial Activities of Macromolecules Derived from Bis‐Chalcone

We investigated the antibacterial activity of some new macromolecules such as bis‐pyrazoline, bis‐pyrazole, bis‐pyrimidines prepared from the reaction of bis‐chalcone with thiosemicarbazide/phenyl hydrazine/guanidine hydrochloride/thiourea. All the macromolecules have been characterized by IR, ¹H NMR, ¹³C NMR, mass and elemental analyses. The antibacterial activity of these compounds was first tested in vitro by the disc diffusion assay against two Gram‐positive and two Gram‐negative bacteria, and then the minimum inhibitory concentration was determined with the reference to standard drug chloramphenicol. The results showed that pyrazoline derivative showed better antibacterial activity on S. typhimurium and E. coli than the reference drug chloramphenicol.     

Synthesis of Ag nanoparticle-decorated 2,4,6-tris(2-pyridyl)-1,3,5-triazine nanobelts and their application for H2O2 and glucose detection

The present paper reports on the first preparation of 2,4,6-tris(2-pyridyl)-1,3,5-triazine nanobelts (TPTNBs) by adjusting the pH value of the solution and the subsequent synthesis of Ag nanoparticle (AgNP)-decorated TPTNBs (AgNP-TPTNBs) by mixing an aqueous AgNO(3) solution with preformed TPTNBs without use of any external reducing agent. It is found that the resultant AgNP-TPTNBs exhibit notable catalytic performance for H(2)O(2) reduction. A glucose biosensor was fabricated by immobilizing glucose oxidase (GOD) onto a AgNP-TPTNBs-modified glassy carbon electrode (GCE) for glucose detection. The constructed glucose sensor has a wide linear response range from 3 mM to 20 mM (r: 0.999) with a detection limit of 190 μM. It is further shown that this glucose biosensor can be used for glucose detection in human blood serum.     

Spectral characteristics and fluorescence quenching of N,N′-bis(4-pyridyl)-3,4:9,10-perylenebis(dicarboximide) (BPPD)

The photophysical properties such as electronic absorption, molar absorptivity, emission spectra, fluorescence quantum yield and fluorescence lifetime of N,N′-bis(4-pyridyl)-3,4:9,10-perylene bis(dicarboximide) (BPPD) have been measured in different solvents. Both electronic absorption and fluorescence spectra are not sensitive to medium polarity, while the fluorescence quantum yield (?_f) is solvent dependent. The ground state geometry has been computed by using density functional theory (DFT), the transition from HOMO to LUMO from perylene core with maximum absorption at 512 nm and HOMO–LUMO energy difference equal 2.53 eV. BPPD dye undergoes molecular aggregation to dimmer or higher aggregates in dimethyl sulfoxide (DMSO). Crystalline solids of BPPD gives excimer-like emission at 676 nm. The fluorescence quenching of BPPD is also studied using hydrated ferric oxide nanoparticle (FeOOH), and the Stern–Volmer rate constants (K_sv) were calculated as 8×10⁶ and 9.2×10⁶ M^?1 in ethanol and ethylene glycol, respectively.     

Synthesis,characterization, luminescence properties and antioxidant activity of Ln(III) complexes with a new aryl amide bridging ligand

A novel Aryl amide ligand H₂L and its eight complexes, [LnH₂L(NO₃)₂·H₂O]NO₃ [Ln=Sm(III), Er(III), Tb(III), Dy(III), La(III), Gd(III), Nd(III), and Pr(III)], are presented. The ligand and complexes were synthesized and characterized based on elemental analyses, molar conductance, IR, ¹H and ¹³C-NMR, UV–VIS., and TGA studies. The conductivity data show a 1:1 electrolytic nature with a general formula [LnH₂L(NO₃)₂·2H₂O]NO₃ The IR spectra reveal coordination of the ligand through the azomethine nitrogen and the phenolic hydroxyl of the ligand to the lanthanide ion. The coordinated nitrate ions behave in a bidentate fashion. The thermal decomposition studies indicate the presence of two water molecules in the inner coordination sphere. Under the excitation at 319 nm, the luminescence emission properties for Sm, Tb, and Dy complexes are observed. These observations show that the ligand favors energy transfers to the emitting energy level of these lanthanide ions. Furthermore, the antioxidant activity of the ligand and its Ln(III) complexes was determined by DPPH radical scavenging method, which indicates that the Ln(III) complexes exhibit more effective antioxidant activity than the ligand alone.     

Enhanced growth of lactobacilli and bioconversion of isoflavones in biotin-supplemented soymilk upon ultrasound-treatment

This study aimed at utilizing ultrasound treatment to further enhance the growth of lactobacilli and their isoflavone bioconversion activities in biotin-supplemented soymilk. Strains of lactobacilli (Lactobacillus acidophilus BT 1088, L. fermentum BT 8219, L. acidophilus FTDC 8633, L. gasseri FTDC 8131) were treated with ultrasound (30 kHz, 100 W) at different amplitudes (20%, 60% and 100%) for 60, 120 and 180 s prior to inoculation and fermentation in biotin-soymilk. The treatment affected the fatty acids chain of the cellular membrane lipid bilayer, as shown by an increased lipid peroxidation (P < 0.05). This led to increased membrane fluidity and subsequently, membrane permeability (P < 0.05). The permeabilized cellular membranes had facilitated nutrient internalization and subsequent growth enhancement (P < 0.05). Higher amplitudes and longer durations of the treatment promoted growth of lactobacilli in soymilk, with viable counts exceeding 9 log CFU/mL. The intracellular and extracellular β-glucosidase specific activities of lactobacilli were also enhanced (P < 0.05) upon ultrasound treatment, leading to increased bioconversion of isoflavones in soymilk, particularly genistin and malonyl genistin to genistein. Results from this study show that ultrasound treatment on lactobacilli cells promotes (P < 0.05) the β-glucosidase activity of cells for the benefit of enhanced (P < 0.05) isoflavone glucosides bioconversion to bioactive aglycones in soymilk.     

A micropolar fluid model of blood flow through a tapered artery with a stenosis

A nonlinear two‐dimensional micropolar fluid model for blood flow in a tapered artery with a single stenosis is considered. This model takes into account blood rheology in which blood consists of microelements suspended in plasma. The classical Navier–Stokes theory is inadequate to describe the microrotations or particles' spin of such suspension in a viscous medium. The governing equations involving unsteady nonlinear partial differential equations are solved using a finite difference scheme. A quantitative analysis performed through numerical computation shows that the axial velocity profile and the flow rate decrease and the wall shear stress increases once the artery is narrower in the presence of the polar effect. Furthermore, the taper angle certainly bears the potential to influence the velocity and the flow characteristics to considerable extent. Copyright © 2010 John Wiley & Sons, Ltd.