Lyapunov-type inequalities for nonlinear systems

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.     

Mn(III)-based C-C bond formation: regioselective α′-allylation of various α,β-unsaturated, α and β-alkoxy α,β-unsaturated ketones

The Manganese(III)-based regioselective α′-keto radical generation of unsaturated ketones is a versatile synthetic procedure with broad applicability. The generated α′-keto radical slowly creates a metal enolate in a solvent at reflux. The resultant metal enolate affords the corresponding α′-allylated α,β-unsaturated ketones in good yields. This method is the first example of the metal mediated regioselective α′-allylation of α,β-unsaturated ketones. The ketones that have α or β-alkoxy groups also work efficiently.     

5-HT1A Serotonergic, α-Adrenergic and Opioidergic Receptors Mediate the Analgesic Efficacy of Vortioxetine in Mice

Vortioxetine is a multimodal antidepressant drug that affects several brain neurochemicals and has the potential to induce various pharmacological effects on the central nervous system. Therefore, we investigated the centrally mediated analgesic efficacy of this drug and the mechanisms underlying this effect. Analgesic activity of vortioxetine (5, 10 and 20 mg/kg, p.o.) was examined by tail-clip, tail-immersion and hot-plate tests. Motor performance of animals was evaluated using Rota-rod device. Time course measurements (30–180 min) showed that vortioxetine (10 and 20 mg/kg) administrations significantly increased the response latency, percent maximum possible effect and area under the curve values in all of the nociceptive tests. These data pointed out the analgesic effect of vortioxetine on central pathways carrying acute thermal and mechanical nociceptive stimuli. Vortioxetine did not alter the motor coordination of mice indicating that the analgesic activity of this drug was specific. In mechanistic studies, pre-treatments with p-chlorophenylalanine (serotonin-synthesis inhibitor), NAN-190 (serotonin 5-HT_1A receptor antagonist), α-methyl-para-tyrosine (catecholamine-synthesis inhibitor), phentolamine (non-selective α-adrenoceptor blocker), and naloxone (non-selective opioid receptor blocker) antagonised the vortioxetine-induced analgesia. Obtained findings indicated that vortioxetine-induced analgesia is mediated by 5-HT_1A serotonergic, α-adrenergic and opioidergic receptors, and contributions of central serotonergic and catecholaminergic neurotransmissions are critical for this effect.     

New antidepressant drug candidate: Hypericum montbretti extract

This study was designed to investigate possible antidepressant-like effects of the extract prepared from the flowers of Hypericum montbretti Spach. (Guttiferae, Clusiaceae). Phytochemical constituents of the methanolic extract were analysed by HPLC method. The main flavonoid component was detected as rutin, and another highly concentrated phenolic compound was quercitrin. Antidepressant activity of the extract was examined by tail suspension and modified forced swimming tests, whereas the motor coordination of the animals was tested by the Rota-Rod apparatus. Reboxetine at a dose of 20 mg?kg?1 was used as a reference drug. Dose-dependent antidepressant activity was observed in both tests following the administration of extract at 100 and 250 mg?kg?1 doses. To the best of our knowledge, this is the first study reporting the antidepressant activity of H. montbretti extract. Additionally, the results of this work support previous papers reporting the antidepressant activity of rutin.     

A Study of Adsorption of Water Vapour on Wool under Static and Dynamic Conditions

Adsorption of water vapour on wool provides not only textile comfort, but also convenience in transportation due to increase in its bulk density. The adsorption and desorption isotherms of water vapour for wool were determined by both volumetric technique using a Coulter Omnisorp 100CX instrument and gravimetric method employing a Cahn 2000 electronic microbalance. Adsorption isotherm fitting to B.E.T. model and hysteresis on desorption was observed. The average effective diffusion coefficient of water in wool was found to be 8.4 × 10^-14 m²s^-1 at 25°C from gravimetric data. The effects of packing height and air velocity on the breakthrough curves were also investigated in the wool packed columns. For pseudo first order model, k values changing between 0.33 × 10^-6 – 69 × 10^-6 s^-1 was obtained for 2.2–6.4 cm s^-1 air velocity and 0.05–0.20 m packing height ranges.     

Photoconductive novel mesomorphic oxotitanium phthalocyanines

The synthesis and photoconductivity properties of the alkylthia and triethyleneoxysulfonyl substituted oxotitanium(IV) phthalocyanines (1a and 2a) are reported for the first time. The new compounds have been characterized by elemental analysis, IR, ¹H and ¹³C NMR spectroscopy, electronic spectroscopy and mass spectroscopy. The mesogenic properties of these new materials were studied by differential scanning calorimetry and optical microscopy. The electrical dark conductivities (σ_d) and photoconductivities (σ_ph) of deposited films of 1a and 2a were investigated in various media with different concentrations of oxygen. Molecular oxygen increases photoconductivities (σ_ph) significantly. The photoconductivity mechanism and formation of Pc⁺ which is positive charge carrier under the light irradiation of the phthalocyanine molecules are demonstrated using the theoretical calculations. The geometries of the oxotitanium(IV) phthalocyanines (TiOPc) are optimized with PM3 semi-empirical method, and their visible absorption maxima are calculated with ZINDO/S method. The results agree well with the observed values. It was found that for the calculation of visible absorption of neutral and positively charged substituted TiOPc molecules using ZINDO/S method could rapidly yield excellent results. Dipole moment, HOMO, LUMO energies and atomic charges are also calculated for clarification of the oxygen effect on the photoconductivity using PM3 and ZINDO/S methods.     

Synthesis and characterization of liquid crystalline tetra- and octa-substituted novel phthalocyanines

Methylene-bridged tetra- and octa-(13,17-dioxa nonacosane-15 sulfanyl)-substituted metal free- and Ni(II) phthalocyanines were synthesized from the corresponding phthalonitrile (3, 4) derivatives in the presence of the anhydrous metal salt (NiCl₂) or a strong organic base. The new compounds were characterized by elemental analyses, UV/Vis, IR, NMR and mass spectra. The mesogenic properties of these materials were studied by differential scanning calorimetry (DSC), optical microscopy and X-ray diffraction investigations. X-ray diffraction patterns of the mesophase confirm that tetra- and octa-substituted compounds (3a–b, 4a–b) form hexagonal columnar mesophases (Col_h). We indicated that addition of the methylene-bridged phthalocyanine (Pc) core can either decrease the liquid crystal phase transition temperatures or extend the liquid crystal temperature range to include room temperature. Also, the Pc compounds (3a, 3b, 4a and 4b) are liquid crystals at room temperature. These properties of the Pc complexes provide some advantages such as easily obtaining an ordered film for sensor applications. Computational modelling work was combined with X-ray diffraction investigation to validate the diameter of the phthalocyanine molecule (3b).     

A note on Tang and He’s paper

In this paper, we establish new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which improve the recent results of Tang and He [X.H. Tang, X. He, Lower bounds for generalized eigenvalues of the quasilinear systems, J. Math. Anal. Appl. 385 (2012) 72-85] when 1 < p_i < 2 for i = 1, 2, … , n.