Square-like Functions Generated by a Composite Wavelet Transform

The classical square functions play important role in Harmonic Analysis and have a very direct connection with L ₂-estimates and Littlewood-Paley theory. In this paper we introduce a new variant of square-like functions generated by some composite wavelet transform. We establish Calderón-type reproducing formula and then prove L ₂-boundedness of newly defined square-like functions.     

Synthesis and characterization of crosslinkable polyimides

A series of copolyimides were prepared from benzophenone-3,3′,4,4′-tetracarboxylic dianhydride (BTDA) and various aromatic diamines which contain a fluorenyl group and/or alkyl substituents in ortho position to the amine groups. The effect of the chemical composition on the glass transition temperature (T_g), thermal stability as well as on the dielectric constant of these polymers was studied. High T_g polymers (T_g ranging from 260 °C to 370 °C), withstanding temperatures as high as 400 °C for 10 h and having a low dielectric constant (from 2.6 to 3.1) were successfully synthesized. All these polymers were able to crosslink under UV or thermal treatments.     

Experimental determination of the isothermal (vapour + liquid) equilibria of binary aqueous solutions of sec-butylamine and cyclohexylamine at several temperatures

The vapour pressures of (sec-butylamine + water), (cyclohexylamine + water) binary mixtures, and of pure sec-butylamine and cyclohexylamine components were measured by means of two static devices at temperatures between 293 (or 273) K and 363 K. The data were correlated with the Antoine equation. From these data, excess Gibbs functions (G^E) were calculated for several constant temperatures and fitted to a fourth-order Redlich–Kister equation using the Barker’s method. The (cyclohexylamine + water) system shows positive azeotropic behaviour for all investigated temperatures. The two binary mixtures exhibit positive deviations in G^E for all investigated temperatures over the whole composition range.     

Integrated 3D-QSAR,molecular docking,and molecular dynamics simulation studies on 1,2,3-triazole based derivatives for designing new acetylcholinesterase inhibitors

Alzheimer’s disease (AD) is a multifactorial and polygenic disease. It is the most prevalent reason for dementia in the aging population. A dataset of twenty-six 1,2,3-triazole-based derivatives previously synthetized and evaluated for acetylcholinesterase inhibitory activity were subjected to the three-dimensional quantitative structure-activity relationship (3D-QSAR) study. Good predictability was achieved for comparative molecular field analysis (CoMFA) (Q² = 0.604, R² = 0.863, r_ext² = 0.701) and comparative molecular similarity indices analysis (CoMSIA) (Q² = 0.606, R² = 0.854, r_ext² = 0.647). The molecular features characteristics provided by the 3D-QSAR contour plots were quite useful for designing and improving the activity of acetylcholinesterase of this class. Based on these findings, a new series of 1,2,3-triazole based derivatives were designed, among which compound A1 with the highest predictive activity was subjected to detailed molecular docking and compared to the most active compound. The selected compounds were further subjected to 20 ns molecular dynamics (MD) simulations to study the comparative conformation dynamics of the protein after ligand binding, revealing promising results for the designed molecule. Therefore, this study could provide worthy guidance for further experimental analysis of highly effective acetylcholinesterase inhibitors.     

Some generalizations of Bessel and Flett potentials associated to the Laplace–Bessel differential operator

We introduce the notion of bi-parametric potential-type operators, which generalize the Bessel and Flett potentials associated to singular Laplace–Bessel differential operator. Explicit inversion formulas for them are obtained by using a special wavelet-like transform, generated by the so-called ‘modified beta-semigroup’.     

Phase equilibrium properties of binary aqueous solutions of benzylamine, 1,2-bis(2-aminoethoxy)ethane,or 2-[2-(dimethylamino)ethoxy]ethanol

The vapour pressures of (benzylamine + water), {1,2-bis(2-aminoethoxy)ethane + water}, or {2-[2-(dimethylamino)ethoxy]ethanol + water} binary mixtures, and pure 2-[2-(dimethylamino)ethoxy]ethanol component were measured by means of two static devices at temperatures between (283.15 and 363.15 (or 323.15)) K. The data were correlated with the Antoine equation. From these data, excess Gibbs functions (G^E) were calculated for several constant temperatures and fitted to a fourth-order Redlich–Kister equation using the Barker’s method. The (benzylamine + water) binary mixture exhibits positive deviations in G^E for (303.15 < T/K < 323.15) and a sinusoidal shape in G^E for T > 323.15 K over the whole composition range. The aqueous 1,2-bis(2-aminoethoxy)ethane or {2-[2-(dimethylamino)ethoxy]ethanol + water} solutions exhibit negative deviations in G^E for all investigated temperatures over the whole composition range.     

On the Gauss-Weierstrass summability of multiple trigonometric series at µ-smoothness points

The notion of μ-smoothness points of periodic functions of several variables is introduced and the rate of convergence of the Gauss-Weierstrass means of relevant Fourier series at these points is investigated.