Solvability of a nonlinear fifth‐order difference equation

Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.     

Non-conservation of excitons in finite molecular chain

We have analyzed a linear molecular chain with exciton excitations when the number of excitons is not conserved. The dispersion law depends on two independent variables and it is surfaced in a 3D plot. The same conclusion is valid for the concentrations of excitons and exciton pairs. As it was expected, physical characteristics of the finite chain depend on spatial coordinates. All results are compared to the corresponding results of an infinite chain.     

Study of the Retention Behavior of Newly Synthesized s-Triazine Derivatives in RP TLC Systems,and the Lipophilicity of the Compounds

JPC – Journal of Planar Chromatography – Modern TLC - The chromatographic behavior of nine newly synthesized s-tri-azines has been studied by thin-layer chromatography on C18/UV254...     

Study of the Lipophilicity and Retention Behavior of Some s-Triazine Derivatives on Aminoplast and Cellulose

JPC – Journal of Planar Chromatography – Modern TLC - The chromatographic behavior of four groups of s-triazine derivatives (15 compounds) has been studied on aminoplast and cellulose...     

A LFER Kinetic Study of The Reaction of 5‐Substituted Orotic Acids with Diazodiphenylmethane

Linear free energy relationships (LFER) were applied to the kinetic data for the reaction of 5‐substituted orotic acids, series 1 , with diazodiphenylmethane (DDM) in N,N–dimethylformamide and compared with results obtained for 2‐substituted benzoic acids, series 2 . The correlation analysis of the kinetic data with σ substituent parameters was carried out using SSP (single substituent parameter) methods. From the sign and value of proportinality constant ρ, lower sensitivity to the substituent effect was obtained in series 1 , 0.876, than in the series 2 , 1.877. Evaluation of substituent “ortho‐effect” was performed using the Charton model, which includes the steric substituent parameter, and Fujita and Nishioka's model, which describes the total ortho‐effect as contribution of ordinary polar effect, the ortho‐steric and ortho‐polar effects. Results of correlations, obtained by using the Charton model, showed highest contribution of the polar effect, 0.861 vs. 2.101, whereas the steric effect is of lowest significance, 0.117 vs. 0.055, for series 1 and 2 , respectively. Also, a low negative value of coefficient with the steric effect, –0.08, obtained from the Fujita–Nishioka model indicated low steric effect, influencing a decrease of the reaction rate in series 1 . The structural and substituent effects were also studied by using the density functional theory method, and together with kinetic data, it gave a better insight into the influence of the effect of both geometry and substituent on the π?electron density shift induced reactivity of investigated acids.     

Pulsed corona discharge driven by Marx generator: Diagnostics and optimization for NOx treatment

A compact, repetitive Marx generator with an external trigger is constructed and coupled with a wire-to-plate corona reactor for a positive pulsed corona discharge studies. The reactor resistance and capacitance behavior during the pulse was observed. It was found that the reactor's capacitance increases three times during the pulse due to the streamer propagation from anode to grounded electrode. Using the time development of the capacitance and resistance during the pulse and the reactor inter-electrode distance, the streamer velocity has been calculated to be 1 × 10⁶ m/s, for system arrangement presented in this work. As an indicator of chemical activity of pulsed corona, ozone production was measured. Emission spectroscopy measurements in the UV region were performed to detect species that appear in the discharge and to determine vibrational and rotational temperatures, which are found to be 3200 K and 340 K respectively. As a measure of pollution control potential of the constructed pulsed corona system, NO oxidation efficiency was investigated and compared with results presented in literature. It was shown that pulsed corona systems with significantly longer pulse durations are competitive with several times shorter pulse duration systems, which implies that chemical efficiency of secondary streamers is comparable with efficiency of primary streamers.     

Disposable Biosensor Based on Amidase/CeO2/GNR Modified Inkjet‐printed CNT Electrodes‐droplet Based Paracetamol Detection in Biological Fluids for “Point‐of‐care” Applications

A disposable acetaminophen biosensor based on inkjet‐printed CNT electrodes (IJPCNT) modified with amidase/cerium dioxide@graphene nanoribbons composite was developed (ACeO2@GNR/IJPCNT). The enzyme amidase A was used for the first time as a recognition element. Inkjet‐printed CNT electrodes served as a basis for the construction of a biosensor that enables droplet detection using 5 μL sample volume. The biosensor showed high selectivity, sensitivity, a low detection limit of 0.18 μM and a wide working linear range from 1 to 100 μM. The proposed approach allows fast and reliable detection of acetaminophen in biological fluids with negligible matrix effect and remarkable reproducibility.     

Study of Quantitative Structure-Retention Relationships for s-Triazine Derivatives in Different RP HPTLC Systems

JPC – Journal of Planar Chromatography – Modern TLC - Quantitative structure-retention relationships (QSRR) have been used to study the chromatographic behavior of some s-triazines....     

Thermodynamic and kinetic properties of phonons in cylindrical quantum dots

The Green's function technique, suitable for analyses of spatially deformed structures, is developed in this paper and applied to phonon system. The thermodynamic and kinetic phonon properties of cylindrical quantum dots are analysed using a developed method. As a consequence of the applied new method the configurational dependence of diffusion coefficient and dot's density were included into calculations. Maximum of diffusion and minimum of density is located in central part of the cylindrical quantum dot. All thermodynamic and kinetic characteristics of quantum dot are exponentially small at low temperatures. The low phonons specific heat as well as the low thermal conductivity lead to conclusion that in cylindrical quantum dots exist more convenient conditions for appearance of electron superconductivity.