Symbolic integration of meromorphic differential systems via Dirichlet functions

We present a symbolic technique for computing the exact or approximate solutions of linear differential systems with meromorphic coefficients. To any system of that form, we attach a non-commutative generating series F. The combinatorial decomposition of F allows to get the solution as a polynomial in Dirichlet functions, or hypergeometric functions, that are built from the coefficients of the system.     

Simultaneous Determination of Paracetamol,Ibuprofen, and Caffeine in Tablets by Molecular Absorption Spectroscopy Combined with Classical Least Square Method

In this paper, the classical least-squares (CLS) method with molecular absorption spectrophotometric measurement was used to determine simultaneously paracetamol (PAR), ibuprofen (IBU), and caffeine (CAF) in tablets. The absorbance spectra of the standard solutions and samples were measured over a wavelength from 220 to 300 nm with a 0.5 nm step. The concentration of PAR, IBU, and CAF in the sample solutions was calculated by using Visual Basic for Applications (VBA) and a program called CLS-Excel written in Microsoft Excel 2016. The method and the CLS-Excel program were tested on mixed standard laboratory samples with different PAR, IBU, and CAF concentration ratios, and they showed only small errors and a satisfying repeatability. An analytical procedure for tablets containing PAR, IBU, and CAF was developed. The reliability of the procedure was proved via the recovery and repeatability of the analysis results with an actual tablet sample and by comparing the mean contents of active substances in the tablets obtained from the analytical procedure with the HPLC method. The procedure is simple with a reduced cost compared with the HPLC standard method.     

Regularization of a two-dimensional strongly damped wave equation with statistical discrete data

In this paper, we consider an inverse problem for a strongly damped wave equation in two dimensional with statistical discrete data. Firstly, we give a representation for the solution and then present a discretization form of the Fourier coefficients. Secondly, we show that the solution does not depend continuously on the data by stating a concrete example, which makes the solution be not stable and thus the present problem is ill-posed in the sense of Hadamard. Next, we use the trigonometric least squares method associated with the Fourier truncation method to regularize the instable solution of the problem. Finally, the convergence rate of the error between the regularized solution and the sought solution is estimated and also investigated numerically.     

Phosphorene-Based Electrocatalysts

Phosphorene, generally defined as two-dimensional (2D) black phosphorus (BP) with monolayered or few-layered structure, has emerged as a promising member of the family of 2D materials. Since its discovery in 2014, extensive research has been focused on broadening its applications, covering the biological, photoelectric, and electrochemical fields, owing to the unique physicochemical and structural properties. As a single-elemental material, phosphorene has demonstrated its applicability for the preparation of efficient electrocatalysts for hydrogen evolution reaction (HER), oxygen evolution reaction (OER), nitrogen reduction reaction (NRR), and other electrocatalytic applications. In this Minireview, a summary of the very recent research progresses of phosphorene in electrocatalysis is offered, with a special focus on the effective synthetic strategies towards performance improvement. In the concluding section, challenges and perspectives are also discussed.     

Intertwined Titanium Carbide MXene within a 3 D Tangled Polypyrrole Nanowires Matrix for Enhanced Supercapacitor Performances

The exploration of the rational design and synthesis of unique and robust architectured electrodes for the high capacitance, rate capability, and stability of supercapacitors is crucial to the future of energy storage technology. Herein, an in situ synthesis of multilayered titanium carbide MXene tightly caging within a 3 D conducting tangled polypyrrole (PPy) nanowire (NW) network is proposed as an effective strategy to prevent the aggregation of MXene, profoundly enhancing the electrochemical performance of the supercapacitor. Owing to the beneficial effects of an ideal 3 D interconnected porous structure and high electrical conductivity, the obtained electrode exhibits fast charge and ion transport kinetics as well as full usage of active material. As expected, the 3 D Ti₃C₂T_x@PPY NW exhibits a specific capacitance five times higher than that of pristine MXene (610 F g⁻¹), a good rate capability up to a current density of 25 A g⁻¹, and excellent stability with 100 % retention after 14 000 cycles at 4 A g⁻¹, outperforming the known state-of-the-art MXene-based supercapacitor. Our work provides a facile method for enhancing the performance of MXene-based energy storage devices.     

A new route to triphenylpyridines utilizing ketoximes as building blocks via cascade reactions under iron‐organic framework catalysis

Iron‐based metal–organic framework VNU‐20 was utilized as a heterogeneous catalyst for cascade reactions between ketoximes and dibenzyl ether to produce 2,4,6‐triphenylpyridines. Additionally, benzyl alcohol and (dimethoxymethyl)benzene could be used as an alternative starting materials for the transformation. The oxidant exhibited a remarkable impact on the reactions, and di‐tert‐butylperoxide was the most appropriate candidate. The VNU‐20 displayed higher efficiency than many homogeneous and heterogeneous catalysts. The catalyst was reusable for the cascade reactions without a noticeable deterioration in catalytic activity. This transformation is new, and would offer alternative routes to triphenylpyridines utilizing ketoximes as building blocks.     

Littlewood-Paley Inequalities on Manifolds with Ends

Potential Analysis - Let M be a manifold with ends $\mathbb {R}^{m}\sharp \mathcal {R}^{n}$ with m > n >?2 which is a non-doubling manifold. In this paper we prove a...     

A Simple Nickel Catalyst Enabling an E-Selective Alkyne Semihydrogenation

Stereoselective alkyne semihydrogenations are attractive approaches to alkenes, which are key building blocks for synthesis. With regards to the most atom-economic reducing agent dihydrogen (H₂), only few catalysts for the challenging E-selective alkyne semihydrogenation have been disclosed, each with a unique substrate scope profile. Here, we show that a commercially available nickel catalyst facilitates the E-selective alkyne semihydrogenation of a wide variety of substituted internal alkynes. This results in a simple and broadly applicable overall protocol to stereoselectively access E-alkenes employing H₂, which could serve as a general method for synthesis.     

Interaction between excitons in 3D and 2D laser-excited semiconductors

Analytical expressions of the exciton-exciton interaction in 3D and 2D laser-excited semiconductors are approximately derived in rather easy-to-handle forms which enable us to study in detail their dependences on the exciton momenta, the momentum transferred between two excitons and the electron-hole mass ratio.We would like to thank Prof. Nguyen Van Hieu and Prof. Dao Vong Due for their support given to us in the research of highly excited media.     

Two-phonon processes in Heisenberg ferromagnet

Using the method of double-time retarded Green function, an expression for the spin energy spectrum including the contributions of one-phonon and two-phonon processes has been derived. Calculations have been performed using the spin wave approximation. The broadening of the energy level is roughly estimated in a peculiar case.I would like to thank Dr. Dagmat Fraitová for her advice and help.