An approach for obtaining approximate formulas for the Rayleigh wave velocity

In this paper, we introduce an approach for finding analytical approximate formulas for the Rayleigh wave velocity for isotropic elastic solids and anisotropic elastic media as well. The approach is based on the least-square principle. To demonstrate its application, we applied it in order to obtain an explanation for Bergmann’s approximation, the earliest known approximation of the Rayleigh wave velocity for isotropic elastic solids, and used it to establish a new approximation. By employing this approach, the best approximate polynomials of the second order of the cubic power and the quartic power in the interval [0, 1] were found. By using the best approximate polynomial of the second order of the cubic power, we derived an approximate formula for the Rayleigh wave speed in isotropic elastic solids which is slightly better than the one given recently by Rahman and Michelitsch by employing Lanczos’s approximation. Also by using this second order polynomial, analytical approximate expressions for orthotropic, incompressible and compressible elastic solids were found. For incompressible case, it is shown that the approximation is comparable with Rahman and Michelitsch’s approximation, while for the compressible case, it is shown that our approximate formulas are more accurate than Mozhaev’s ones. Remarkably, by using the best approximate polynomials of the second order of the cubic power and the quartic power in the interval [0, 1], we derived an approximate formula of the Rayleigh wave velocity in incompressible monoclinic materials, where the explicit exact formulas of the Rayleigh wave velocity so far are not available.     

Luminescent Ink Based on Upconversion of NaYF4:Er,Yb@MA Nanoparticles: Environmental Friendly Synthesis and Structural and Spectroscopic Assessment

NaYF₄:Er,Yb upconversion luminescent nanoparticles (UCNPs) were prepared by hydrothermal methods at 180 °C for 24 h. The X-ray diffraction (XRD) and TEM (transmission electron microscopy) images show that the resulting 60 nm UCNPs possess a hexagonal structure. In this work, maleic anhydride (MA) was grafted on the surface of UCNPs to induce hydrophilic properties. The photoluminescence spectra (PL) show upconversion emissions centered around 545 nm and 660 nm under excitation at 980 nm. The luminescent inks, including UCNPs@MA, polyvinyl alcohol (PVA), deionized water (DI), and ethylene glycol (EG), exhibit suitable properties for screen printing, such as high stability, emission intensity, and tunable dynamic viscosity. The printed patterns with a height of 5 mm and a width of 1.5 mm were clearly observed under the irradiation of a 980 nm laser. Our strategy provides a new route for the controlled synthesis of hydrophilic UCNPs, and shows that the UCNPs@MAs have great potential in applications of anti-counterfeiting packing.     

Screening and evaluation of α-glucosidase inhibitors from indigenous medicinal plants in Dak Lak Province,Vietnam

α-Glucosidase inhibitors have received much attention due to their important use in treating diabetes mellitus. Although some synthetic α-glucosidase inhibitors have been available for a long time, they often cause various unexpected side effects. Thus, the present study was aimed at finding a safe, natural source of α-glucosidase inhibitors. Twenty-six samples of 22 medicinal plants were collected in the Dak Lak province of Vietnam and evaluated for α-glucosidase inhibitory activity. Trunk bark extract from Euonymus laxiflorus Champ (ELC extract) was selected as the best α-glucosidase inhibitor with the smallest IC₅₀ = 0.36 mg/mL against rat-derived α-glucosidase. This extract had a stronger inhibitory activity against α-glucosidase from Saccharomyces cerevisiae (IC₅₀ = 1.32 µg/mL) and Bacillus stearothermophilus (IC₅₀ = 5.15 µg/mL). The potential inhibition against some other enzymes were tested, and the results showed that the ELC extract did not inhibit fungal cellulase but strongly inhibited porcine α-amylase (IC₅₀ = 6.7 µg/mL). The ELC extract also inhibited the proteases papain and bromelain, with IC₅₀ = 339 µg/mL and IC₅₀ = 226 µg/mL, respectively. The thermal and pH stabilities of the ELC extract were also investigated.     

Design,Synthesis, and Biological Evaluation of Tetra-Substituted Thiophenes as Inhibitors of p38α MAPK

p38α mitogen-activated protein kinase (MAPK) plays a role in several cellular processes and consequently has been a therapeutic target in inflammatory diseases, cancer, and cardiovascular disease. A number of known p38α MAPK inhibitors contain vicinal 4-fluorophenyl/4-pyridyl rings connected to either a 5- or 6-membered heterocycle. In this study, a small library of substituted thiophene-based compounds bearing the vicinal 4-fluorophenyl/4-pyridyl rings was designed using computational docking as a visualisation tool. Compounds were synthesised and evaluated in a fluorescence polarisation binding assay. The synthesised analogues had a higher binding affinity to the active phosphorylated form of p38α MAPK than the inactive nonphosphorylated form of the protein. 4-(2-(4-fluorophenyl)thiophen-3-yl)pyridine had a K_i value of 0.6 μm to active p38α MAPK highlighting that substitution of the core ring to a thiophene retains affinity to the enzyme and can be utilised in p38α MAPK inhibitors. This compound was further elaborated using a substituted phenyl ring in order to probe the second hydrophobic pocket. Many of these analogues exhibited low micromolar affinity to active p38α MAPK. The suppression of neonatal rat fibroblast collagen synthesis was also observed suggesting that further development of these compounds may lead to potential therapeutics having cardioprotective properties.     

Conformational Transformations of Sulfur‐Containing Rings: 2‐Methyltetrahydrothiophene Gas‐Phase Structures

Stable conformations of five‐member rings with the prototype cyclopentane are well‐known to exist as twist or envelope structures and are of general interest in chemistry. Here, we report on the conformational analysis of the sulfur‐containing ring 2‐methyltetrahydrothiophene studied by a combination of molecular beam Fourier transform microwave (MB‐FTMW) spectroscopy and quantum chemistry. Two twist conformers were observed, whereby highly accurate molecular parameters could be determined. In addition, the ³⁴S‐isotopologue of the most stable conformer was assigned in natural abundances. Geometry optimizations were performed at different levels of theory and the calculated rotational constants were compared with experimental values. Two transition states optimized at the MP2/6‐311++G(d,p) level using the Berny algorithm could illustrate the intramolecular conversion between both conformers.     

Computational study of the release of H2 from ammonia borane dimer (BH3NH3)2 and its ion pair isomers

High-level electronic structure calculations have been used to map out the relevant portions of the potential energy surfaces for the release of H2 from dimers of ammonia borane, BH3NH3 (AB). Using the correlation-consistent aug-cc-pVTZ basis set at the second-order perturbation MP2 level, geometries of stationary points were optimized. Relative energies were computed at these points using coupled-cluster CCSD(T) theory with the correlation-consistent basis sets at least up to the aug-cc-pVTZ level and in some cases extrapolated to the complete basis set limit. The results show that there are a number of possible dimers involving different types of hydrogen-bonded interactions. The most stable gaseous phase (AB)2 dimer results from a head-to-tail cyclic conformation and is stabilized by 14.0 kcal/mol with respect to two AB monomers. (AB)2 can generate one or two H2 molecules via several direct pathways with energy barriers ranging from 44 to 50 kcal/mol. The diammoniate of diborane ion pair isomer, [BH4-][NH3BH2NH3+] (DADB), is 10.6 kcal/mol less stable than (AB)2 and can be formed from two AB monomers by overcoming an energy barrier of approximately 26 kcal/mol. DADB can also be generated from successive additions of two NH3 molecules to B2H6 and from condensation of AB with separated BH3 and NH3 molecules. The pathway for H2 elimination from DADB is characterized by a smaller energy barrier of 20.1 kcal/mol. The alternative ion pair [NH4+][BH3NH2BH3-] is calculated to be 16.4 kcal/mol above (AB)2 and undergoes H2 release with an energy barrier of 17.7 kcal/mol. H2 elimination from both ion pair isomers yields the chain BH3NH2BH2NH3 as product. Our results suggest that the neutral dimer will play a minor role in the release of H2 from ammonia borane, with a dominant role from the ion pairs as observed experimentally in ionic liquids and the solid state.     

Application of the Mass Spectrometry for Determining Lead Isotopic Composition in Galena Samples of Vietnam

Lead isotopic composition of galena in lead- zine deposits play an important role in determining their age and genesis.     

A strong convergence theorem for Tseng’s extragradient method for solving variational inequality problems

In this paper, we introduce a new algorithm for solving variational inequality problems with monotone and Lipschitz-continuous mappings in real Hilbert spa     

On a Furstenberg-Katznelson-Weiss Type Theorem over Finite Fields

Using Fourier analysis, Covert, Hart, Iosevich, and Uriarte-Tuero (2008) showed that if the cardinality of a subset of the 2-dimensional vector space over a finite field with q elements is ≥ ρq ², with q^-1/2 << r ￡ 1{q^{-1/2} \ll \rho \leq 1} then it contains an isometric copy of ≥ cρq ³ triangles. In this note, we give a graph theoretic proof of this result.     

Numerical study of wave overtopping of a seawall supported by porous structures

This paper presents a VOF-based two-phase flow model for the simulation of wave interactions with seawall supported by a porous terrace. Firstly, the model was verified against laboratory data in a simple case for wave overtopping of a vertical wall. Comparison of computed and measured wave properties showed reasonably good agreement. The model was then applied to study the interactions of waves and a seawall protected by porous structures with a permeable terrace. The application results showed that the overtopping rate was strongly related to the energy dissipation through the drag force; the porous reef and terrace were very effective to produce a low crest type seawall. It is concluded that there exist two optimum values of porosity of the submerged reef, about of 0.25 and 0.7, that give minimum overtopping rates. Whereas, there is an effective range of porosity of the permeable terrace varying from 0.4 to 0.65 for significantly reducing the overtopping rate. The verification results confirm that the VOF-based two-phase flow model is sufficient robust to simulate the wave overtopping of coastal structures with reasonable accuracy.