New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Synthesis of Highly Functionalized N,N-Diarylamides by an Anodic C,N-Coupling Reaction

We report an innovative, sustainable and straightforward protocol for the synthesis of N,N-diarylamides equipped with nonprotected hydroxyl groups by using electrosynthesis. The concept allows the application of various substrates furnishing diarylamides with yields up to 57 % within a single and direct electrolytic protocol. The method is thereby easy to conduct in an undivided cell with constant current conditions offering a versatile and short-cut alternative to conventional pathways.     

Kinetics and mechanism of trichloroisocyanuric acid/NaNO2-triggered nitration of aromatic compounds under acid-free and Vilsmeier-Haack conditions

Kinetics and mechanism of nitration of aromatic compounds using trichloroisocyanuric acid (TCCA)/NaNO₂, TCCA-N,N-dimethyl formamide (TCCA-DMF)/NaNO₂, and TCCA-N,N-dimethyl acetamide (TCCA-DMA)/NaNO₂ under acid-free and Vilsmeier-Haack conditions. Reactions followed second-order kinetics with a first-order dependence on [Phenol] and [Nitrating agent] ([TCCA], [(TCCA-DMF)], or [(TCCA-DMA)] >> [NaNO₂]). Reaction rates accelerated with the introduction of electron-donating groups and retarded with electron-withdrawing groups, but did not fit well into the Hammett's theory of linear free energy relationship or its modified forms like Brown-Okamoto or Yukawa-Tsuno equations. Rate data were analyzed by Charton's multiple linear regression analysis. Isokinetic temperature (β) values, obtained from Exner's theory for different protocols, are 403.7 K (TCCA-NaNO₂), 365.8 K (TCCA-DMF)/NaNO₂, and 358 K (TCCA-DMA)/NaNO₂. These values are far above the experimental temperature range (303-323 K), indicating that the enthalpy factors are probably more important in controlling the reaction.     

Ultrasonic assisted synthesis of nanocrystalline cellulose as support and reducing agent for Ag nanoparticles: green synthesis and novel effective nanocatalyst for degradation of organic dyes

In this study, nanocrystalline cellulose (NCC) prepared from microcrystalline cellulose using high‐intensity ultrasonication as mechanical method without any chemical treatment. The obtained NCC with around 30–50 nm diameters, utilized as support, reducing and stabilizing agent for in‐situ green and eco‐friendly synthesis of silver nanoparticles (Ag NPs). The catalytic activity of composite was examined for degradation of environmental pollutants. The structure of as‐synthesized composite (Ag@NCC) was characterized by ultraviolet–visible spectroscopy (UV–vis), field emission scanning electron microscopy (FE‐SEM); Transmission electron microscopy (TEM); Energy dispersive spectroscopy (EDS), Fourier transform infrared spectroscopy (FT‐IR), X‐ray diffraction (XRD) and thermogravimetric analysis (TGA). The results of the catalytic reaction experiments showed that spherically shaped silver nanoparticles of around 20 nm distributed on the surface of nanocellulose demonstrated high catalytic efficiency towards the removal of methyl orange (MO) and 4‐nitrophenol (4‐NP).     

Directing-Group-Free C7-Alkylations of N-Alkylindoles Mediated by Cationic Zirconium Complexes: Role of Brønsted Acid for Catalytic Manifold

Highly position selective alkylations of N-alkylindoles at C7-positions have been enabled by cationic zirconium complexes. The strategy provides a straightforward access to install alkyl groups at C7-positions of indoles without a complex directing group. Mechanistic studies provided support for the importance of Brønsted acids in the catalytic manifold.     

Synthesis of Novel Triazole Incorporated Thiazolone Motifs Having Promising Antityrosinase Activity through Green Nanocatalyst CuI-Fe3O4@SiO2 (TMS-EDTA)

In the present work, novel 5-((1-benzyl-1,2,3-triazol-4-yl)methoxybenzylidene)-2-(arylamino)thiazol-4-one thiazolone incorporated triazole derivatives have been designed as tyrosinase inhibitors. The compounds were synthesized through click reaction in good yield. Moreover, the antityrosinas activity of the synthesized derivatives was evaluated. In the search for establishing a click copper-catalyzed azide/alkyne cycloaddition (CuAAC) reaction under strict conditions, in terms of a novel air-stable, a recyclable and efficient magnetic catalyst was planned for new triazole derivatives as a well-organized copper iodide supported on the functionalized Fe₃O₄@SiO₂ core-shell (CuI/Fe₃O₄@SiO₂(TMS-EDTA) nanoparticles). The engineered nanocatalyst synthesized for the first time and characterized by different methods, including FT-IR spectroscopy, XRD, FESEM, EDX, TEM, TGA, and BET analysis. The excellent catalytic performance in ethanol with high surface area (351.7 m²g⁻¹) and short reaction time for diverse functional groups (120–200 min), no use of toxic solvents, reusability of the catalyst, and using eco-friendly conditions are the advantageous of this work. Moreover,the nanocatalyst can be used at least five times without any significant decrease in the yield of the reaction. The thiazolidine-triazole derivatives 9a , 9c , 9e , and 9 g showed promising tyrosinase inhibitory activity with IC₅₀ values in the range of 5.90–9.81 μM. The compounds were found to be considerably more potent tyrosinase inhibitors than the reference inhibitor kojic acid (IC₅₀ = 18.36 μM).     

Mg-catalyzed one-pot preparation of benzimidazoles and spirooxindoles by an immobilized chlorophyll b on magnetic nanoparticles

Chlorophyll b was extracted from Heliotropium europaeum plant, then immobilized on magnetic nanoparticles (Fe₃O₄@SiO₂@Chl-Mg) and found as an efficient and green catalyst for the preparation of a variety of benzimidazoles and spirooxindoles in mild conditions. The catalyst was fully characterized by Fourier-transform infrared (FTIR), ultraviolet–visible (UV–vis) spectroscopy, X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDX), thermogravimetric (TGA), vibrating sample magnetometer (VSM), transmission electron microscopy (TEM), and dynamic light scattering (DLS) analyses. To prove the catalytic influence of Mg over the reactions, the catalytic activity of the demetalated chlorophyll b as well as some other control experiments was investigated. High to excellent yields were achieved for all entries, whether benzimidazole or spirooxindole derivatives at short reaction times. The catalyst could be recovered and reused for several consecutive runs by a simple external magnetic field without any considerable reactivity loss. The properties of the recovered catalyst were investigated by various analyses. Finally, the reasonable mechanisms were proposed for the reactions based on the literature.     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

Study on the mechanism of catalytic synthesis of dimethyldichlorosilane by AlCl3/MIL‐53(Al)@γ‐Al2O3

Dimethyldichlorosilane, one of the most consumed organosilicon monomers in the industry, can be prepared in a highly efficient and environmentally friendly synthesis method of disproportionating methylchlorosilanes. However, the internal mechanism of the reaction remains unclear. In this paper, the mechanism catalyzed by AlCl₃/MIL‐53(Al) and AlCl₃/MIL‐53(Al)@γ‐Al₂O₃ catalysts was calculated at B3LYP/6‐311++G(3df, 2pd) level by using the density functional theory (DFT). The results showed that although the two catalysts had similar active structures, the catalytic effects were significantly different. The Lewis acid center on the surface of γ‐Al₂O₃ in the core‐shell catalyst is complementary to the classic Lewis acid AlCl₃ through the spatial superposition effect, which greatly improves the Lewis acid catalytic activity of AlCl₃/MIL‐53(Al)@γ‐Al₂O₃.