An efficient Levenberg–Marquardt method with a new LM parameter for systems of nonlinear equations

A modified Levenberg–Marquardt method for solving singular systems of nonlinear equations was proposed by Fan [J Comput Appl Math. 2003;21;625–636]. Using trust region techniques, the global and quadratic convergence of the method were proved. In this paper, to improve this method, we decide to introduce a new Levenberg–Marquardt parameter while also incorporate a new nonmonotone technique to this method. The global and quadratic convergence of the new method is proved under the local error bound condition. Numerical results show the new algorithm is efficient and promising.     

KF/clinoptilolite nanoparticles as a novel catalyst for the green synthesis of chromens using three component reactions of 4‐hydroxycoumarins: Study of antioxidant activity

In this research, the green synthesis of chromen derivatives in good yields is described via three‐component reactions of 4‐hydroxycumarine, aldehydes or ketones, and methyl ketones in the presence of KF/clinoptilolite nanoparticles (KF/CP‐NPs) under solvent‐free conditions at 50°C in low time. The present methodology suggests some advantages such as low reaction time, easy and simple procedure, green method, inexpensive catalyst, high yield of product, and existence of different substrates for performing these reactions. In addition, it should be mentioned that antioxidant activity was studied for some prepared compounds, such as 4a–4d, by DPPH radical trapping and reducing potential tests of ferric ion and then comparing results with TBHQ and BHT as synthetic antioxidants. In this study, compounds 4c was shown to have moderate DPPH radical trapping, and compounds 4b and 4d displayed good reducing power of ferric ion.     

Predict the thermal conductivity of SiO2/water–ethylene glycol (50:50) hybrid nanofluid using artificial neural network

Journal of Thermal Analysis and Calorimetry - In the current work, after generating experimental data points for different volume fraction of nanoparticles ( $$\phi$$ ) and different temperatures,...     

Laccase-catalyzed,aerobic oxidative coupling of 4-substituted urazoles with sodium arylsulfinates: Green and mild procedure for the synthesis of arylsulfonyl triazolidinediones

The direct aerobic oxidation of 4-substituted urazoles using the laccase enzyme from Trametes versicolor in a phosphate buffer solution at ambient temperature, and subsequent cross-coupling with sodium benzenesulfinates was investigated to afford arylsulfonyl-1,2,4-triazolidine-3,5-dione derivatives in good to high yields.     

Zeolite nanoparticles (H-ZSM5) as a highly efficient,green, and reusable heterogeneous catalyst for selective oxidation of sulfides to sulfoxides under mild conditions

H-ZSM5 is applied as an efficient, highly reusable, and heterogeneous catalyst for the oxidation of sulfides to sulfoxides using 30% H₂O₂ under solvent-free conditions at room temperature. A variety of aromatic and aliphatic sulfides with different functional groups were successfully oxidized with good to excellent yields in short reaction times. The catalyst can be easily recovered by simple filtration and recycled for several consecutive runs without any significant loss of its catalytic activity.     

Spectrophotometric determination of acidity constants by two-rank annihilation factor analysis

Annihilation of the contribution of one chemical component from the original data matrix is a general method in rank annihilation factor analysis (RAFA). However, RAFA is not applicable for studying the protonation equilibria of multiprotic acids. In this work, a two-rank annihilation factor analysis (TRAFA) method was proposed for determination of the acidity constants of diprotic acids. After recording the electronic absorbance spectra of the acids at different pH, the contributions of both H₂A and A²⁻ were annihilated from the absorbance data, which made feasible the determination of two successive acidity constants. The method was validated by analysis of simulated data and its application to the determination of the acidity constants of calmagite, as a reference compound. A close agreement was obtained between the resulted values by TRAFA and the declared values. Indeed, the method was used for determination of the acidity constants of two new chromenone derivatives in binary solvents mixtures of methanol and water. The effects of changing solvent composition on acidity constant data were explained by linear solvation free energy relationships (LSFER) utilizing solvatochromic parameters.     

General fractional variational problem depending on indefinite integrals

In this report, we consider two kind of general fractional variational problem depending on indefinite integrals include unconstrained problem and isoperimetric problem. These problems can have multiple dependent variables, multiorder fractional derivatives, multiorder integral derivatives and boundary conditions. For both problems, we obtain the Euler-Lagrange type necessary conditions which must be satisfied for the given functional to be extremum. Also, we apply the Rayleigh-Ritz method for solving the unconstrained general fractional variational problem depending on indefinite integrals. By this method, the given problem is reduced to the problem for solving a system of algebraic equations using shifted Legendre polynomials basis functions. An approximate solution for this problem is obtained by solving the system. We discuss the analytic convergence of this method and finally by some examples will be showing the accurately and applicability for this technique.     

A cellular uptake and cytotoxicity properties study of gallic acid-loaded mesoporous silica nanoparticles on Caco-2 cells

In this study, the effects of intracellular delivery of various concentrations of gallic acid (GA) as a semistable antioxidant, gallic acid-loaded mesoporous silica nanoparticles (MSNs-GA), and cellular uptake of nanoparticles into Caco-2 cells were investigated. MSNs were synthesized and loaded with GA, then characterized using transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy, N₂ adsorption isotherms, X-ray diffraction, and thermal gravimetric analysis. The cytotoxicity of MSNs and MSNs-GA at low and high concentrations were studied by means of 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide (MTT) test and flow cytometry. MSNs did not show significant toxicity in various concentrations (0–500 μg/ml) on Caco-2 cells. For MSNs-GA, cell viability was reduced as a function of incubation time and different concentrations of nanoparticles. The in vitro GA release from MSNs-GA exhibited the same antitumor properties as free GA on Caco-2 cells. Flow cytometry results confirmed those obtained using MTT assay. TEM and fluorescent microscopy confirmed the internalization of MSNs by Caco-2 cells through nonspecific cellular uptake. MSNs can easily internalize into Caco-2 cells without deleterious effects on cell viability. The cell viability of Caco-2 cells was affected during MSNs-GA uptake. MSNs could be designed as suitable nanocarriers for antioxidants delivery.