Statistically disordered short hydrogen bonds in (pipzH2)(cdoH)2 and a comparison with (pipzH2)(cdo)·H2O (pipz is piperazine and cdoH2 is chelidonic acid)

Two related proton‐transfer compounds, namely piperazine‐1,4‐diium 4‐oxo‐4H‐pyran‐2,6‐dicarboxylate monohydrate, C₄H₁₂N₂²⁺·C₇H₂O₆²⁻·H₂O or (pipzH₂)(cdo)·H₂O, (I), and piperazine‐1,4‐diium bis(6‐carboxy‐4‐oxo‐4H‐pyran‐2‐carboxylate), C₄H₁₂N₂²⁺·2C₇H₃O₆⁻ or (pipzH₂)(cdoH)₂, (II), were obtained by the reaction of 4‐oxo‐4H‐pyran‐2,6‐dicarboxylic acid (chelidonic acid, cdoH₂) and piperazine (pipz). In (I), both carboxyl H atoms of chelidonic acid have been transferred to piperazine to form the piperazine‐1,4‐diium ion. The structure is a monohydrate. All potential N—H donors are involved in N—H...O hydrogen bonds. The water molecule spans two anions via the 4‐oxo group of the pyranose ring and a carboxylate O atom. The hydrogen‐bonding motif is essentially two‐dimensional. The structure is a pseudomerohedral twin. In the asymmetric unit of (II), the anion consists of monodeprotonated chelidonic acid, while the piperazine‐1,4‐diium cation is located on an inversion centre. The single carboxyl H atom is disordered in two respects. Firstly, the disordered H atom is shared equally by both carboxylic acid groups. Secondly, the H atom is statistically disordered between two positions on either side of a centre of symmetry and is engaged in a very short hydrogen‐bonding interaction; the relevant O...O distances are 2.4549 (11) and 2.4395 (11) Å, and the O—H...O angles are 177 (6) and 177 (5)°, respectively. Further hydrogen bonding of the type N—H...O places the (pipzH₂)²⁺ cations in pockets formed by the chains of (cdoH)⁻ anions. In contrast with (I), the (pipzH₂)²⁺ cations form hydrogen‐bonding arrays that are perpendicular to the anions, yielding a three‐dimensional hydrogen‐bonding motif. The structures of both (I) and (II) also feature π–π stacking interactions between aromatic rings.     

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.     

Existence of solutions for k-dimensional system of multi-term fractional q-integro-differential equations under anti-periodic boundary conditions via quantum calculus

We prove the existence and uniqueness of solutions for a $k$-dimensional system of multi-term fractional $q$-integro-differential equations via anti-periodic boundary conditions by using some well-known tools of fixed point technique such as Arzelà–Ascoli theorem. We firstly give the corresponding Green function for the boundary value problem and some of its attributes. In addition to, we give a numeric method to verify the analysis for checking the existence of a solution of the system. Finally, an interesting example is presented to illustrate the results.     

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.     

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.