A fully second order implicit/explicit time integration technique for hydrodynamics plus nonlinear heat conduction problems

We present a fully second order implicit/explicit time integration technique for solving hydrodynamics coupled with nonlinear heat conduction problems. The idea is to hybridize an implicit and an explicit discretization in such a way to achieve second order time convergent calculations. In this scope, the hydrodynamics equations are discretized explicitly making use of the capability of well-understood explicit schemes. On the other hand, the nonlinear heat conduction is solved implicitly. Such methods are often referred to as IMEX methods [2], [1], [3]. The Jacobian-Free Newton Krylov (JFNK) method (e.g. [10], [9]) is applied to the problem in such a way as to render a nonlinearly iterated IMEX method. We solve three test problems in order to validate the numerical order of the scheme. For each test, we established second order time convergence. We support these numerical results with a modified equation analysis (MEA) [21], [20]. The set of equations studied here constitute a base model for radiation hydrodynamics.     

A new Rabotnov fractional-exponential function-based fractional derivative for diffusion equation under external force

This work suggested a new generalized fractional derivative which is producing different kinds of singular and nonsingular fractional derivatives based on different types of kernels. Two new fractional derivatives, namely Yang-Gao-Tenreiro Machado-Baleanu and Yang-Abdel-Aty-Cattani based on the nonsingular kernels of normalized sinc function and Rabotnov fractional-exponential function are discussed. Further, we presented some interesting and new properties of both proposed fractional derivatives with some integral transform. The coupling of homotopy perturbation and Laplace transform method is implemented to find the analytical solution of the new Yang-Abdel-Aty-Cattani fractional diffusion equation which converges to the exact solution in term of Prabhaker function. The obtained results in this work are more accurate and proposed that the new Yang-Abdel-Aty-Cattani fractional derivative is an efficient tool for finding the solutions of other nonlinear problems arising in science and engineering.     

Unanimity games and Pareto optimality

A central question in group decision theory is the existence of a simple mechanism that necessarily leads to Pareto optimal outcomes despite noncooperative behavior of the participants. It is shown that the multistage unanimity game is such a mechanism if we assume that the non-cooperative players end at an equilibria which is symmetric and persistent.     

Synthesis of heterocyclic systems with a carbohydrate fragment

Levoglucosenone, the ,ß-unsaturated ketone obtained by the pyrolysis of cellulose, reacts with NH-azoles in the presence of bases. In this process not only normal Michael adducts are formed, but in some cases their hydrates (gem-diols) are also formed. In all cases the addition proceeds stereospecifically and with good yields. 3-Nitro-s-triazole, 3-nitro- and 4-nitropyrazoles, 3-methyl-4-nitropyrazole, 5-nitrotetrazole, 4,5-dicarbomethoxy-v-triazole, 3,4-dinitropyrazole, 3(5)-methylpyrazole, pyrazole, and imidazole have been studied in this reaction. All of the adducts are characterized by NMR- and IR-spectroscopy.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1135–1140, June, 1994.     

Synthesis of fused indoles from 2,4,6-trinitrotoluene

4,6-Dinitro-1-tosylindoline prepared from trinitrotoluene undergoes base-catalyzed condensation with aromatic aldehydes. With salicylaldehyde and 2-hydroxynaphthalene-1-carbaldehyde, the condensation is accompanied by intramolecular nucleophilic substitution for one of the nitro groups to give benzo- and naphthooxepino[4,3,2-cd]indoles, respectively.     

Synthesis of dibenzo[b,f][1,4]oxazepin-11(10H)-ones from 2-nitrobenzoic acids

Base-catalyzed intramolecular nucleophilic substitution for the 2-nitro group in 2-hydroxyanilides of 2-nitrobenzoic acids gave dibenzo[b,f][1,4]oxazepin-11(10H)-ones. In particular, 3-nitrodibenzo[b, f][1,4]oxazepin-11(10H)-one was obtained from N-(2-hydroxyphenyl)-2,4-dinitrobenzamide. The nitro group in the product could also be replaced under the action of O- and S-nucleophiles. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 529–533, March, 2006.     

Interaction of levoglucosenone with malononitrile

Levoglucosenone reacts with malononitrile to form a product with a complex structure, which contains two levoglucosenone molecules and three malononitrile molecules. The conclusion about the structure of the product was based on the data of NMR, IR, and UV spectroscopy and mass spectrometry. The suggested reaction mechanism involves cascade cyclization. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 208–210, January, 1999.     

Antioxidant and Antimicrobial Activities of Erodium arborescens Aerial Part Extracts and Characterization by LC-HESI-MS2 of Its Acetone Extract

The phytochemical analysis of antioxidant and antibacterial activities of Erodium arborescens aerial part extracts constitute the focus of this research. The chemical composition of an acetone extract was investigated using LC-HESI-MS², which revealed the presence of 70 compounds. The major identified components were tannin derivatives. Total polyphenol and total flavonoid contents were assessed in plant extracts (hexane, ethyl acetate, acetone and methanol). The results showed that the acetone extract exhibited the highest contents of polyphenols and flavonoids, 895.54 and 36.39 mg QE/g DE, respectively. Furthermore, when compared to other extracts, Erodium arborescens acetone extract was endowed with the highest antioxidant activity with 2,2-diphenyl-1-picrylhydrazyl (DPPH), ferric reducing antioxidant power (FRAP) and total antioxidant capacity (TAC) tests. In addition, the four extracts of Erodium arborescens showed variable degrees of antimicrobial activity against the tested strains, and the interesting activity was obtained with acetone and methanol extracts.     

Abstract convexity of topical functions

In this paper, we examine properties of topical (increasing and plus-homogeneous) functions defined on a normed linear space ${X}$ . We also study many results of abstract convexity such as support set, polarity and subdifferential set of these functions. Finally, we give a characterization for topical functions with respect to closed downward sets.     

Decolorization Potential of Some Reactive Dyes with Crude Laccase and Laccase-Mediated System

In this study, decolorization of dyestuffs, such as Reactive Red 198, Rem Blue RR, Dylon Navy 17, Rem Red RR, and Rem Yellow RR was studied using laccase and laccase-mediated system. The laccases are known to have an important potential for remediation of pollutants. Among these dyestuffs, decolorization of Rem Blue RR and Dylon Navy 17 was performed with crude laccase under optimized conditions. Vanillin was selected as laccase mediator after screening six different compounds with Rem Yellow RR, Reactive Red 198, and Rem Red RR as substrates. However, Rem Yellow RR was not decolorized by either laccase or laccase-mediated system. It is observed that the culture supernatant contained high laccase activity after treatment with catalase that was responsible for the decolorization. Besides, culture supernatant with high laccase activity as enzyme source was treated with catalase; in this way, the hypothesis that laccase was the enzyme responsible for decolorization was supported. The Rem Blue RR was decolorized with 64.84% under the optimum conditions and Dylon Navy 17 with 75.43% with crude laccase. However, using the laccase and vanillin, the decolorization of Reactive Red 198 and Rem Red RR was found to be 62% and 68%, respectively. Our study demonstrated that the decolorization abilities of laccase and/or laccase mediator systems were based on the types of mediator, the dye structure, and the standard experimental conditions. Also, the electrochemical behaviors of some samples were studied. The redox potentials of these samples were determined using cyclic voltammetry on glassy carbon electrode in phosphate buffer (pH 6) solution.