Weak Module Amenability for Semigroup Algebras

We study the weak module amenability of Banach algebras which are Banach module over another Banach algebra with compatible actions. As an example we show that the semigroup algebra of a commutative inverse semigroup is always weakly amenable as a module over the semigroup algebra of its subsemigroup of idempotents.     

The mechanism of reaction of tetraalkyltins with mercuric carboxylates in methanol

In the reaction of mercuric carboxylates with tetraalkyltins in methanol, rate constrants for attack of the species (RCO₂)₂ Hg increase along the series R = t-Bu < Et < Me < Ph < ClCH₂CH₂ < MeOCH₂ < ClCH₂ which suggests an open transition state for these S_E2 substitutions.     

Electrochemical oxidation of catechol in the presence of cyclopentadiene. Investigation of electrochemically induced Diels-Alder reactions

We describe the synthesis and kinetic evaluation of compounds from [4 + 2] alone and [4 + 2] followed by [2 + 2] cycloaddition reactions of electrochemically generated o-benzoquinone with 1,3-cyclopentadiene.     

2-Domination number of generalized Petersen graphs

Let \(G=(V,E)\) be a graph. A subset \(S\subseteq V\) is a k-dominating set of G if each vertex in \(V-S\) is adjacent to at least k vertices in S. The k-domination number of G is the cardinality of the smallest k-dominating set of G. In this paper, we shall prove that the 2-domination number of generalized Petersen graphs \(P(5k+1, 2)\) and \(P(5k+2, 2)\), for \(k>0\), is \(4k+2\) and \(4k+3\), respectively. This proves two conjectures due to Cheng (Ph.D. thesis, National Chiao Tung University, 2013). Moreover, we determine the exact 2-domination number of generalized Petersen graphs P(2k, k) and \(P(5k+4,3)\). Furthermore, we give a good lower and upper bounds on the 2-domination number of generalized Petersen graphs \(P(5k+1, 3), P(5k+2,3)\) and \(P(5k+3, 3).\)     

Analytical Holographic Superconductor with Backreaction Using AdS 3/CFT 2

The holographic model for a two-dimensional superconductor has been investigated by considering the three-dimensional gravity in the bulk. To find the critical temperature, we used the Sturm–Liouville variational method. Where as the same method is applied for calculating the condensation of the dual operators on the boundary. We included the back reactions on the metric by a combination of the perturbation method of the fields with respect to the small parameter and then applying the variational integrals on the resulting equations of the motion. The critical temperature has been successfully obtained on the backreaction effects, and we showed that it dropped with a rise in the backreaction of the fields, and it makes the condensation harder. We can use our analytical results to support the numerical data which was reported previously.     

Geometrothermodynamics of higher dimensional black holes

We study the thermodynamics and geometrothermodynamics of different black hole configurations in more than four spacetime dimensions. We use the response functions to find the conditions under which second order phase transitions occur in higher-dimensional static Reissner–Nordström and stationary Kerr black holes. Our results indicate that the equilibrium manifold of all these black hole configurations is in general curved and that curvature singularities appear exactly at those places where second order phase transitions occur.     

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.     

The effect of rib shape on the behavior of laminar flow of oil/MWCNT nanofluid in a rectangular microchannel

Journal of Thermal Analysis and Calorimetry - In this research, the laminar and forced flow and heat transfer of oil/multi-walled carbon nanotubes nanofluid in a microchannel have been numerically...     

Microwave‐promoted oxidation of 1,3,5‐trisubstituted 4,5‐dihydro‐1H‐pyrazoles by in‐situ generation of NO+ and NO respectively from sodium nitrite and sodium nitrate in acetic acid

Microwave‐assisted aromatization of 1,3,5‐trisubstituted 4,5‐dihydro‐1H‐pyrazoles by in‐situ generation of NO⁺ and NO₂⁺ respectively from sodium nitrite and sodium nitrate in acetic acid has been carried out efficiently under mild reaction conditions in good to excellent yields.     

Sulfonic acid–functionalized magnetic Fe3-xTixO4 nanoparticles: New recyclable heterogeneous catalyst for one-pot synthesis of tetrahydrobenzo[b]pyrans and dihydropyrano[2,3-c]pyrazole derivatives

In this work, titanomagnetite nanoparticles (Fe_3-xTi_xO₄) have been used as a novel suppport for the synthesis of a magnetic acidic catalyst. These nanoparticles were functionalized with sulfonic acid groups to prepare the Fe_3-xTi_xO₄@SO₃H nanoparticles. The synthesized acidic nanoparticles have been explored as new and efficient recyclable heterogeneous catalyst for a one-pot, three-component synthesis of tetrahydrobenzo[b]pyrans known as 4H-chromenes and 1,4-dihydropyrano[2,3-c]pyrazoles. The structure of the catalyst was established by infrared, energy dispersive x-ray (EDX), and scanning electron microscopy analyses. The reactions proceed smoothly to furnish the respective products in excellent yields and short reaction times. The facile reaction conditions, easy isolation of the products, versatility, and easy magnetic separation and reusability of the catalyst with no significant loss of activity are the main merits of the present method.