Topologically Irreducible Representations and Radicals in Banach Algebras

It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of ‘topologicalradicals’ in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx.     

Phosphomolybdic acid catalyzed facile one‐pot synthesis of 2,4,5‐triaryl‐1H‐imidazoles from benzil and aromatic aldehydes

A facile one‐pot synthesis of 2,4,5‐triaryl‐1H‐imidazoles with better yields and shorter reaction time from the condensation of benzil, ammonium acetate and aromatic aldehydes using the catalyst phosphomolybdic acid is described     

Linear and Weakly Nonlinear Stability Analyses of Two-Dimensional,Steady Brinkman–Bénard Convection Using Local Thermal Non-equilibrium Model

Effect of local thermal non-equilibrium (LTNE) on onset of Brinkman–Bénard convection and on heat transport is investigated. Rigid–rigid and free–free, isothermal boundaries are considered for investigation. The assumption of LTNE leads to an ‘advanced onset’ situation compared to that predicted by the local thermal equilibrium (LTE) assumption. This results in the ‘enhanced heat transport’ situation in the problem. Asymptotic analysis for small and large values of inter-phase heat transfer coefficient is also carried out on critical Rayleigh number, critical wave number and Nusselt number. In respect of boundary influences on onset and heat transport, it is found that classical results hold even under the LTNE assumption. The other parameters’ influences on onset and heat transport are qualitatively similar in LTNE and LTE cases.     

Palladium‐Catalyzed Intramolecular Trost–Oppolzer‐Type Alder–Ene Reaction of Dienyl Acetates to Cyclopentadienes

A new approach to the synthesis of highly substituted cyclopentadienes, indenes, and cyclopentene‐fused heteroarenes by means of the Pd‐catalyzed Trost–Oppolzer‐type intramolecular Alder–ene reaction of 2,4‐pentadienyl acetates is described. This unprecedented transformation combines the electrophilic features of the Tsuji–Trost reaction with the nucleophilic features of the Alder–ene reaction. The overall outcome can be perceived as a hitherto unknown “acid‐free” iso‐Nazarov‐type cyclization. The versatility of this strategy was further demonstrated by the formal synthesis of paucifloral F, a resveratrol‐based natural product.     

Correction to: Effect of trigonometric sine,square and triangular wavetype time-periodic gravity-aligned oscillations on Rayleigh–Bénard convection in Newtonian liquids and Newtonian Nanoliquids

Meccanica - The original article has been updated due to typesetting mistakes made in Section 2.2 Mathematical formulation, Table 1 and in Equation (51).     

An efficient synthesis of anti-microbial 1,2,4-triazole-3-thiones promoted by acidic ionic liquid

Acidic ionic liquid, [(Py)₂SO][HSO₄]₂ has been used as an efficient catalyst for the reaction of ketone with thiosemicarbazide in ethanol at room temperature for the eco-friendly synthesis of spiro-1,2,4-triazolidine-3-thiones. Smooth reactions, ambient temperature, use of alcohol as a solvent, high yields, easy work-up procedure and excellent recyclability of ionic liquid and high atom economy are the auxiliary advantages of the present protocol, which makes it ecofriendly. All the synthesized 1,2,4-trioazoles were screened for antimicrobial activity. Most of compounds displayed moderate to good biological activity.     

Linear and non-linear analyses of convection in a micropolar fluid occupying a porous medium

Linear and weakly non-linear analyses of convection in a micropolar fluid occupying a high-porosity medium are performed. The Brinkman–Eringen momentum equation is considered. The linear and non-linear analyses are, respectively, based on the normal mode technique and truncated representation of Fourier series. The linear theory for a two-phase system reiterates that the preferred mode of convection is stationary as in the case of a single-phase system. An autonomous system of differential equations representing cellular convection arising in the study is considered to analyse the critical points. The Nusselt number is obtained as a function of micropolar and porous medium parameters.