The class of infinite dimensional neat reducts of quasi‐polyadic algebras is not axiomatizable

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi‐polyadic algebras and quasi‐polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α ‐dimensional neat reducts of algebras in K_β is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heck Reaction Catalyzed by Palladacycle in Neat Water

Cydopalladated ferrocenylimine has been found to be a type of excellent phosphine-free catalyst for Heck reactions in neat water with both higher yields and turnover numbers than those reported in the literature up to now. Some commercial emulsifying agents, indodin~ the commonly used quaternary ammonium salts, have been proved to be excellent additives in the catalysis of the reactions. Not only aromatic iodide, but also aromatic bromide could be coupled with the olef‘ms. All rcactions were able to be conducted in air under refluxlng condition.     

Magnetically recoverable AlFe/Te nanocomposite as a new catalyst for the facile esterification reaction under neat conditions

In this work, a new Fe₃O₄/AlFe/Te nanocomposite was synthesized by a one‐step sol–gel method. The Fe₃O₄ magnetic nanoparticles (MNPs) were prepared and then mixed with aluminum telluride (Al₂Te₃) in an alkali medium to produce the desired catalyst. After characterization of the Fe₃O₄/AlFe/Te nanocomposite by SEM, TEM, EDS, XRD, and ICP analyses, it was used in the esterification reaction. This heterogeneous catalyst showed high catalytic activity in the esterification of commercially available carboxylic acids with various alcohols to produce the desired esters at high conversions under neat conditions. The Fe₃O₄/AlFe/Te nanocomposites were separated from the reaction mixture via an external magnet and re‐used 8 times without significant loss of catalytic activity.     

Microwave-Induced Synthesis of 2-Aminoimidazolines Under Neat Conditions

2-Aminoimidazolines were synthesized by the nucleophilic substitution reaction of 2-methylmercapto-4,5-dihydroimidazole hydroiodide with various amine compounds under neat conditions.     

Commutative neat group rings

A ring R is called clean if every element of it is a sum of an idempotent and a unit. A ring R is neat if every proper homomorphic image of R is clean. When R is a field, then a complete characterization has been obtained for a commutative group ring RG to be neat, but not clean. And if R is not a field, then necessary conditions are obtained for a commutative group ring RG to be neat, but not clean. A counterexample is given to show that these necessary conditions are not sufficient.     

An Efficient and Solvent-Free Reaction for Synthesis of Bis（indol-3-yl）methanes Catalyzed by Sulfamic Acid

SA （sulfamic acid） catalyzes the reaction of indole with aldehyde and ketone to afford bis（indol-3-yl）methanes in good to excellent yields under solvent-free condition at ambient temperature.     

Polyadic and cylindric algebras of sentences

In this note we give an interpretation of cylindric algebras as algebras of sentences (rather than formulas) of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Conventional and Microwave-Assisted Facile One-Pot Synthesis of N-Substituted Pyrrole-2,3,4,5-tetracarboxylates Under Neat Conditions

Highly substituted pyrroles 3a,f were prepared conveniently in a reaction of (dimethyl- and diethyl-)acethylenedicarboxylates 1a–b with N-(methyl- and aryl-) hydroxylamines 2a–d in the presence of NaHCO₃ using both conventional heating and microwave irradiation. Excelent yields of the very pure products were isolated under solvent-free conditions both at classical as well as microwave heating.     

Modules with Few Types Over A Serial Ring and Over A Commutative Prüfer Ring

It is proved that the theory of a module M over a countable serial ring has few models iff M is ∑-pure—injective iff the theory of M has few types. It is also proved that the theory of a module M over a countable commutative Prüfer ring has few types if and only if M is ∑-pure—injective.