Synthesis and thermolysis of the 2,3‐dihydro‐1H‐pyrole‐2,3‐diones,pseudopericyclic reactions of formyl(N‐phenylimidoyl)ketene: Experimental data and PM3 calculations

The reactions of the 2,3‐dihydro‐1H‐furan‐2,3‐dione 1 with Schiff bases 2a‐f at 60–70°C furnish the corresponding 2,3‐dihydro‐1H‐pyrole‐2,3‐diones 3a‐f . The heating of 3a‐d afforded the corresponding 4‐methoxybenzoyl(N‐arylimidoyl)k:etenes 4a‐d as intermediates which undergo a very facile cyclization to quinoline‐4‐ones 5a‐d . According to our PM3 calculations, fragmentation of 4‐formyl‐2,3‐dihydro‐1H‐pyrole‐2,3‐dione and 1,4‐cyclization of formyl(N‐phenylimidoyl)k:etene IN1 to azetin‐2‐one IN2 and oxe‐tone IN3 are pseudopericyclic reactions with two orbital connections, proceed via planar transition structures. Due to to the possibility of syn and anti conformations of the imine phenyl, there are eight E/Z‐iso‐mers of IN1 . In addition, we have also calculated reaction mechanism of formation of quinoline‐4‐ones by the PM3 method.     

Preparation and characterization of Co(II), Ni(II) and Cu(II) complexes of a ligand containing 1,3,4-thiadiazole groups

(1R,2R)-1,2-bis-(5-amino-1,3,4-thiadiazole-2-yl)ethane-1,2-diol (L) has been prepared by the reaction of thiosemicarbazide with (2R,3R)-(+)-tartaric acid (I) and phosphorous oxychloride, and its complexes with Co(II), Ni(II) and Cu(II) have been obtained. The structures of the ligand and its complexes have been established by i. r., ¹H- and ¹³C-n.m.r. spectra, u.v.–vis–nir spectroscopy, elemental analyses, T.g.-D.t.a. and magnetic susceptibility measurements.     

On co-ordinated quasi-convex functions

A function f: I → ?, where I ? ? is an interval, is said to be a convex function on I if $$f(tx + (1 - t)y) \le tf(x) + (1 - t)f(y)$$ holds for all x, y ∈ I and t ∈ [0, 1]. There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensenconvex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex functions on the coordinates. We also prove some inequalities of Hadamard-type as Dragomir’s results in Theorem 5, but now for Jensen-quasi-convex and Wright-quasi-convex functions. Finally, we give some inclusions which clarify the relationship between these new classes of functions.     

On a generalization of semisimple modules

Let R be a ring with identity. A module \(M_R\) is called an r-semisimple module if for any right ideal I of R, MI is a direct summand of \(M_R\) which is a generalization of semisimple and second modules. We investigate when an r-semisimple ring is semisimple and prove that a ring R with the number of nonzero proper ideals \(\le \)4 and \(J(R)=0\) is r-semisimple. Moreover, we prove that R is an r-semisimple ring if and only if it is a direct sum of simple rings and we investigate the structure of module whenever R is an r-semisimple ring.     

Enamines of 1,3-dimethylbarbiturates and their symmetrical palladium(II) complexes: synthesis,characterization and biological activity

Transition Metal Chemistry - Three 1,3-dimethylbarbiturate-enamine derivatives and their symmetrical palladium(II) complexes were prepared and characterized by spectroscopic methods. In addition,...