Quantum chemical and experimental studies on the mechanism of alkylation of beta-dicarbonyl compounds. The synthesis of five and six membered heterocyclic spiro derivatives

The alkylation of beta-dicarbonyl compounds in a K2CO3/DMSO system was found to afford O- and C-alkylated derivatives, depending on the type of the beta-dicarbonyl compound involved. The alkyl derivatives obtained were used in the synthesis of some new spiro barbituric acid derivatives. Quantum chemical calculations were carried out to elucidate the reaction mechanisms for some typical synthesis.     

Microscopic interacting boson model calculations for even-even <Superscript>128–138</Superscript>Ce nuclei

In this study, we determined the most appropriate Hamiltonian that is needed for the present calculations of energy levels and B(E2) values of ^128–138Ce nuclei which have a mass around A≅130 using the interacting boson model (IBM). Using the best-fitted values of parameters in the Hamiltonian of the IBM-2, we have calculated energy levels and B(E2) values for a number of transitions in ^{128,130,132,134,136,138}Ce. The results were compared with the previous experimental and theoretical (PTSM model) data and it was observed that they are in good agreement. Also some predictions of this model have better accuracy than those of PTSM model. It has turned out that the interacting boson approximation (IBA) is fairly reliable for calculating spectra in the entire set of ^{128,130,132,134,136,138}Ce isotopes and the quality of the fits presented in this paper is acceptable.      

The Momentum Four-Vector in Brans–Dicke Wormholes

In this work, in order to compute energy and momentum distributions (due to matter plus fields including gravitation) associated with the Brans–Dicke wormhole solutions we consider Møller’s energy-momentum complexes both in general relativity and the teleparallel gravity, and the Einstein energy-momentum formulation in general relativity. We find exactly the same energy and momentum in three of the formulations. The results obtained in teleparallel gravity is also independent of the teleparallel dimensionless coupling parameter, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. Furthermore, our results also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerful concept of energy and momentum. (c) The results calculated supports the hypothesis by Cooperstock that the energy is confined to the region of non-vanishing energy-momentum tensor of matter and all non-gravitational fields.     

Involutions of Complexified Quaternions and Split Quaternions

An involution or anti-involution is a self-inverse linear mapping. Involutions and anti-involutions of real quaternions were studied by Ell and Sangwine [15]. In this paper we present involutions and antiinvolutions of biquaternions (complexified quaternions) and split quaternions. In addition, while only quaternion conjugate can be defined for a real quaternion and split quaternion, also complex conjugate can be defined for a biquaternion. Therefore, complex conjugate of a biquaternion is used in some transformations beside quaternion conjugate in order to check whether involution or anti-involution axioms are being satisfied or not by these transformations. Finally, geometric interpretations of real quaternion, biquaternion and split quaternion involutions and anti-involutions are given.     

Spline Split Quaternion Interpolation in Minkowski Space

Spherical spline quaternion interpolation has been done on sphere in Euclidean space using quaternions. In this paper, we have done the spline split quaternion interpolation on hyperbolic sphere in Minkowski space using split quaternions and metric Lorentz. This interpolation curve is called spherical spline split quaternion interpolation in Minkowski space (MSquad).     

On solutions of the simultaneous Pell equations $$ x^{2}-\left( a^{2}-1\right) y^{2}=1$$ and $$y^{2}-pz^{2}=1$$y2-pz2=1

Let \(a\ge 2\) be an integer and p prime number. It is well-known that the solutions of the Pell equation have recurrence relations. For the simultaneous Pell equations

$$\begin{aligned}&x^{2}-\left( a^{2}-1\right) y^{2} =1 \\&y^{2}-pz^{2} =1 \end{aligned}$$

assume that \(x=x_{m}\) and \(y=y_{m}\). In this paper, we show that if \(m\ge 3\) is an odd integer, then there is no positive solution to the system. Moreover, we find the solutions completely for \(5\le a\le 14\) in the cases when \(m\ge 2\) is even integer and \(m=1\).

     

Microwave‐assisted synthesis of 1,3′‐diaza‐flavanone/flavone and their alkyl derivatives with antimicrobial activity

A simple environmentally friendly solid‐phase microwave‐assisted method was used to synthesis of the 1,3′‐diazaflavanone ( 2 ) and 1,3′‐diazaflavone ( 3 ) from the cyclization of 2′‐amino (E)‐3″‐azachalcone ( 1 ). Ten new N‐alkyl (C_5–12,14,15)‐substituted 1,3′‐diazaflavanonium bromides ( 2a–j ) were prepared from compound 2 with corresponding alkyl halides in acetonitrile under reflux. In addition, nine new N,N′‐dialkyl (C_5–12,14)‐substituted 1,3′‐diazaflavonium bromides ( 3a–i ) were also synthesized from compound 3 with corresponding alkyl halides using basic silica in acetonitrile. The antimicrobial activities of compounds 1–3 , 2a–j , and 3a–i were tested against Gram‐positive (G+) (Bacillus subtilis, Staphylococcus epidermidis, Staphylococcus aureus, and Enterococcus faecalis) and Gram‐negative (G?) (Escherichia coli, Klebsiella pneumonia, Pseudomonas aeruginosa, Proteus vulgaris, Salmonella typhimirium, Yersinia pseudotuberculosis, and Enterobacter cloaceae) microorganisms. They showed good antimicrobial activity against the Gram‐positive bacteria tested with the minimal inhibitory concentration values less than 7.8 μg/mL in most cases. The optimum length of the alkyl chain for better and broader activity is situated in the range of 9–12 carbon atoms in the series of compounds 2a–j and five to six carbon atoms in the series of compounds 3a–i . The nonalkylated compounds 1–3 were not effective, as were the ones alkylated with five or six C alkyl groups ( 2a and 2b ) and 8–13 C alkyl groups for N,N′‐dialkyl compounds ( 3c–3i ). The antimicrobial activity increased as the length of the alkyl substitution increased from 8 to 12 carbons in compounds 2a–j . However, antimicrobial activity decreased as the length of the alkyl substitution increased from 7 to 13 carbons in compounds 3c–i . J. Heterocyclic Chem., (2012)