Finite groups with a given number of relative centralizers

We will study all finite groups and their subgroups with at most four relative centralizers.     

Novel 1,2,3,4‐Tetrahydroquinazolinones via Reaction of 2‐Amino‐N‐substituted Benzamides and Dimethyl Acetylenedicarboxylate

Reaction of 2‐amino‐N‐substituted benzamides and dimethyl acetylenedicarboxylate (DMAD) in the presence of 1,8‐diazabicyclo[5.4.0]undec‐7‐ene (DBU) in H₂O at room temperature led to the formation of novel 1,2,3,4‐tetrahydroquinazolinones.     

Synthesis and In Vitro Cytotoxic Activity of Novel Triazole‐Isoxazole Derivatives

New derivatives of triazole‐isoxazole were synthesized through a four‐step reaction starting from various ethyl 4‐aryl‐2,4‐dioxobutanoate derivatives. Finally, all compounds were examined by MTT assays for cytotoxic activity in two human breast cancer cell lines (MCF‐7 and T‐47D).     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

A computational investigation of the electronic properties of Octahedral Al n N n and Al n P n cages (n = 12, 16, 28, 36, and 48)

Density functionla theory (DFT) calculations are performed to characterize geometric and electronic features of the octahedral Al _n N _n and Al _n P _n cages (n = 12, 16, 28, 32, and 48). Toward this aim, ¹⁵N, ²⁷Al, and ³¹P chemical shielding (CS) tensors as well as natural charge analyses are calculated for the optimized structures. CS parameters detect three distinct electronic environments for atoms within the Al _n N _n and Al _n P _n cages. The chemical shifts of N2 sites belonging to a hexagon and surrounded by three hexagons and a square obtained are different from those of N3 sites belonging to a hexagon that is surrounded only by hexagons—due to different curvatures exerted at the sites with different local structures. In addition, there is an increasing tendency in the Δσ values of the three local structures, Δσ (N1) > Δσ (N2) > Δσ (N3), N1 sites belonging to four-membered rings. The chemical shieldings of those Al and P sites belonging to a hexagon that is surrounded only by hexagons in the cages (360.7–366.7 and 496.5–514.7 ppm) are close to those previously reported for AlP nanotubes. Three distinct electrostatic environments around the N, Al, and P nuclei are also confirmed by the calculated natural charges. It should be noted that the positively charged Al atoms on the cages turn out to be the available sites for adsorption of H2 molecules.     

Kinetic Study of Radical Polymerization v. Determination of Reactivity Ratio in Copolymerization of Acrylonitrile and Itaconic Acid by 1H‐NMR

Many reports exist in the literature about the application of ¹H and ¹³C‐NMR techniques to analyze the copolymer structure and composition and also determination of reactivity ratios. In this work, on‐line ¹H‐NMR spectroscopy has been applied to identify reactivity ratios of itaconic acid and acrylonitrile in the solution phase (DMSO as the solvent) and in the presence of AIBN as the radical initiator. All the peaks corresponding to the existing protons were assigned quietly. Therefore, the kinetics of the copolymerization reaction was investigated by studying the variation of integral of two characteristic peaks regarding each monomer. The obtained data were used to find the reactivity ratios of acrylonitrile and itaconic acid by linear least‐squares methods such as Finemann‐Ross, inverted Finemann‐Ross, Mayo‐Lewis, Kelen‐Tudos, extended Kelen‐Tudos and Mao‐Huglin. In addition, a non‐linear least‐square method (Tidwell‐ Mortimer) was used at low conversions. Extended Kelen‐ Tudos and Mao‐Huglin were applied to determine reactivity ratio values at high conversions as well.     

Microwave-Assisted Aminomethylation of Electron-Rich Compounds Under Solvent-Free Condition

Electron-rich aromatic compounds react with formaldehyde and a secondary amine under solvent-free condition, in the presence of acidic alumina in a commercial microwave oven or at room temperature to produce aminomethylated products in good to excellent yields.