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.     

Korovkin type approximation theorem for BBH type operators via <Emphasis Type="Italic">J</Emphasis>-convergence

This paper provides a Korovkin type approximation theorem for a class of positive linear operators including Bleimann-Butzer and Hahn operators via J-convergence.     

A Lagrangean relaxation based approach for the capacity allocation problem in flexible manufacturing systems

This study considers the operation assignment and capacity allocation problem in flexible manufacturing systems. A set of operations is selected to be processed and assigned to the machines together with their required tools. The purchase or usage of the required tools incurs a cost. The machines have scarce time and tool magazine capacities. The objective is to maximize the total weight of the assigned operations minus the total tooling costs. We use Lagrangean relaxation approach to obtain upper and lower bounds on the optimal objective function values. The computational experiments show that our approach provides near optimal bounds in reasonable solution times.     

Multifractality of self-avoiding walks on percolation clusters

We consider self-avoiding walks on the backbone of percolation clusters in space dimensions d=2,3,4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the peculiarities of the model. We obtain estimates for the set of critical exponents that govern scaling laws of higher moments of the distribution of percolation cluster sites visited by self-avoiding walks, in a good correspondence with an appropriately summed field-theoretical epsilon=6-d expansion [H.-K. Janssen and O. Stenull, Phys. Rev. E 75, 020801(R) (2007)10.1103/PhysRevE.75.020801].     

Thermodynamic parameters for the complexation of water‐insoluble betulin derivatives with (2‐hydroxypropyl)‐γ‐cyclodextrin determined by phase‐solubility technique combined with capillary zone electrophoresis

The complexation of betulinic and betulonic acids (BIA and BOA) (pentacyclic lupane triterpenoids) with (2‐hydroxypropyl)‐γ‐cyclodextrin (HP‐γ‐CD) was studied at different temperatures using the method combining phase‐solubility technique and CZE. In contrast to mobility shift ACE utilizing the electrophoretic mobility, in this approach, the peak areas are used. The apparent binding (stability, formation) constants are obtained by the Higuchi and Connors method from the linear segment of compound solubility diagrams in CD solutions. It was found that the apparent binding constants of the HP‐γ‐CD complexes of BIA and BOA decrease with increasing temperature. The binding constants of BOA complexes are slightly higher than those of BIA complexes; this can be explained by difference in the hydration degrees of carbonyl and hydroxyl groups. On the basis of the binding constants obtained and their temperature dependences (van't Hoff plot), the enthalpy as well as entropy changes and Gibbs free energies were calculated. It was found that the complexation was characterized by negative changes of enthalpy and entropy, that is, it was controlled by enthalpy changes. The results obtained can be used for the optimization of microcapsulation processes of BOA and BIA with the HP‐γ‐CD application in order to increase solubility and bioavailability of these compounds.     

Electrophoretic mobility of ester betulin derivatives and their complexation with γ-cyclodextrin studied by capillary electrophoresis in aqueous solutions at different pH values

In this article, capillary electrophoresis was used to measure the effective electrophoretic mobility of ester betulin derivatives as a pH function and to study their complexation with γ-cyclodextrin (γ-CD). The electrophoretic mobility of betulin 3,28-diphthalate (DPhB) and 3,28-disuccinate (DScB) changed unusually with decreasing pH: instead of decreasing, it first increased and then decreased. This fact as well as the turbidity of sample solutions at pH from 2.5 to 6, broadening of electrophoretic peaks and a decrease in the surface tension of the solutions indicates that these betulin derivatives, being amphiphilic compounds and weak acids, exist as micelles in aqueous solutions at pH 6 and below. The inclusion complexation of betulin derivatives with γ-CD at pH 9.18 and 4.5 was studied by mobility shift affinity capillary electrophoresis. At pH 9.18, the apparent binding (stability) constant logarithms for 1:1 γ-CD complexes of DPhB, betulin 3,28-disulfate (DSB) and DScB with 95% confidence interval limits were equal to 7.44 ± 0.02, 7.09 (7.01–7.19), and 6.97 (6.87–7.08) at 25°C, respectively. At pH 4.5, the binding constant for the DSB complex was slightly lower, while the micelle formation did not allow determining the exact values of the constants for the DPhB and DScB complexes.     

Microstructural properties of sintered Al–Cu–Mg–Sn alloys

A non-commercial Al4Cu0.5Mg alloy has been used for investigating the effects of the elemental Sn additions. Uniaxial die compaction response of the alloys in terms of green density was examined, and the results showed that Sn addition has no effect when compacting conducted under high pressures. In total, 93–95% green density was achieved with an applied pressure of 400 MPa. Thermal events occurring during the sintering of the emerging alloys were studied by using differential scanning calorimetry (DSC). First thermal event on the DSC analysis of the Al4Cu0.5Mg1Sn alloy is the melting of elemental Sn, whereas for Al4Cu0.5Mg alloy, it is the formation of Al–Mg liquid nearly at 450 °C. Also it is clearly seen on the DSC analysis that Sn addition led to an increase in the formation enthalpy of Al–Mg liquid phase. High Sn content and high sintering temperature (620 °C), therefore high liquid-phase content, caused decrease on the mechanical properties due to thick intergranular phases and grain coarsening. Highest transverse rupture strength and hardness values were obtained from Al4Cu0.5Mg0.1Sn alloy sintered at 600 °C and measured as 390 MPa and 73 HB, respectively.     

2-pyrrolidone - capped Mn<Subscript>3</Subscript>O<Subscript>4</Subscript> nanocrystals

Water-soluble Mn₃O₄ nanocrystals have been prepared through thermal decomposition in a high temperature boiling solvent, 2-pyrrolidone. The final product was characterized with XRD, SEM, TEM, FTIR and Zeta Potential measurements. Average crystallite size was calculated as ∼15 nm using XRD peak broadening. TEM analysis revealed spherical nanoparticles with an average diameter of 14±0.4 nm. FTIR analysis indicated that 2-pyrrolidone coordinates with the Mn₃O₄ nanocrystals only via O from the carbonyl group, thus confining their growth and protecting their surfaces from interaction with neighboring particles.      

Crystal structures of n-BuLi adducts with (R,R)-TMCDA and the consequences for the deprotonation of benzene

Combinations of organolithium compounds and diamine bases have become a powerful tool in synthetic chemistry. Because of the structure-reactivity relationship, the elucidation of reaction mechanisms of these reagents is strongly connected with the structural determination of intermediate species. In mixtures of the diamine TMCDA (N,N,N',N'-tetramethylcyclohexane-1,2-diamine) and n-butyllithium, two different structures, the dimeric [n-BuLi x (R,R)-TMCDA]2 and the aggregate [(n-BuLi)2 x (R,R)-TMCDA]2, can be isolated, depending on the n-BuLi/TMCDA ratio. Thereby, [(n-BuLi)2 x (R,R)-TMCDA]2 is a rare example of an organolithium compound with a ladder arrangement of the central four-membered Li-C-Li-C rings. Two isomers of the ladder structure are formed in the crystal by changing from the enantiomerically pure to racemic TMCDA. As n-BuLi/TMCDA mixtures are also able to deprotonate benzene, these structures give hint to possible mechanisms. Supported by theoretical studies, transition states based on the dimer, the ladder structure, and a hypothetical monomer are discussed.     

Synthesis of 2-(2,3,4-trimethoxyphenyl)-1-(substituted-phenyl)acrylonitriles: in vitro anticancer activity against MCF-7, PC-3 and A2780 cancer cell lines

A series of 2-(2,3,4-trimethoxyphenyl)-1-(substituted-phenyl)acrylonitrile (2–9) were designed and synthesized to develop new cancer drugs. The structures of synthesized compounds 2–9 were described by using melting point, mass (MALDI-TOF-MS), FT-IR, elemental analysis, ¹H, ¹³C, ¹³C-APT and 2D NMR spectroscopy. The in vitro anticancer activities of 2–9 against human breast cancer (MCF-7), human prostate cancer (PC-3) and human ovarian cancer cells (A2780) were investigated by [3-(4,5-dimethylthiazol)-2-yl]-2,5-diphenyl-2H-tetrazolium bromide] (MTT) assay method. Additionally, the LogIC₅₀ values of these compounds on A2780, MCF-7 and PC-3 cell lines were calculated by using inhibition % values by the GraphPad Prism 6 program on a computer. The results indicated that these compounds have high anticancer activity against MCF-7, PC-3 and A2780 cell lines (especially A2780 cell lines, p < 0.05).