Gorenstein Homological Dimension with Respect to a Semidualizing Module and a Generalization of a Theorem of Bass

Let C be a semidualizing module for a commutative ring R. In this paper, we study the resulting modules of finite G _C -projective dimension in Bass class, showing that they admit G _C -projective precover. Over local ring, we prove that dim _R (M) ≤ 𝒢? _C  ? id _R (M) for any nonzero finitely generated R-module M, which generalizes a result due to Bass.     

Theoretical study on the mono and multiply oxygenated Si60H60 fullerene

We have applied density functional theory (DFT) calculations to study the structures, stabilities, electronic and magnetic properties of mono and multiply oxygenated Si₆₀H₆₀ fullerenes (Si₆₀H_60–2nO_n, n = 1, 3, 6, 9, 10, 12, 18, 20, 21, 27 and 30). DFT results show that rearrangement between the closed [6,6] and [5,6] isomers of Si₆₀H₅₈O follows a two-step pathway involving an intermediate and two transition states. Preserving the C₃ symmetry in the cage structure, extra epoxidation of Si₆₀H₆₀ has been accomplished. Based on our results, formation energies per oxygen atom for the multiple additions of oxygen atoms on Si₆₀H₆₀ cage are positive (endothermic character), and increase with the increasing of the number of oxygen atoms. In general, the oxygenation of Si₆₀H₆₀ cage leads to an increase in the electrophilicity of the Si₆₀H_60–2nO_n oxides. The oxygenation of Si–Si bonds not only introduces a substantial broadening of the NMR pattern but also yield individual peaks, indicating different electrostatic environments of silicon nuclei in the Si₆₀H_60–2nO_n oxides.     

A molecular dynamics study on the role of attractive and repulsive forces in excess heat capacity at constant volume of dense fluids

The curves of experimental heat capacity against density show a minimum around and below the critical temperature (Tc), but at higher temperatures, this minimum is not observed. In this study, the role of attractive and repulsive forces on excess heat capacity of Lennard–Jones (LJ) dense fluids has been investigated using a molecular dynamics simulation technique. LJ potential is divided into attractive and repulsive parts. From the molecular dynamics calculations, potential energy and heat capacities have been obtained for Argon at temperatures of 100–500?K. The repulsive forces play the main role in causing the heat capacities at temperatures greater than critical point. Around and below the critical temperature, the role of repulsion is dominant at high densities, but attraction has the main role at low densities, consequently at middle densities, a minimum is formed.     

Extending the dynamic range of an energy harvester using nonlinear damping

This paper introduces the use of nonlinear damping for extending the dynamic range of vibration energy harvesters. A cubic nonlinear damper is initially considered and the average harvested power and the throw are obtained for different sinusoidal base excitation amplitudes and frequencies, both numerically and analytically. It is demonstrated that when excited at resonance, at an amplitude below its maximum operational limit, the harvested power using a nonlinear damper can be significantly larger than that of a linear energy harvester, therefore expanding its dynamic range. A potential approach to implementing cubic nonlinearity using a shunted electromagnetic device is also presented.     

Application of a new equation of state to energy carriers

A new equation of state (IR EOS) recently reported for liquids and gases has been utilized to predict the densities of some energy carriers at different temperatures, pressures. The ability of IR EOS is examined by comparing its results with experimental data for some energy carriers in homogeneous gas, homogeneous liquid and gas–liquid transition region from low to very high pressures. The IR EOS gives excellent results in homogenous gas and homogeneous liquid region while its predictions in gas–liquid transition have more deviations. The average absolute deviation between calculated and experimental densities for 968 data points of 12 energy carriers is 0.33% over the entire range of data with a maximum pressure of 1000 MPa.     

New metal complexes supported on Fe3O4 magnetic nanoparticles as recoverable catalysts for selective oxidation of sulfides to sulfoxides

Fe₃O₄ nanoparticles were coated with aminopropyltriethoxysilane and subsequently reacted with isatin to obtain imine‐bonded Fe₃O₄ nanoparticles. The addition of ZrOCl₂?8H₂O or CuCl₂ led to the formation of complexes of Zr(IV)/isatin@Fe₃O₄ or Cu (II)/isatin@Fe₃O₄ as new magnetically separable catalysts. The synthesized catalysts were characterized using various techniques. These catalysts are shown to be efficient for chemo‐selective oxidation of sulfides to sulfoxides using hydrogen peroxide as oxidative agent. This system has many advantages, such as excellent level of reusability of magnetic catalysts, high yields, simplicity of separation of catalysts using an external magnet, environmental benignity and ease of handling. Copyright © 2016 John Wiley & Sons, Ltd.     

Selective tetrahydropyranylation of alcohols and phenols using titanium(IV) salophen trifluoromethanesulfonate as an efficient catalyst

Titanium(IV) salophen trifluoromethanesulfonate, [Ti^IV(salophen)(OSO₂CF₃)₂], as a catalyst enables selective tetrahydropyranylation of alcohols and phenols with 3,4‐dihydro‐2H‐pyran. Using this catalytic system, primary, secondary and tertiary alcohols, as well as phenols, were converted to their corresponding tetrahydropyranyl ethers in high yields and short reaction times at room temperature. Investigation of the chemoselectivity of this method showed discrimination between the activity of primary alcohols in the presence of secondary and tertiary alcohols and phenols. This heterogenized catalyst could be reused several times without loss of its catalytic activity. Copyright © 2016 John Wiley & Sons, Ltd.