Aromaticity of pentafulvene’s complexes with alkaline metal atoms

Geometry of pentafulvene’s complexes with the atoms of the first group of Periodic Table (Li, Na, K, Rb, and Cs) are optimized at the B3LYP/6-311 ++G(d, p) level of theory. Two kinds of complexes are considered: (1) those which are in equilibrium geometry, and (2) complexes which are formed by gradual change in the distance between the metal atom and penta-fulvene ring. Aromaticities of the considered complexes in their equilibrium geometries are investigated using different indices included geometry-based (HOMA), magnetism-based (NICS, NICS(1), and NICS(1)zz), π-electron count-based (pEDA), and electronic-based (Shannon Aromaticity; (SA)) indices. All indices are well correlated to each other and to some local (atomic charges) and global (binding-energy) properties, with one exception—HOMA. The same regularity is observed for non-equilibrium complexes.     

Modules of finite homological dimension with respect to a semidualizing module

We prove versions of results of Foxby and Holm about modules of finite (Gorenstein) injective dimension and finite (Gorenstein) projective dimension with respect to a semidualizing module. We also verify special cases of a question of Takahashi and White. This research was conducted while S.S.-W. visited the IPM in Tehran during July 2008. The research of S.Y. was supported in part by a grant from the IPM (No. 87130211).     

DFT Study of Endohedral Atoms Effect on Electrophilicity of B16N16 Boron Nitride Nanocage: Comparative Analyses

Endohedral derivatives of B₁₆N₁₆ nanocage (M@B₁₆N₁₆, M?=?Li⁺, Na⁺, K⁺, Mg²⁺, Ne, O^2?, S^2?, F^?, Cl^?) and its iso-electronic fullerne M@C₃₂ have been employed to investigate the relation between the trapped atom/ion and electrophilicity of the B₁₆N₁₆ and C₃₂ nanocages. The electrophilicity index, ??, of these endohedral nanocages has been evaluated from the ionization potential and the electron affinity computed by vertical ionization/affinity at the B3LYP/6-311++G(df,pd) level. Obtained results illustrate that the nature of trapped atom/ion affects HOMO-LUMO band gap, global electrophilicity indices and reactivity of B₁₆N₁₆ and C₃₂ nanocages. Encapsulation B₁₆N₁₆ with different atom/ions may be a possible method for modifying HOMO-LUMO energy gap, electrophilicity and so chemical characteristics of and C₃₂ nanocages.     

Compact all-optical switch for WDM networks based on Raman effect in silicon nanowavegide

We propose an all-optical switching scheme based on Raman gain in a silicon nanowaveguide suitable for multichannel optical communication. Raman gain is used for amplification of a control pulse with a higher wavelength, which depletes the tuned channel signal. Separation between control and signal pulses should be equal to the Raman shift in silicon. By employing a 3 mm channel nanowaveguide, we demonstrate a channel attenuation of about 12 dB, while the suppression ratios for the first and second neighboring channels are about 1.6 dB and 1 dB, respectively. This scheme can be used as an all-optical switch in dense wavelength division multiplexing networks. Moreover, we demonstrate that the depleted channel can be retrieved by a control pulse with lower wavelength in which the pulse amplifies the channel in contrast to the prior situation.     

Assessing the equation of state and comparing it with other relationships used for determining the surface tension of solids

Some facts regarding the equation of state (EQS) in calculating the surface tension of solids by means of contact angle measurements were manifested. In the present investigation, it was mathematically proved that the surface tension of a solid as estimated by the EQS is in fact equivalent to the Zisman critical surface tension for that same solid. Additionally, the applicability of the EQS's approach in attaining the surface tension of powdered solids by the aid of the capillary rise procedure is also discussed and its limitations are clarified. Furthermore, a methodology was devised so that the surface tension of solids as determined by the EQS could be compared with those calculated by approaches using components of surface tension. This methodology revealed that the applications of approaches based on the geometric mean (i.e. Owens/Wendt and van Oss et al. relationships) are restricted to achieving only high surface tensions of solids.     

Radial breathing mode frequencies of carbon nanotubes for determination of their diameters

In this paper, exact formulas are obtained for the radial breathing mode (RBM) frequencies of triple-walled carbon nanotubes (TWCNTs) using symbolic package in MAPLE software. For this purpose, TWCNT is considered as triple concentric elastic thin cylindrical shells, which are coupled through van der Waals (vdW) forces between two adjacent tubes. Lennard–Jones potential is used to calculate the vdW forces between adjacent tubes. Then, explicit formulas for RBM frequencies of single-walled (SW), and double-walled (DW) CNTs have been deduced from TWCNT formulas that show an excellent agreement with the available experimental results and the other theoretical model results. The advantage of this analytical approach is that the elastic shell model considers all degrees of freedom in the vibrational analysis of CNTs. To demonstrate the accuracy of this work, the RBM frequencies of different multi-walled carbon nanotubes (MWCNTs) are compared with the available experimental or atomistic results with relative errors of less than 1.5%. To illustrate the application of this approach, the diameters of DWCNTs are obtained from their RBM frequencies which show an excellent agreement with the available experimental results. Also, this approach can be used to determine the diameters of the TWCNTs and MWCNTs. The influence of changing the geometrical and mechanical parameters of a TWCNT on its RBM frequencies has been investigated, too.     

Global Reactivity of Heterostructure Armchair BC2N‐(4,4) Nanotubes: A Density Functional Theory Investigation

Electronic structures of three types of heterostructure armchair BC₂N nanotube besides armchair (4,4)CNT and (4,4)BNNT were calculated by the B3LYP method of density functional theory. The reactivities of nanotubes were discussed by means of obtained vertical ionization potentials and electron affinity potentials. The corresponding electrophilicity values are well correlated with those obtained from the HOMO and LUMO energies of the nanotubes. The good linear correlation found between ω(I,A) and ω(H,L) allows to confirm the use of the easily available B3LYP/6‐31G(d) HOMO and LUMO energies to obtain reasonable values of the global electrophilicity index of nanotubes at a lower computational cost. © 2013 Wiley Periodicals, Inc. Heteroatom Chem 24:168–173, 2013; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.21078     

Hopf bifurcation analysis of asymmetrical rotating shafts

The Hopf and double Hopf bifurcations analysis of asymmetrical rotating shafts with stretching nonlinearity are investigated. The shaft is simply supported and is composed of viscoelastic material. The rotary inertia and gyroscopic effect are considered, but, shear deformation is neglected. To consider the viscoelastic behavior of the shaft, the Kelvin–Voigt model is used. Hopf bifurcations occur due to instability caused by internal damping. To analyze the dynamics of the system in the vicinity of Hopf bifurcations, the center manifold theory is utilized. The standard normal forms of Hopf bifurcations for symmetrical and asymmetrical shafts are obtained. It is shown that the symmetrical shafts have double zero eigenvalues in the absence of external damping, but asymmetrical shafts do not have. The asymmetrical shaft in the absence of external damping has a saddle point, therefore the system is unstable. Also, for symmetrical and asymmetrical shafts, in the presence of external damping at the critical speeds, supercritical Hopf bifurcations occur. The amplitude of periodic solution due to supercritical Hopf bifurcations for symmetrical and asymmetrical shafts for the higher modes would be different, due to shaft asymmetry. Consequently, the effect of shaft asymmetry in the higher modes is considerable. Also, the amplitude of periodic solutions for symmetrical shafts with rotary inertia effect is higher than those of without one. In addition, the dynamic behavior of the system in the vicinity of double Hopf bifurcation is investigated. It is seen that in this case depending on the damping and rotational speed, the sink, source, or saddle equilibrium points occur in the system.     

Relative Tor Functors with Respect to a Semidualizing Module

Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an isomorphism $\operatorname{Tor}^{{\mathcal{F}_C}\mathcal{M}}_{i}(-,-) \cong \operatorname{Tor}^{{\mathcal{P}_C}\mathcal{M}}_{i}(-,-)$ between the bifunctors defined via C-flat and C-projective resolutions. We show how the vanishing of these functors characterizes the finiteness of ${{\mathcal{F}_C}\text{-}\operatorname{pd}}$ , and use this to give a relation between the ${{\mathcal{F}_C}\text{-}\operatorname{pd}}$ of a module and of a pure submodule. On the other hand, we show that other isomorphisms force C to be trivial.     

Multi‐component reaction‐functionalized chitosan complexed with copper nanoparticles: An efficient catalyst toward A3 coupling and click reactions in water

A novel bio‐nanocomposite nanocatalyst with highly dispersed particles is synthesized through covalent functionalization of chitosan biopolymer by the multicomponent reaction (MCR) strategy. Surface functionalization of chitosan through MCR is led to the grafting of carboxamide type ligands with a high affinity toward complexation with copper nanoparticles. The catalytic activity of the synthesized catalyst was explored in various transformations such as A³ coupling and click reactions in water. Reusability and non‐hazardous nature of the catalyst, mild reaction conditions, operational simplicity, high yielding, and using water as a solvent are the main advantages of this catalytic protocol.