On pre-Λ-Sets and pre-v-Sets

We introduce the notions of a pre--set and a pre-V-set in a topological space. We study the fundamental properties of pre--sets and pre-V-sets and investigate the topologies defined by these families of sets.     

Some properties of almostS-continuous functions

Noiri et al. in [16] introduced and investigated the notion of almosts-continuous functions. The object of this paper is to investigate some more properties of this type of functions.     

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.     

Investigating the effect of nanolayered silicates on blend segmental dynamics and minor component relaxation behavior in poly(ethylene oxide)/poly(methyl methacrylate) miscible blends

Polymer–silicate nanocomposites based on poly (ethylene oxide), PEO, poly(methyl methacrylate), PMMA, and sodium montmorillonite clay were fabricated and characterized to investigate the effect of nanolayered silicates on segmental dynamics of PEO/PMMA blends. X‐ray results indicate the formation of an exfoliated morphology in the nanocomposites. At low silicate contents, an enhancement in segmental dynamics of blend nanocomposites and also PEO, minor component in blend, is observed at temperature region below blend glass transition. This result can be attributed to the improvement of the confinement effect of rigid PMMA matrix on the PEO chains by introducing a low amount of layered silicates. On the other hand, at high silicate contents, an enhancement in segmental dynamics of blend nanocomposites and PEO is observed at temperature region above blend glass transition. This behavior could be interpreted based on the reduction of monomeric friction between two polymer components, which can facilitate segmental motions of blend components in nanocomposite systems. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Two‐dimensional prediction of time dependent,turbulent flow around a square cylinder confined in a channel

This paper presents two‐dimensional and unsteady RANS computations of time dependent, periodic, turbulent flow around a square block. Two turbulence models are used: the Launder–Sharma low‐Reynolds number k–ε model and a non‐linear extension sensitive to the anisotropy of turbulence. The Reynolds number based on the free stream velocity and obstacle side is Re=2.2×10⁴. The present numerical results have been obtained using a finite volume code that solves the governing equations in a vertical plane, located at the lateral mid‐point of the channel. The pressure field is obtained with the SIMPLE algorithm. A bounded version of the third‐order QUICK scheme is used for the convective terms. Comparisons of the numerical results with the experimental data indicate that a preliminary steady solution of the governing equations using the linear k–ε does not lead to correct flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are discretized using the second‐order Crank–Nicolson scheme. The unsteady computations using the linear and non‐linear k–ε models significantly improve the velocity field predictions. However, the linear k–ε shows a number of predictive deficiencies, even in unsteady flow computations, especially in the prediction of the turbulence field. The introduction of a non‐linear k–ε model brings the two‐dimensional unsteady predictions of the time‐averaged velocity and turbulence fields and also the predicted values of the global parameters such as the Strouhal number and the drag coefficient to close agreement with the data. Copyright © 2009 John Wiley & Sons, Ltd.     

Semi-empirical and ab initio quantum chemical characterisation of pyridine derivatives as HCl inhibitors of aluminium surface

Quantum chemical methods are becoming ever more prevalent for assessing surface interactions of different molecules using cluster models and semi-empirical, ab initio Hartree–Fock and density functional theory (DFT) studies considering the standard potential energy surfaces. Examination of the efficacy of some pyridine derivatives to counter aluminium corrosion in hydrochloric acid using ab initio and semi-empirical quantum chemical deductions and its comparison with the available experimental data forms the basis of this research. It is believed that the inhibition efficiency has lucid correlation with the total energy of inhibitor molecules and highest occupied molecular orbital energy levels calculated by DFT study methods and thus the adsorption energy for the pyridine on Al₁, Al₅, Al₁₄, Al₁₈ and Al₂₆ clusters are determined to assess the convergence of the results with respect to size of the cluster. Subsequently, Al₂₆ is used for the inhibitor/aluminium cluster interface investigations. Results highlight the reaction between pyridine molecules and appropriately active sites such as corners and steps or kinks and screw dislocations towards which pyridine molecules are attracted as is evident from a three times rise in adsorption energy from (−35) to (−107) kJ mol⁻¹. Therefore, inhibition mechanism is primarily associated with local properties. Interactions take place between the surface defect and the nitrogen group of the pyridine molecule however, the possibility of ion pair formation between protonated pyridine and chloride ion and its influence on the general adsorption of pyridine on aluminium is also examined. The interaction energies of pyridine and aluminium cluster with the natural bond orbital are also reported.     

ZnBr2 catalyzed domino Knoevenagel-hetero-Diels–Alder reaction: An efficient route to polycyclic thiopyranoindol annulated [3,4-c]quinolone derivatives

Various novel polycyclic thiopyranoindol annulated [3,4-c]quinolone derivatives were synthesized via domino Knoevenagel-hetero-Diels–Alder reactions of indoline-2-thions and novel N-acrylated anthranilaldehydes in refluxing ethanol as a solvent in the presence of 20 mol% ZnBr₂ as a Lewis acid catalyst. All reactions proceed with high yields with excellent regio- and stereoselectivity.