Global Aspects of Age-Structured Cigarette Smoking Model

Smoking impacts health and as a result creates several problems related to age which means smoking has a strong correlation with age. Keeping this problem in view, we consider the global asymptotic properties of age-structured smoking model. First, we formulate the model and present the existence and uniqueness of solution. Then we discuss the equilibrium points and construct the Lyapunov function to examine global stability of the free smoking and positive smoking equilibrium points. Finally, we fixed the age factor and use the non-standard finite difference (NSFD) scheme for numerical solutions and compare our results obtained with RK4 and ODE45 graphically with the help of MATLAB.     

Effect of selected residual Ziegler-Natta and metallocene catalysts on the UV-induced degradation of unstabilized ethylene homopolymer films

Catalyst creates new grades of polyethylenes while their degradation phenomena determine the resulting application profiles. The resins and the end-products eventually contain residual catalysts. Therefore, the effects of the following two residual catalysts—one Ziegler-Natta [PQ Silica/Bu₂Mg/^tBuCl/TiCl₄], and the other metallocene [PQ Silica/MAO/(ⁿBuCp)₂ZrCl₂]—on the UV-induced degradation of the resulting unstabilized ethylene homopolymer films were studied. The MetCat HomoPE film was found to be more susceptible to UV-induced degradation degradation than the Z-N HomoPE one despite the residual Zr level was 1/15th of the Ti content. Therefore, the zirconocene residual catalyst better (i) facilitated the UV-initiated reaction, and (ii) decreased the activation energy required for the decomposition of the resulting hydroperoxide. These findings were explained from the differences in (i) electronic configuration and atomic radius, and (ii) surface chemistry and solid-state electronic environment of these catalyst systems. In both films, T_pm and T_pc did not significantly vary with the exposure time. The change of % crystallinity showed to be irregular and disturbed. As a function of carbonyl index, T_pm and T_pc,varied in a similar fashion in the MetCat HomoPE film. However, they significantly differed for the Z-N HomoPE film. Here, T_pm did not appreciably change whereas T_pc initially increased very mildly; then it did not essentially differ.     

Preparation, structure and spasmolytic activities of some derivatives of harmine series of alkaloids

Keeping in view the interesting chemistry and pharmacological importance of harmine series of bases -- the beta-carboline alkaloids, a number of new derivatives of tetrahydroharmine and harmalol have been prepared and characterized through spectral studies. Some of these derivatives showed spasmolytic activity. It was observed that all the N-acyl tetrahydroharmine derivatives are stable, not labile and no ring opening occurs in these compounds, as reported recently.     

A note on: Quasi-linear quotients and shellability of pure simplicial complexes

The purpose of this note is to point out a careless error in the algebraic criterion of shellability of a pure simplicial complex Δ given in [1 Anwar, I., Raza, Z. (2015). Quasi-linear quotients and shellability of pure simplicial complexes. Commun. Algebra 43:4698–4704.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].     

CFD analysis of an oscillating wing at various reduced frequencies

The effect of various reduced frequencies has been examined for an oscillating aspect ratio 10 NACA 0015 wing. An unsteady, compressible three‐dimensional (3D) Navier–Stokes code based on Beam and Warming algorithm with the Baldwin–Lomax turbulence model has been used. The code is validated for the study against published experimental data. The 3D unsteady flow field is simulated for reduced frequency values of 0.1, 0.2 and 0.3 for a fixed mean angle of attack position and fixed amplitude. The type of motion is sinusoidal harmonic. The force coefficients, pressure distributions and flow visualization show that at the given conditions the flow remains attached to the wing surface even at high angles of attack with no clear separation or typical light‐to‐deep category of dynamic stall. Increased magnitude of hysteresis and higher gradients are seen at higher reduced frequencies. The 3D effects are even found at midspan locations. In addition, the rate of decrease in lift near the wing tips compared with the wing root is not much like in the static cases. Copyright © 2008 John Wiley & Sons, Ltd.     

Preface

Journal of Sol-Gel Science and Technology -     

Numerical study of magnetohydrodynamic viscous plasma flow in rotating porous media with Hall currents and inclined magnetic field influence

A numerical solution is developed for the viscous, incompressible, magnetohydrodynamic flow in a rotating channel comprising two infinite parallel plates and containing a Darcian porous medium, the plates lying in the x–z plane, under constant pressure gradient. The system is subjected to a strong, inclined magnetic field orientated to the positive direction of the y-axis (rotational axis, normal to the x–z plane). The Navier–Stokes flow equations for a general rotating hydromagnetic flow are reduced to a pair of linear, viscous partial differential equations neglecting convective acceleration terms, for primary velocity (u′) and secondary velocity (v′) where these velocities are directed along the x and y axes. Only viscous terms are retained in the momenta equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless ordinary differential equations are solved using a robust numerical method, Network Simulation Methodology. Full details of the numerics are provided. The present solutions are also benchmarked against the analytical solutions presented recently by Ghosh and Pop [Ghosh SK, Pop I. An analytical approach to MHD plasma behaviour of a rotating environment in the presence of an inclined magnetic field as compared to excitation frequency. Int J Appl Mech Eng 2006;11(4):845–856] for the case of a purely fluid medium (infinite permeability). We study graphically the influence of Hartmann number (Ha, magnetic field parameter), Ekman number (Ek, rotation parameter), Hall current parameter (Nh), Darcy number (Da, permeability parameter), pressure gradient (Np) and also magnetic field inclination (θ) on primary and secondary velocity fields. Additionally we investigate the effects of these multiphysical parameters on the dimensionless shear stresses at the plates. Both primary and secondary velocity are seen to be increased with a rise in Darcy number, owing to a simultaneous reduction in Darcian drag force. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) but there is a decrease in secondary velocity. The study finds important applications in magnetic materials processing, hydromagnetic plasma energy generators, magneto-geophysics and planetary astrophysics.     

The distribution of solutions of the congruence

For a cube of size , we obtain a lower bound on so that is nonempty, where is the algebraic subset of defined by

a positive integer and an integer not divisible by . For we obtain that is nonempty if , for we obtain that is nonempty if , and for we obtain that is nonempty if . Using the assumption of the Grand Riemann Hypothesis we obtain is nonempty if .