The Effect of Magnetic Field on Compressible Boundary Layer by Homotopy Analysis Method

We analyse the effect of applied magnetic field on the flow of compressible fluid with an adverse pressure gradient. The governing partial differential equations are solved analytically by Homotopy analysis method (HAM) and numerically by finite difference method. A detailed analysis is carried out for different values of the magnetic parameter, where suction/ injection is imposed at the wall. It is also observed that flow separation is seen in boundary layer region for large injection. HAM is a series solution which consists of a convergence parameter h which is estimated numerically by plotting <em>h</em> curve. Singularities of the solution are identified by Pade approximation.

2-Absorbing Primary Subsemimodules Over Partial Semirings

A partial semiring is a structure possessing an infinitary partial addition and a binary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional compo- sition is a partial semiring. In this paper we obtain the characteristics of 2-absorbing primary subsemimodules and weakly 2-absorbing primary subsemimodules in partial semirings.

The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions

We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

Approximation of Signals by Harmonic-Euler Triple Product Means

Our paper deals with the approximation of signals by <em>H₁.E^θ.E^θ</em> product means of Fourier and its conjugate series. New theorems based on <em>H₁.E^θ.E^θ</em> product summability have been established and proved under general conditions. The established theorems extend, generalize and improve various existing results on summability of Fourier series and its conjugate series.

Non-linear Rayleigh-Benard Magnetoconvection in Temperature-sensitive Newtonian Liquids with Variable Heat Source

The present paper aims at weak non-linear stability analysis followed by linear analysis of nite-amplitude Rayleigh-Benard magneto convection problem in an electrically conducting Newtonian liquid with heat source/sink. It is shown that the internal Rayleigh number, ther- morheological parameter, and the Chandrasekhar number in uence the onset of convection. The generalized Lorenz model derived for the prob- lem is essentially the classical Lorenz model but with some coecient depending on the variable heat source (sink), viscosity, and the applied magnetic eld. The result of the parameters' in uence on the critical Rayleigh number explains their in uence on the Nusselt number. It is found that an increasing strength of the magnetic eld is to stabilize the system and diminishes heat transport whereas the heat source and variable viscosity in-tandem to work system unstable and enhances heat transfer.

Lie Group Analysis of the Time-delayed Inviscid Burgers' Equation

In this paper, we discuss group analysis of rst-order delay partial di erential equations and use it to obtain symmetries of the Invis- cid Burgers' equation with delay, its kernel and extensions of the kernel. We obtain a Lie type invariance condition for rst-order delay partial di erential equations by using Taylor's theorem for a function of several variables. We obtain the symmetries admitted by this delay partial di er- ential equation. Further, we obtain representations of analytic solutions and the reduced equations from the symmetries.

A Critical Remark - Some Fixed Point Results Using Property (E.A.)

The aim of this note is to point out some mistakes in some recent xed point results using property (E.A.). Also, we rectify these mistakes and improve the results.

Star-Hurewicz Modulo an Ideal Property In Topological Spaces

In this paper, a class of star-Hurewicz modulo an ideal spaces is introduced and studied. For an ideal <em>K</em> of finite subsets of N, a characterization of weakly star-<em>K</em>-Hurewicz extremally disconnected spaces is given using ideal. It is shown that star-Hurewicz modulo an ideal property is hereditary under clopen subspaces. In this manner we obtained relationships of star-Hurewicz modulo an ideal property with other existing Hurewicz properties in literature.

On Conformal Kropina Transformation of m-TH Root Metrics

In this paper, we consider conformal Kropina transformation of <em>m</em>-th root metric and for this find Fundamental metric tensors and Spray coefficients. Moreover, condition for locally projectively flat on conformal Kropina transformation of <em>m</em>-th root metric has been found.

Application of q-Bessel Functions in the Solution of Generalized Fractional Kinetic Equations

The present investigation aims to extract a solution from the generalized fractional kinetic equations involving the generalized q-Bessel function by applying the Laplace transform. Methodology and results can be adopted and extended to a variety of related fractional problems in mathematical physics.