Hydromagnetic laminar and turbulent free jet

The flow of a laminar and turbulent plane free jet of a viscous, incompressible, electrically conducting fluid in the presence of a transverse magnetic field is studied. Using the Prandtlvon Mises transformation, in both the cases, closed form solutions are obtained. A remarkable similarity with the nonmagnetic solutions is noticed. Critical values of the magnetic interaction parameter are determined when the dragging action of the initial momentum is exactly balanced by the retarding effect of the magnetic field resulting in the zero axial velocity field.On leave from V.V. (P.G.) College, Shamli-247776, INDIA.     

On the evolution of a vortical motion in a turbulent fluid

A model turbulence field consisting of essentially discrete but interacting eddies is presented. The development of a single eddy is described by considering its interaction with the remainder of the turbulence field. Vortex line stretching is found to produce initially an increase in the mean square vorticity of the eddy. Consideration of the decay rate of vorticity suggests that the rate of dissipation of turbulent energy per unit mass depends weakly upon the Reynolds number of the turbulence.     

Rayleigh surface waves in the theory of thermoelastic materials with voids

In this paper we analyze the behavior of plane harmonic waves and Rayleigh waves in a linear thermoelastic material with voids. We take into account the damped effects of the thermal field upon the propagation waves. Consequently, the propagation condition is established in the form of an algebraic equation of 9th degree whose coefficients are complex numbers while the eigensolutions of the thermoelastodynamic with voids system are explicitly obtained in terms of the characteristic solutions. We show that the transverse waves are undamped in time and they are not influenced by the thermal and porous effects while the longitudinal waves are all damped in time and they are coupled with the thermal and porous effects. The related solution of the Rayleigh surface wave problem is expressed as a linear combination of the eigensolutions in concern. The secular equation is established in an implicit form and afterwards an explicit form is written for an isotropic and homogeneous thermoelastic with voids half-space. Furthermore, we use the numerical methods and computations to solve the secular equation for a specific material.     

LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits \mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.     

Banks’ criterion and symmetric stable laws with index of stability between one-half and one

In this paper we compare the sample mean and the sample median of independent and identically distributed data that come from a symmetric stable distribution using Banks’ (1997) criterion, which is an alternative to Pitman’s (1937) criterion for comparing estimators of a parameter of interest. For data from a symmetric stable distribution with index of stability between one half and one and odd sample size, we show that Banks’ criterion choses the sample median as an estimator of the location parameter of the distribution. For data from a normal distribution with even sample size, we show that Banks’ criterion favours the sample mean (thus “complementing” a similar result about odd sample sizes in Karunaratne and Hadjicostas (2009)). In the process, we prove some trigonometric inequalities, which are interesting in their own right.     

LIMIT CYCLES OF THE GENERALIZED POLYNOMIAL LINARD DIFFERENTIAL EQUATION

We investigate the generalized polynomial Linard differential equations. Using the averaging theory of first and second order, we obtain the maximum number of limit cycles of the system.     

The complete asymptotic expansion for Bernstein operators

In this paper we study the asymptotic behavior of the classical Bernstein operators, applied to q-times continuously differentiable functions. Our main results extend the results of S.N. Bernstein and R.G. Mamedov for all q-odd natural numbers and thus generalize the theorem of E.V. Voronovskaja. The exact degree of approximation is also proved.