Journal of Applied & Computational Mathematics

The purpose of this paper is to show that the category of normed spaces can be embedded in the category of Menger probabilistic normed spaces, and that C( Ω ) is probabilistic normable, whereas it is not normable in the classical case, when Ω is an open subset of Rn. So, the spectrum of the category of Menger probabilistic normed spaces is broader than the category of classical normed spaces. Therefore, it can be a meaningful replacement in some model of security markets. As our model is suitably generalized, that fact can help us to adapt and improve within natural problems of finance, especially, in portfolio optimization of insurance.

n the present paper damped vibrations of homogeneous rectangular plate of linearly varying thickness resting on elastic foundation has been studied. Following Lévy approach, the equation of motion of plate of varying thickness in one direction is solved by quintic spline method. The effect of damping, elastic foundation and taperness is discussed with permissible range of parameters. The frequency parameter Ω decreases as damping parameter Dk increases and it decreases faster in simply supported as compared to clamped-clamped boundary conditions in case of damping parameter and reverses in case of taperness.

During past years Dragomir, Taneja and Pranesh kumar have contributed a lot of work providing different kinds of bounds on the distance, information and divergence measures. These are very useful and play an important role in many areas like as Sensor Networks, Testing the order in a Markov chain, Risk for binary experiments, Region segmentation and estimation etc. In this paper, we have established an upper and lower bounds of new f-divergence measure in terms of Relative J-divergence measure. Its particular cases have also considered using a new f-divergence and inequalities.

The paper deals with the unsteady two-dimensional (2D) non-linear shallow-water equations (SWE) in conservation-law form to capture the fluid flow in transition. Numerical simulations of dam-break flood wave in channel transitions have been performed for inviscid and incompressible flow by using two new implicit higher-order compact (HOC) schemes. The algorithm is second order accurate in time and fourth order accurate in space, on the nine-point stencil using third order non-centered difference at the wall boundaries. To solve the algebraic system, bi-conjugate gradient stabilized method (BiCGStab) with preconditioning has been employed. Although, both the schemes are able to capture both transient and steady state solution of shallow water equations, the scheme expressed in conservative law form is unconditionally stable. The model results have been validated for dam-break problem and compared with the experimental data for dry and wet bed conditions. The model results are found to be in good agreement with the experimental observations. The proposed scheme is useful to solve to capture flow transition with minimal number of nodal points, particularly for hyperbolic system.

The particle swarm optimization (PSO) is a population-based optimization method inspired by flocking behavior of birds and human social interactions. So far, numerous modifications of PSO algorithm have been published, which make the PSO method more complex. Several improved PSO versions succeed in keeping the diversity of the particles during the searching process, but at the expense of convergence speed. This paper is aimed at increasing the rate of convergence and diversity of solutions in the population via two easy techniques: (a) Applying improved acceleration coefficients (b) Dividing search space into blocks. In particular, the second technique is efficient in the case of functions with optimal design variables situated in the one block. Hence, instead of proposing more complex variant of PSO, a simplified novel technique, called Partitioned Particle Swarm Optimizer (PPSO), has been proposed. In order to find optimal coefficients of this method, an extensive set of experiments were conducted. Experimental results and analysis demonstrate that PPSO outperforms nine well-known particle swarm optimization algorithms with regard to global search.

In the Present study, the steady flow and heat transfer of Casson fluid from a permeable horizontal cylinder in the presence of slip condition in a non-Darcy porous medium is analyzed. The cylinder surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite-difference scheme. Increasing the velocity slip parameter is found to decrease the velocity and boundary layer thickness and increases the temperature and the boundary layer thickness. The velocity decreases with the increase the non- Darcy parameter and is found to increase the temperature. The velocity increases with the increase the Casson fluid parameter and is found to decrease the temperature. The Skin-friction coefficient and the local Nusselt number are found to decrease with the increase in velocity and thermal slip parameters respectively