Volume 14 – Issue 3

In [8] and [9] we showed that Pompeiu’s equation and Hosszú’s equation are particular cases of a large class of functional equations related by Cauchy kernel with respect to two binary operations. In this paper by using the operations x°y = x+y +xy and x*y = x+y -xy, which defines Pompeiu and Hosszú equations, we study a pexiderized version of them, i.e.f(x+y+xy) +g(x+y-xy) = h(x) +k(y).

In mathematics, a conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. In this paper, we construct some new identities and proposed the concept of the power of a point with respect to a conic

This paper deals with the study of the integral representations involving the product of the Aleph function with exponential function, Gauss hypergeometrc function and Fox’s H-function. The results derived in this paper are basic in nature and include a number of known and new results as special cases.

In this paper are given some generalizations of Holder’s inequalities for isotonic linear functionals using several generalizations of Young’s inequality, KittanehManasrah’s inequality and the difference-type reverse inequality. Then, as applications, these inequalities will be rewritten for several important particular cases of isotonic linear functionals.

The aim of this paper is to describe new efficient method for solving general two-point boundary value problems subject to first boundary conditions. We present the construction of non-standard algorithm. The order of the method is six. This new algorithm is suitable for solving different kind of problems. Numerical examples are presented to illustrate the efficiency of the method, to demonstrate the accuracy of the method. Results are compared with the exact solution.

In this note, we have obtained some novel results on mixed trilateral generating relations involving the polynomials,Y^ʹα-nk _n (x;k), a modified form of Konhauser biorthogonal polynomials, Y^α- _n (x;k) α by group theoretic method. As special cases, we have obtained the corresponding results on generalised Laguerre polynomials. Some applications of our results are also discussed.

The basic ideas and ways of thought of algebra permeate nearly every part of mathematics. Moreover, modern algebra cultivates the ability to handle abstract ideas. From the most basic ideas of the modern and abstract algebra, the notions of group and subgroup are fundamental. We all know that a group G is an algebraic structure, more precisely a nonempty set endowed with an operation which combines between them two elements from G, obtaining in this way new and spectacular results and properties for the elements and also, for the subsets of G. In this article, we present how a subgroup of a group can receive interesting properties by using nonempty subsets of the main group and a positive integer previously fixed. Also, in this paper we give a few applications which are related to the new construction, namely the radical of a subgroup of a group.

The aim of the study on CdS/CdTe/Si multilayer is the determination of the optical properties: reflectance in visible [0.4 -0.8 µm] and infrared [0.8 -1.5 µm] ranges. The spectra obtained allowed us to plot the refractive index (n) and the extinction coefficient (k) of our multilayer, which was chosen due to the large use in solar cells applications. In this work, we use wafer silicon (Si) as a substrate with preferential orientation (111), the first layer of CdTe has been deposited in vacuum chamber by thermal evaporation, the second layer of CdS, is done by chemical reaction in the liquid phase. The layers of CdS and CdTe deposited on silicon have been characterized by Fourier Infrared Transformer (FTIR) to get optical properties. Finally, the Kramers-Kronig Transformer (KKT) applied to the reflectance allowed us to plot the refractive index and the extinction coefficient of the system for studied range.

The moisture dependent electrical properties of neem seeds have been reported in the present paper. The dielectric constant and dielectric loss have been measured for indian neem (azadirachta indica) seed over the temperature range 15 – 45 °C at varying frequency from 5 kHz to 10 MHz. The measurements have been carried out using electrical impedance spectroscopy. The electrical properties were found to increase with increases in moisture content. The electrical properties for dead seeds have also been measured and compared with the properties of viable seeds for different moisture levels.

A study is made of the influence of a coplanar magnetic field on the linear stability of a electrically conducting fluid flowing between two infinite parallel fixed plates in a porous media using the energy method. The sufficient condition for stability is obtained using the nature of growth rate, c_i as well as sufficiently small values of the Reynolds number, R_e . From this condition we found that the strengthening or weakening of the stability criterion is dictated by the strength of the magnetic field and porous parameter. In particular, we found that the interaction of magnetic field with porous parameter is more effective in stabilizing the electrically conducting fluid in a porous medium compared to that of ordinary Newtonian viscous fluid.