Volume 14 – Issue 2

In this paper, we defined the correlations based on the extended fractional Fourier transform domain. The correlation uses two functions to produce a third function in its own form. This third function is called the correlation of the two functions. Properties of correlations on the extended fractional Fourier transform domain are also presented.

In this note, we have obtained some novel results on bilateral generating relations involving P_ n^ (α,β-α) (x) , modified Jacobi polynomials by group-theoretic method. In fact, in section 1, we have introduced a linear partial differential operator R which do not seem to have appeared in the earlier investigations and then we obtained the extended form of the group generated by R. Finally, in section 2, we have obtained a novel generating relation involving the polynomials under consideration with the help of which, we have proved a general theorem on bilateral generating relations of P_ n^ (α,β-α) (x) .

The fractional calculus operators has gained noticeable importance and popularity due to its established applications in describing/modeling and solving various integral equations, ordinary differential equations and partial differential equations in many fields of science and engineering. The Mittag-Leffler functions are important special functions, that provides solutions to number of problems formulated in terms of fractional order differential, integral and difference equations; therefore, it has recently become a subject of interest for many authors in the field of fractional calculus and its applications. The aim of this paper is to evaluate two unified fractional integrals involving the product of generalized Mittag-Leffler function and Appell function F_3(.) . These integrals are further applied in proving two theorems on Marichev-Saigo-Maeda fractional integral operators. The results are expressed in terms of generalized Wright function and hypergeometric functions _pFq_ . Further, we point out also their relevance.

If F is a family of functions, we define a sequence by alternative recurrence with respect to the family F a sequence (a_n)_n that verifies the relation a_n+1∈ {f(a_n, a_n-1)│ f ∈ F for any n ≥ 1, where the first two terms a_0, a_1 are given. We prove that for particular cases of family we can obtain the regular networks in the complex plane.

In this paper, Laplace decomposition method using He’s polynomial is employed to determine the exact solution of the Burger equation which 1-dimensional nonlinear partial differential equation. This method is combined form of the Laplace Transforms Adomian decomposition method .The nonlinear term can be easily handled by the use of He’s Polynomials. The explicit solutions obtained were compared the exact solutions. The method finds the solution without any restrictive assumptions and free from round-off errors and therefore reduce the numerical computation to a great extent. The method is tested on two examples and results show that new method is more effective and convenient to use and high accuracy of it is evident.

Our research intends to apply the stochastic processes theory in modelling of the high allied steel laboratory trials. How long the physics and mechanics allied steel tests are aleatory processes that depends of the time parameter is appropriate to design an absorbent Markov chain which can describes the stages by whom the process passes with time passing.

We construct the asymptotic series and some estimates for a sequence converging to Euler-Mascheroni constant presented by Mortici in [3].

We propose in this paper some approximation formulas of Ramanujan type of odd order.

In this paper we determine all grouplike elements of some some classes of coalgebras over a field k, as well as: trigonometric coalgebras and hyperbolic coalgebras. Also we prove that matrix coalgebra M_C (2,k) doesn’t have any grouplike element.

Both the processes of refining oil and gas processing and petroleum products and in phase storage and delivery of finished products, petro chemical plants generate emissions in the atmosphere, waters and along the ground. Therefore environmental management and pollutants has become a major activity in the development of refineries . The type and quantity of environmental emissions from refineries are usually cuantificate and so well known. The main pollutants generated by the petrochemical industry are oxides of carbon, nitrogen and sulfur, particulates (mainly generated from combustion processes) and volatile organic compounds. This paper aims to introduce the reader to the study of sulfur recovery technologies from flue gases and numerical modeling of the effect of pH on the absorption of sulfur dioxide.

Globalization is a term currently used in the world today, but its precise meaning is not always clearly defined. This paper is trying to explore the type of globalization Romania is going through. It discusses its international impact on the development of higher education in „Valahia” University of Targoviste with practical examples that illustrate the main points

Flow equations in a rotating reference frame are considered. Flow is with uniform angular velocity and absence of body forces. All the flow variables in the physical plane are transformed into orthogonal curvilinear coordinate system. Using the results of differential geometry, it is proved that the flow must satisfy ∆vJ + µ_e δQ/δψ – p δξ/ δφ = 0. The theoretical part is illustrated by two applications. The geometry of streamlines is discussed in these two applications.