Image of polynomials under generalized Szasz operators

The motivation behind this paper is a sequence Sn of generalized Szasz operators using multiple Appell polynmials.The purpose of the present paper is to find the image of the polynomials under these operators.We find that as n→∞,S_(n)(t^(m);x)approaches to x^(m)for every m∈N.Finally,We prove the image of a polynomial of degree m under these operators is another polynomial of degree m by using the linearity of these operators.

Laplacian Energies of Regular Graph Transformations

Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.

COMPARISON OF MODELING TECHNIQUES FOR SELECTING OPTIMIZED AND AUTOMATED PLASMA CUTTING PROCESS PARAMETERS

The advancement in technologies made the entire manufacturing system,to be operated with more efficient,flexible,user friendly,more productive and cost effective.One such a system to be focused for advancement is plasma cutting system,which has wider industrial applications.There are many researches pursuing at various area of plasma cutting technology,still the automated and optimized parameters value selection is challenging.The work is aimed to eliminate the manual mode of feeding the input parameters for cutting operation.At present,cutting parameters are fed by referring the past cut data information or with the assistance of experienced employers.The cutting process parameters selections will have direct impact on the quality of the material being cut,and life of the consumables.This paper is intended to automate the process parameters selection by developing the mathematical model with existing cutting process parameters database.In this,three different approaches,multiple regression,multiple polynomial regression and AI technique,are selected and analyzed with the mathematical relations developed between the different cutting process parameters.The accuracy and reliability of those methods are detailed.The advantage and disadvantage of those methods for optimal setting conditions are discussed.The appropriate method that can be preferred for automated and optimal settings are elucidated.Finally,the selected technique is checked for accuracy and reliability for the existing cut data.

Dual Lie bialgebra structures of Poisson types

Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.