This paper presents some applications using several properties of three important symmetric polynomials: elementary symmetric polynomials, complete symmetric polynomials and the power sum symmetric polynomials. The applications includes a simple proof of El-Mikkawy conjecture in [M.E.A. El-Mikkawy, Appl. Math. Comput. 146 (2003) 759–769] and a very easy proof of the Newton–Girard formula. In ad...

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In partic...

In the present article, buckling analysis of functionally graded annular thin and moderately thick plates under mechanical and thermal loads is investigated. The equilibrium and stability equations of the plate are obtained based on both classical and first order shear deformation plate theories. By using an analytical method, the coupled stability equations are converted to independent equatio...

We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the clas...

We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the clas...

We present a novel slanted faces of thin-disk composite Yb:YAG YAG laser which is side-pumped by four non-symmetric hollow- ducts. The pump light distribution in the disk is modeled by using Monte-Carlo ray tracing method. The temperature distribution inside the crystal is calculated by taking into account either the concentration of Yb+3 ion or the different transmission of laser output coupl...

In this paper family of multilevel inverter topology with reduced number of power switches is presented. The proposed inverter can generate both even and odd level. The proposed topology is suitable for symmetric structure. The proposed symmetric inverter results in reduction of power switches, power diode and gate driver circuits and also it may further minimize the installation area and cost....

In this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minimum potential energy. Afterwards, displacement field is solved using Galerkin method and the proposed process is examined throug...

We give a basis for the space spanned by the sum ŝλ of the lowest degree terms in the expansion of the Schur symmetric functions sλ in terms of the power sum symmetric functions pμ, where deg(pi) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned by ŝλ, where λ is a partition of n, is equal to the number of partitions of n into pa...