Two Finite Classes of Orthogonal Functions

Two Classes of Special Functions Using Fourier Transforms of Some Finite Classes of Classical Orthogonal Polynomials

Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The best-known example of this type is the Hermite functions, i.e., the Hermite polynomials multiplied by exp(−x2/2), which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a com...

Solving a class of nonlinear two-dimensional Volterra integral equations by using two-dimensional triangular orthogonal functions

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

Buckling and vibration analysis of angle -ply symmetric laminated composite plates with fully elastic boundaries

The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that o...

On two classes of third order boundary value problems with finite spectrum

‎The spectral analysis of two classes of third order boundary value problems is investigated‎. ‎For every positive integer $m$ we construct two classes of regular third order boundary value problems with at most $2m+1$‎ ‎eigenvalues‎, ‎counting multiplicity‎. ‎These kinds of finite spectrum results are previously known only for even order boundary value problems‎.

On Pre-θ-Open Sets and Two Classes of Functions