Rook polynomials have been studied extensively since 1946, principally as a method for enumerating restricted permutations. However, they have also been shown to have many fruitful connections with other areas of mathematics, including graph theory, hypergeometric series, and algebraic geometry. It is known that the rook polynomial of any board can be computed recursively. [19, 18] The naturall...

In this paper, we consider the linearly structured partial polynomial inverse eigenvalue problem (LPPIEP) of constructing matrices Ai∈Rn×n for i=0,1,2,…,(k−1) specified linear structure such that matrix P(λ)=λkIn+∑i=0k−1λiAi has m (1⩽m⩽kn) prescribed eigenpairs as its eigenvalues and eigenvectors. Many practical applications give rise to polynomials. Typical are symmetric, skew-symmetric, tridi...

It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev invariant is derived from the Conway polynomial for virtual knots. Furthermore, i...

This study is devoted to the numerical solution of an inverse coefficient problem for a density dependent nonlinear reaction-diffusion equation. The method is based on approximating the unknown coefficient by polynomials. An optimal idea for solving the inverse problem is to minimize an error functional between the output data and the additional data. For this purpose, we find a polynomial of d...

T HIS INTRODUCTORY section applies to general binary rate k/n convolutional codes. In Section II we specialize to rate one-half to describe a class of codes that allows an interesting mod ification of the stack decoding algorithm [l]-[2]. Section III presents our simulation results. Let G be a conventional convolutional encoder [3] whose rows are the first k rows of a polynomial n X n matrix B ...

In this paper we introduce an interpolation method for computing the Drazin inverse of a given polynomial matrix. This method is an extension of the known method from [15], applicable to usual matrix inverse. Also, we improve our interpolation method, using a more effective estimation of degrees of polynomial matrices generated in Leverrier-Faddev method. Algorithms are implemented and tested i...

Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...