Let be any -type Lie algebra with ≥ 2 over an algebraically closed field of characteristic 5. Let be an irreducible -module corresponding to some points and let be its corresponding representation. In this paper, in order to prove that the equality about the versus problem out of the 7 Clay...

A formal linear vector field representation for scientific equations is developed to rationalize the intuitive methods that are constantly employed. It is shown that unlike mechanical units that appear in the basis of the space, the reduced temperature and Boltzmann parameter cannot be described...

An enlargement of the domain of multiindex regular Hausdorff matrices is constructed. Its elements can be viewed as multiindex and multidiagonal regular Hausdorff-like matrices. The above matrices are subordinated to sequences of finite variation functions on [0,1] satisfying a boundary...

A Laplacian matrix, , has nonpositive off-diagonal entries and zero row sums. As a matrix associated with a weighted directed graph, it generalizes the Laplacian matrix of an ordinary graph. A standardized Laplacian matrix is a Laplacian matrix with at . We study the spectra of Laplacian...

In this study, we propose simple test statistics for identifying the source of spatial dependence in spatial autoregressive models with endogenous weights matrices. Elements of the weights matrices are modelled in such a way that endogenity arises when the unobserved factors that affect elements...

In this paper we consider Sturm-Liouville eigenvalue problems of the formfor 0 ≤ ≤ − with = ⋯ = = = ⋯ = = 0, where and are integers with 1 ≤ ≤ and under the assumption that () ≠ 0 for all . These problems correspond to eigenvalue problems for symmetric, banded matrices with...

This paper concerns accurate computation of the singular value decomposition (SVD) of an × matrix . As is well known, cross-product matrix based SVD algorithms compute large singular values accurately but generally deliver poor small singular values. A new novel cross-product matrix based SVD...