Vol. 56 No. 3 (2024)

The aims of this study were to determine the most likely Mu trapping sites based on total energy consideration as well as identifying the associated muon hyperfine coupling constant of 1, 2, and 3 methylated guanine-cytosine base pair double-strand DNA. The Density Functional Theory method was used at B3LYP/6-31G level of theory to accomplish the objectives of the investigation. The relative energy in the 3 methylated guanine-cytosine base pair double-strand DNA molecule showed that N7 sites in the guanine base have the lowest energy, followed by N3, and C8 sites. It was found that the…

The computation of matrix eigenvalues is vital for understanding various scientific phenomena. The QR method, which is based on the QR factorization of a matrix, is a common approach in numerical linear algebra. In integrable systems, the one-step process of the QR method is related to the time evolution of the Lax equation. In this paper, we clarify the relationship between the QR method, which incorporates an origin shift parameter, and the Lax equation with skew-symmetry. Furthermore, we show the asymptotic convergence of discretization based on matrix factorization of the Lax equation…

This paper presents an algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified matrix entries. The proposed algorithm addresses inverse eigenvalue problems (IEPs) constrained by LR decomposition. Using techniques from discrete soliton theory, we derive recurrence relations that connect matrix entries and eigenvalues. The algorithm systematically computes unknown entries in the matrix from given spectrum data and partial matrix information. Several examples, including cases with real, complex, and multiple eigenvalues, demonstrate…