Considered is a linear set of ordinary differential equations with a matrix depending on a set of adiabatically varying parameters. Asymptotic solutions have been constructed. As has been shown, an important characteristic determining the qualitative portrait of the system is the real part of Berry’s complex geometric phase, which we call the geometric amplitude. For systems with purely imagina...

The research of geometric means of matrices is attracting more and more attention from scholars since it has very important applications in mathematics and physics, especially in the von Neuman entropy involving the quantum physics and statistical thermal physical. There are many achievements on the entropy, among which the entropy uncertainty relation, the generalization of the Heisenberg unce...

In 1969, V. Strassen improves the classical~2x2 matrix multiplication algorithm. The current upper bound for 3x3 matrix multiplication was reached by J.B. Laderman in 1976. This note presents a geometric relationship between Strassen and Laderman algorithms. By doing so, we retrieve a geometric formulation of results very similar to those presented by O. Sykora in 1977.

In many of the studies concerning Accelerated life testing (ALT), the log linear function between life and stress which is just a simple re-parameterization of the original parameter of the life distribution is used to obtain the estimates of original parameters but from the statistical point of view, it is preferable to work with the original parameters instead of developing inferences for the...

The performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation (PDE) models. It is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of...

In this paper, we present a novel algorithmic approach , the hybrid matrix geometric/invariant subspace method, for nding the stationary probability distribution of the nite QBD process which arises in performance analysis of computer and communication systems. Assuming that the QBD state space is deened in two dimensions with m phases and K + 1 levels , the solution vector for level k, k ; 0 k...

In this paper, we present a novel algorithmic approach , the hybrid matrix geometric/invariant subspace method, for nding the stationary probability distribution of the nite QBD process which arises in performance analysis of computer and communication systems. Assuming that the QBD state space is deened in two dimensions with m phases and K + 1 levels , the solution vector for level k, k ; 0 k...

In a previous paper [J. Combin. Theory Ser. A, 2019], the author constructed geometric crystal on variety Xk:=Gr(k,n)×C× which tropicalizes to affine structure rectangular tableaux with n−k rows. this sequel, we define and study R-matrix, birational map R:Xk1×Xk2→Xk2×Xk1 combinatorial R-matrix pairs of tableaux. We show that R is an isomorphism crystals, it satisfies Yang–Baxter relation. case ...