Homogeneous Eigenvalue Analysis of Homogeneous Systems

Transformation from Real Homogeneous Systems of Degree L to Complex Homogeneous Systems of Degree (l, 0)

In eigenvalue analysis, transformation from real systems to complex systems is very important. First, we clarify a necessary and sufficient condition that solutions of real nonlinear systems coincide with solutions of transformed complex nonlinear systems in the real subspace. Moreover, we propose a complex transformation such that a) real homogeneous systems of degree with respect to r are tra...

Evolution of the first eigenvalue of buckling problem on Riemannian manifold under Ricci flow

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

On Convergence Rate of Distributed Consensus for Homogeneous Graphs

We propose a new criteria called normalized eigenvalue variance as the measure of the convergence rate of a large scale network system with consensus. It permits an assessment of the convergence performance of an important class of systems whose graphs are homogeneous. We propose a design method of the feedback gains to minimize the proposed index. Furthermore, numerical examples exhibits its e...

Instability Analysis of Miscible Displacements in Homogeneous Porous Media

Three Dimensional Thermal Shock Problem in Magneto-Thermoelastic Orthotropic Medium

The paper is concerned with the study of magneto-thermoelastic interactions in three dimensional thermoelastic medium under the purview of three-phase-lag model of generalized thermoelasticity. The medium under consideration is assumed to be homogeneous orthotropic medium. The fundamental equations of the three-dimensional problem of generalized thermoelasticity are obtained as a vector-matrix ...