On the second eigenvalues of matrices associated with TCP
نویسندگان
چکیده
We consider a convex combination of matrices that arise in the study of communication networks and the corresponding convex combination of Kronecker squares of these matrices. We show that the spectrum of the first convex combination is contained in the spectrum of the second set and that the second largest eigenvalues coincide.
منابع مشابه
A mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...
متن کاملFree Vibration Analysis of Repetitive Structures using Decomposition, and Divide-Conquer Methods
This paper consists of three sections. In the first section an efficient method is used for decomposition of the canonical matrices associated with repetitive structures. to this end, cylindrical coordinate system, as well as a special numbering scheme were employed. In the second section, divide and conquer method have been used for eigensolution of these structures, where the matrices are in ...
متن کاملOn the eigenvalues of some matrices based on vertex degree
The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.
متن کاملEffects of time, temperature and precursor on solid state synthesis of α-TCP
The effects of solid state synthesis process parameters (time and temperature) and primary calcium precursor on the amount of produced α-tricalcium phosphate (Ca3(PO4)2 or α -TCP) have been investigated. α-TCP was synthesized by firing of stoichiometric amount of calcium carbonate and monetite in first group and calcium carbonate and brushite in the second group, once at 1350°C for 3,6,8,16 h d...
متن کاملEigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....
متن کامل