This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast εY -periodic conductivity. When the conductivity is bounded in L1 and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ε−2, the first Bloch eigenvalue converges as ε → 0 to a limit which preserves the second-order expansion w...

In this paper, we first give a short review of the eigenvalue estimates of Laplace operator and Schrödinger operators. Then we discuss the evolution of eigenvalues along the Ricci flow, and two new bounds of the first eigenvalue using gradient estimates. 2000 Mathematics Subject Classification: 58J50, 35P15, 53C21.

In this thesis, we studied eigenvalues of directed and undirected graphs and their applications. In the first part, a detailed study of the largest eigenvalue of the normalized Laplace operator ∆ for undirected graphs was presented. In contrast to the smallest nontrivial eigenvalue λ1, the largest eigenvalue λn−1 has not been studied systematically before. However, it is well-known that λ1 can ...

We consider a conforming finite element approximation of the Reissner-Mindlin eigenvalue system, for which a robust a posteriori error estimator for the eigenvector and the eigenvalue errors is proposed. For that purpose, we first perform a robust a priori error analysis without strong regularity assumption. Upper and lower bounds are then obtained up to higher order terms that are superconverg...

In the previous lecture we saw the definitions of eigenvalue expanders, edge expanders, and vertex expanders for d-regular graphs. To recap, in an eigenvalue expander, all except the first eigenvalue of the graph’s adjacency matrix are bounded below d. In an edge expander, every subset of vertices of size below a certain threshold has a large number of edges “going out” of the subset. And in a ...

Let x : M → Sn+1(1) be an n-dimensional compact hypersurface with constant scalar curvature n(n − 1)r, r ≥ 1, in a unit sphere Sn+1(1), n ≥ 5, and let Js be the Jacobi operator of M . In 2004, L. J. Aĺıas, A. Brasil and L. A. M. Sousa studied the first eigenvalue of Js of the hypersurface with constant scalar curvature n(n− 1) in Sn+1(1), n ≥ 3. In 2008, Q.-M. Cheng studied the first eigenvalue...

This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pe...

Abstract We study the first eigenvalue of the Laplace equation in a bounded domain in R (d = 2, 3) with mixed Neumann–Dirichlet (Zaremba) boundary conditions. The Neumann condition is imposed on most of the boundary and the Dirichlet boundary consists of a cluster of small windows. When the windows are well separated the first eigenvalue is asymptotically the sum of eigenvalues of mixed problem...

a method for solving the descriptor discrete-time linear system is focused. for easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. in partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

In this paper, we examine the maximum eigenvalue function of an even order real symmetric tensor. By using the variational analysis techniques, we first show that the maximum eigenvalue function is a continuous and convex function on the symmetric tensor space. In particular, we obtain the convex subdifferential formula for the maximum eigenvalue function. Next, for an mth-order n-dimensional s...