A matrix iterative method is developed for modal sensitivify analysis of structures, which can be utilized ,a both distinct and repeated eigenvalue cases. The novel method needs only firs: order derivatives of the system motrices in the repeated e;genvalue case, and is easy to be implemented. A matrix iterative algorithm is presented based on the existence and uniqueness of the governing equati...

1. The inertia of a square matrix A with complex elements is defined to be the integer triple In A = (ir(A), V(A), 8(4)), where ir(A) {v(A)} equals the number of eigenvalues in the open right {left} half plane, and 8(A) equals the number of eigenvalues on the imaginary axis. The best known classical inertia theorem is that of Sylvester : If P > 0 (positive definite) and H is Hermitian, then In ...

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial–Meshulam model X(n, p) of random k-dimensional simplicial complexes on n vertices. We show that for p = Ω(log n/n), the eigenvalues of each of the matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of...

We construct an infinite class of eigenmodes with integer eigenvalues for the Vacuum Modular Hamiltonian a single interval $N$ in 2d CFT and study some its interesting properties, which includes action on OPE blocks as well bulk duals. Our analysis suggests that these eigenmodes, like have natural description so called kinematic space CFT$_2$ particular realize Virasoro algebra theory this spac...

Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect generalizing inversion symmetry. The generalization of symmetry is unique non-Hermitian systems. We show that parities the numbers can be determined from energy eigenvalues on inversion-invariant momenta when generalized pre...

1 Hermitian eigenvalue problem For any n × n Hermitian matrix A, let λA = (λ1 ≥ · · · ≥ λn) be its set of eigenvalues written in descending order. (Recall that all the eigenvalues of a Hermitian matrix are real.) We recall the following classical problem. Problem 1. (The Hermitian eigenvalue problem) Given two n-tuples of nonincreasing real numbers: λ = (λ1 ≥ · · · ≥ λn) and μ = (μ1 ≥ · · · ≥ μ...

Let 1 (G) : : : n (G) be the eigenvalues of the adjacency matrix of a graph G of order n; and G be the complement of G: Suppose F (G) is a …xed linear combination of i (G) ; n i+1 (G) ; i G ; and n i+1 G ; 1 i k: We show that the limit lim n!1 1 n max fF (G) : v (G) = ng always exists. Moreover, the statement remains true if the maximum is taken over some restricted families like “Kr-free”or “r...

The objective of this paper is to find numerical bounds on the performances of algorithms for the placements of phasor measurement units (PMUs) in the power grid. Given noisy measurements and knowledge of the state correlation matrix, we use a linear minimum mean squared error estimator as the state estimator to formulate the PMU placement problem as an integer programming problem. Finding the ...

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n = 9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5, . . . , 9 for the qua...

It is known [6] that for every function f in the generalized Schur class Sκ and every nonempty open subset Ω of the unit disk D, there exist points z1, . . . , zn ∈ Ω such that the n × n Pick matrix h 1−f(zi)f(zj)∗ 1−ziz̄j in j,i=1 has κ negative eigenvalues. In this paper we discuss existence of an integer n0 such that any Pick matrix based on z1, . . . , zn ∈ Ω with n ≥ n0 has κ negative eigen...