In this study, the effective parameters on the inelastic response of asymmetric buildings is evaluated for an ensemble of real Iranian earthquake records by considering soil-structure interaction. Then, the design eccentricity obtained from the inelastic dynamic soil-structure analysis is compared with the design eccentricity of seisimic codes of Iran, ATC-3, New Zeland, Canada, Mexico, Austral...

Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the weighted number of closed walks of all lengths and can be regarded as the average eigenvalue obtained from the graph spectrum. In this article, we explore the n...

l(i,j) denotes the distance between the point (xi, yi) and the point (xj, yi) in graphical representation. By classifying li,j, i, j = 1, 2,…, N according to the number of points between (xi, yi) and (xj, yi), N - 1 types are obtained. The average and variance of every type are assembled by the novel invariant v = (a1, d1, a2, d2,…, aN, d>N). Compared with the traditional invariants, the leadin...

We consider testing graph expansion in the bounded-degree graph model. Specifically, we refer to algorithms for testing whether the graph has a second eigenvalue bounded above by a given threshold or is far from any graph with such (or related) property. We present a natural algorithm aimed towards achieving the foregoing task. The algorithm is given a (normalized) eigenvalue bound λ < 1, oracl...

We find lower bounds on the difference between the spectral radius λ1 and the average degree 2e n of an irregular graph G of order n and size e. In particular, we show that, if n ≥ 4, then λ1 − 2e n > 1 n(∆ + 2) where ∆ is the maximum of the vertex degrees in G. Brouwer and Haemers found eigenvalue conditions sufficient to imply the existence of perfect matchings in regular graphs. Using the ab...

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix valued function is computationally expensive. Such problems arise, e.g., from boundary integral formulations of elliptic PDE-eigenvalue problems and typically exclude the use of establis...