During the 2008 September–October outburst of the accreting millisecond pulsar SAX J1808.4−3658, the source was observed by both Suzaku and XMM-Newton approximately 1 day apart. Spectral analysis reveals a broad relativistic Fe Kα emission line which is present in both data sets, as has recently been reported for other neutron star low-mass X-ray binaries. The properties of the Fe K line observ...

Let S = {S 1, S 2} ⊂ Rd×d have a common, but not necessarily strict, Lyapunov matrix (i.e. there exists a symmetric positive-definite matrix P such that P − S T k PS k ≥ 0 for k = 1, 2). Based on a splitting theorem of the state space Rd (Dai, Huang and Xiao, arXiv:1107.0132v1[math.PR]), we establish several stability criteria for the discrete-time linear switched dynamics xn = S σn · · · S σ1 ...

A graph is called k-extendable if each k-matching can be extended to a perfect matching. We give spectral conditions for the k-extendability of graphs and bipartite using Tutte-type Hall-type structural characterizations. Concretely, we sufficient condition in terms radius distance matrix completely characterize corresponding extremal graphs. similar result obtained

In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. The trace norm is just one of the Ky Fan k-norms, given by the sum of the k largest singular values, which are studied more generally in the present paper. Several relations to chromatic number, spectral radius, spread, and to other fundamental parameters are outlined. Some results are ext...

We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue (G) of its adjacency matrix. In particular, writing ks (G) for the number of s-cliques of G, we show that, for all r 2; r+1 (G) (r + 1) kr+1 (G) + r X s=2 (s 1) ks (G) r+1 s (G) ; and, if G is of order n; then kr+1 (G) (G) n 1 + 1 r r (r 1) r + 1 n r r+1 :

We consider spectral radius algebras associated to operators of the form h(S), where h ∈ H∞ and S is the unilateral shift. We show that, for a large class of H∞ functions, Bh(S) is weakly dense in LH. In this paper we continue the study of the spectral radius algebras (SRA) initiated in [2]. These algebras represent a very interesting class of non-selfadjoint, non-closed operator algebras. Furt...

The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generali...

Let Fk denote the k-fan consisting of k triangles which intersect in exactly one common vertex, and Sn,k complete split graph order n a clique on vertices an independent set remaining each vertex is adjacent to set. In this paper, it shown that unique attaining maximum signless Laplacian spectral radius among all graphs containing no Fk, provided k?2 n?3k2?k?2.

We prove the `p-spectral radius formula for n-tuples of commuting Banach algebra elements. This generalizes results of [6], [7] and [10]. Let A be a Banach algebra with the unit element denoted by 1. Let a = (a1, . . . , an) be an n-tuple of elements of A. Denote by σ(a) the Harte spectrum of a, i.e. λ = (λ1, . . . , λn) / ∈ σ(a) if and only if there exist u1, . . . , un, v1, . . . , vn ∈ A suc...

The structure of graphs whose largest eigenvalue is bounded by 3 2 √ 2 (≈ 2.1312) is investigated. In particular, such a graph can have at most one circuit, and has a natural quipu structure.