This is a sequel to an accepted talk of WAW 2011, where we introduced a set of generalized Laplacians of hypergraphs through the high-ordered random walks. In that paper, we proved the eigenvalues of these Laplacians can effectively control the mixing rate of highordered random walks, the generalized distances/diameters, and the edge expansions. In this talk, we will give a preliminary report o...

We study the mean size of wavelet packets in Lp. An exact formula for the mean size is given in terms of the p-norm joint spectral radius. This will be a corollary of an asymptotic formula for the Lp-norms on the subdivision trees. Then the stability and Schauder basis property of wavelet packets in Lp, and the instability of biorthogonal wavelet packets in L2 are analyzed. AMS Subject Classifi...

The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of...

In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the ex...

Abstract. The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic depends on the joint spectral radius of the linear representation of...

Abstract We prove new mixing rate estimates for the random walks on homogeneous spaces determined by a probability distribution finite group $G$ . introduce switched walk set of distributions , that its long-term behaviour is Fourier joint spectral radius distributions, and give Hermitian sum-of-squares algorithms effective estimation this quantity.

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...

In this paper, we study some extremal problems of three kinds of spectral radii of k-uniform hypergraphs (the adjacency spectral radius, the signless Laplacian spectral radius and the incidence Q-spectral radius). We call a connected and acyclic k-uniform hypergraph a supertree. We introduce the operation of “moving edges” for hypergraphs, together with the two special cases of this operation: ...

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.