The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts, in particular it characterizes the growth rate of switched linear systems. The joint spectral radius is notoriously difficult to compute and to approximate. We in...

We consider a self-interacting scalar field whose mass saturates the BreitenlohnerFreedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D ≥ 3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall–off than that of pure gravity with a localized distribution of matter, due to the backreaction of the scalar field, which has a l...

We study string propagation in a spacetime with positive cosmological constant, which includes a circle whose radius approaches a finite value as |t| → ∞, and goes to zero at t = 0. Near this cosmological singularity, the spacetime looks like IR/ZZ. In string theory, this spacetime must be extended by including four additional regions, two of which are compact. The other two introduce new asymp...

Department of Mathematical Statistics and Actuarial Science University of Bern, Sidlerstrasse 5 CH-3012 Bern, Switzerland October 8, 2008 Abstract: Let (S1, S2) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditio...

A bipartite graph is subcubic if it an irregular with maximum degree three. In this paper, we prove that the asymptotic value of spectral radius over graphs order n 3 − Θ ( π 2 ) . Our key approach taking full advantage eigenvalues a certain tridiagonal matrix, due to Willms [SIAM J. Matrix Anal. Appl. 30 (2008) 639–656]. Moreover, for large degree, i.e., at least ⌊ / ⌋ , characterize radius. F...

We use numerical simulations in a ΛCDM cosmology to model density profiles in a set of sixteen dark matter haloes with resolutions of up to seven million particles within the virial radius. These simulations allow us to follow robustly the formation and evolution of the central cusp over a large mass range of 10 to 10 M⊙, down to approximately 0.5% of the virial radius, and from redshift 5 to t...

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

We compute an asymptotic formula for the supremum of resolvent norm ||(ζ−T)−1|| over |ζ|≥1 and contractions T acting on n-dimensional Hilbert space, whose spectral radius does not exceed a given r∈(0,1). prove that this is achieved unit circle by analytic Toeplitz matrix.