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 odderon equation is studied in terms of the variable suggested by the modular invariance of the 3 Reggeon system. Odderon charge is identified with the cross-product of three conformal spins. A complete set of commuting operators: ĥ2 and q̂ is diagonalized and quantization conditions for eigenvalues of the odderon charge q̂ are solved for arbitrary conformal weigth h. PACS: 12.38.Cy; 11.55.Jy.

We propose a framework for the unified analysis of mixed methods for elasticity with weakly symmetric stress. Based on a commuting diagram in the weakly symmetric elasticity complex and extending a previous stability result, stable mixed methods are obtained by combining Stokes stable and elasticity stable finite elements. We show that the framework can be used to analyze most existing mixed me...

Abstract Let G be a compact connected Lie group, and let $\operatorname {Hom}({\mathbb {Z}}^m,G)$ the space of pairwise commuting m -tuples in . We study problem which primes $p \operatorname {Z}}^m,G)_1$ , component containing element $(1,\ldots ,1)$ has p -torsion homology. will prove that for $m\ge 2$ homology if only divides order Weyl group $G=SU(n)$ some exceptional groups. also compute t...

Let $G$ be a finite group, let $p$ prime and ${\rm Pr}_p(G)$ the probability that two random $p$-elements of commute. In this paper we prove Pr}_p(G) > (p^2+p-1)/p^3$ if only has normal abelian Sylow $p$-subgroup, which generalizes previous results on widely studied commuting group. This bound is best possible in sense for each there are groups with = classify all such groups. Our proof based b...

"This paper evaluates the influence of residential density on commuting behavior across U.S. cities while controlling for available opportunities, the technology of transportation infrastructure, and individual socio-economic and demographic characteristics. The measures of metropolitan and local density are addressed separately.... Regressions are conducted to predict commuting time, speed, an...