We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint n× n matrices.

Past research suggests that mixed land-uses encourage non-auto commuting; however, the evidence remains sketchy. This paper explores this question by investigating how the presence of retail activities in neighborhoods influences the commuting choices of residents using data from the 1985 American Housing Survey. Having grocery stores and other consumer services within 300 feet of one’s residen...

Abstract The daily commuting out of the city residence for labor purposes is a complex phenomenon driven by various geographical, transportation, economic, and social forces. Due to its high level complexity, current modeling approaches are mainly disciplinary thus lack multifaceted approach incorporating diverse conceptualization this phenomenon. To contribute demand, paper develops methodolog...

This paper documents a little-noticed feature of US labor markets—very large variation in the labor supply of married women across cities. We focus on cross-city differences in commuting times as a potential explanation for this variation. We start with a model in which commuting times introduce non-convexities into the budget set. Empirical evidence is consistent with the model’s predictions: ...

Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every grou...

OBJECTIVE Automobile dependency and longer commuting are associated with current obesity epidemic. We aimed to examine the urban-rural differential effects of neighborhood commuting environment on obesity in the US METHODS: The 1997-2005 National Health Interview Survey (NHIS) were linked to 2000 US Census data to assess the effects of neighborhood commuting environment: census tract-level auto...

Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...

The commuting graph C(G,X) , where G is a group and X a subset of G, has X as its vertex set with two distinct elements of X joined by an edge when they commute in G. Here the diameter and disc structure of C(G,X) is investigated when G is the symmetric group and X a conjugacy class of G.