We propose a way to separate variables in rational integrable $\mathfrak{gl}(n)$ spin chain with an arbitrary finite-dimensional irreducible representation at each site and generic twisted periodic boundary conditions. Firstly, we construct basis that diagonalises higher-rank version of the Sklyanin B-operator; construction is based on recursive usage embedding $\mathfrak{gl}(k)$ into $\mathfra...

Two operations commute if the result of their execution is independent of the order in which they execute. Commuting operations can be executed concurrently provided they execute atomically on the objects they access. Statically recognizing commuting operations is of great interest because they increase the amount of concurrency a compiler can exploit. In this document we introduce commutativit...

BACKGROUND The current study examined the associations between active commuting to school, cognitive performance, and academic achievement in Dutch adolescents. In addition, it was explored whether these associations were moderated by sex and mediated by depressive symptoms. METHODS Students in grades 7 and 9 (N = 270; mean age 13.4 years; 53% boys) were included. Active commuting to school w...

in this paper we introduce the construction of free profinite products of profinite groups withcommuting subgroups. we study a particular case: the proper free profinite products of profinite groups with commuting subgroups. we prove some conditions for a free profinite product of profinite groups with commuting subgroups to be proper. we derive some consequences. we also compute profinite comp...

BACKGROUND Walking or bicycling to school (ie, active commuting) has shown promise for improving physical activity and preventing obesity in youth. Our objectives were to examine, among US youth, whether active commuting was inversely associated with adiposity and positively associated with moderate-to-vigorous physical activity (MVPA). We also examined whether MVPA mediated the relationships b...

‎‎Let $R$ be a non-commutative ring with unity‎. ‎The commuting graph‎ of $R$ denoted by $Gamma(R)$‎, ‎is a graph with a vertex set‎ ‎$Rsetminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if‎ $ab=ba$‎. ‎In this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. It is shown that‎, ‎$Gamma(R)$ is the disjoint ...

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.

The focus of the present work was on the association between commuting (business and private), life satisfaction, stress, and (over-) use of the Internet. Considering that digital devices are omnipresent in buses and trains, no study has yet investigated if commuting contributes to the development of Internet addiction. Overall, N = 5039 participants (N = 3477 females, age M = 26.79, SD = 10.68...

Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|...

"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...