An extension of the classical van der Waerden and Szemerédi the-orems is proved for commuting operators whose exponents are polynomials.As a consequence, for example, one obtains the following result: Let S ⊆ Zlbe a set of positive upper Banach density, let p1(n), . . . , pk(n) be polynomialswith rational coefficients taking integer values on the integers and satisfyingpi(0)...

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.

"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...

We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety is determined by its arcs at a point. Using differential arcs, we show that if (K,+,×, δ1, . . . , δn) is a differentially closed field of characteristic zero with n commuting derivations and p ∈ S(K) is a regular type over K, then either p is locally modular or there is a definable ...

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

BACKGROUND Insufficient physical activity is a determinant of obesity and cardiovascular disease. Active travel to work has declined in high-income countries in recent decades. We aimed to determine which socioeconomic and demographic characteristics predicted switching to or from active commuting, whether switching from passive to active commuting (or the reverse) independently predicts change...

‎Let $G$ be a finite non-abelian group with center $Z(G)$‎. ‎The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$‎. ‎In this paper‎, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups‎..

Aldous and Fill conjectured that the maximum relaxation time for random walk on a connected regular graph with n $n$ vertices is ( 1 + o ) 3 2 ? $(1+o(1))\frac{3{n}^{2}}{2{\pi }^{2}}$ . This conjecture can be rephrased in terms of spectral gap as follows: (algebraic connectivity) k $k$ -regular at least $(1+o(1))\frac{2k{\pi }^{2}}{3{n}^{2}}$ , bound attained one value We determine structure qu...

Given a representation of a unimodular locally compact group, we discuss criteria for associated coherent state expansions in terms of the commuting algebra. It turns out that for those representations that admit such expansions there exists a unique finite trace on the commuting algebra such that the admissible vectors are precisely the tracial vectors for that trace. This observation is immed...