We give a short proof of the theorem of Brown, Douglas and Fillmore that an essentially normal operator on a Hilbert space is a compact perturbation of a normal operator if and only if the Fredholm index of its translates are zero whenever deened. The proof is a modiication of the short proof of Lin's theorem on almost commuting self-adjoint elements we gave in 7]. Using similar methods we prov...

Let G be a non-abelian group. The non-commuting graph AG of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Γ the maximum size of a complete subgraph of Γ is called the clique number of Γ and it is denoted by ω(Γ). In this paper we characterize all non-solvable groups G with ω(AG)...

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. Here I revisit that question, and bring a number of additional considerations to it. I will first analyze Hardy’s argument, which was meant to show that Lorentz-invariant elements of reality are indeed inconsistent with quantum mechanics. I will then inve...

Active commuting could contribute to increasing physical activity. The objective of this study was to characterise patterns of active commuting to and from schools in children and adolescents in Chile. A total of 453 Chilean children and adolescents aged between 10 and 18 years were included in this study. Data regarding modes of commuting and commuting distance was collected using a validated ...

ESPON ATTREG project aims to investigate the motivation and behaviour of migration flows and daily commuting of students, tourists, aging population migrating to their secondary homes, students and other “part time” commuters – but especially behaviour of human resources in gross migrations and daily commuting – between regions. One of the key elements of the cohesion policy of the European Com...

Let ξ1, . . . , ξr be complex numbers with K = Q(ξ1, . . . , ξr) having transcendence degree r − 1 over Q. Consider the equation a1x1 + · · ·+ akxk = 1, (1) in which the ai’s are fixed elements of K ×, no proper subsum ai1xi1 + · · ·+ aijxij vanishes, and we seek solutions xi ∈ Γ = ξ1, . . . , ξr . It is well–known that (1) has only finitely many solutions; we present here an elementary proof o...

The spin 1/2 Calogero-Gaudin system and its q-deformation are exactly solved: a complete set of commuting observables is diagonalized, and the corresponding eigenvectors and eigenvalues are explicitly calculated. The method of solution is purely algebraic and relies on the co-algebra symmetry of the model. Running T itle: Spin 1/2 CG System and its q−Deformation P.A.C.S.: 03.65 Fd, 02.20 Sv

INTRODUCTION Active commuting - walking and bicycling for travel to and/or from work or educational addresses - may facilitate daily, routine physical activity. Several studies have investigated the relationship between active commuting and commuting stress; however, there are no studies examining the relationship between solely bicycle commuting and perceived stress, or studies that account fo...

Public transit ridership offers valuable opportunities for modest amounts of daily physical activity (PA). Transit is a more feasible option for most Canadian commuters who live too far from work to walk or cycle, yet public transit usage in midsized Canadian cities has historically remained low due to inefficient transit service. The objectives of this longitudinal study were threefold: to ass...

It is shown in the paper that each Hecke symmetry R with R-symmetric algebra freely generated by 3 commuting elements determined a bivector and symmetric bilinear form on 3-dimensional vector space. A general formula for such symmetries given equivalence classes are described.