Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

A commuting row contraction is a d-tuple of commuting operators T1, . . . , Td such that ∑d i=1 TiT ∗ i ≤ I. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers Ad on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-∗ continuous functional calculus on the full multiplier algebra. In ...

We prove generalizations of Löwner’s results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuting self-adjoint n-by-n matrices. We prove a generalization to several variables of Nevanlinna’s theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth con...

A common fixed-point generalization of the results of Dotson, Tarafdar, and Taylor is obtained which in turn extends a recent theorem by Jungck and Seasa to locally convex spaces. As applications of our work, we improve and unify well-known results on fixed points and common fixed points of beat approximation. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords--common fixed point, Best ...

The classical (m, k)-Landen transform Fm,k is a self-map of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m’th roots of unity. Identifying the set of rational maps of degree d with an affine open subset of P, we prove that Fm,0 induces a dominant rational self-map Rd,m,0 of P 2d+1 of algebraic degree m, and for 1 ≤ k < m, the t...

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 ...

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

The exact scattering solutions of the Klein-Gordon equation in cylindrically symmetric field are constructed as eigenfunctions of a complete set of commuting operators. The matrix elements and the corresponding differential scattering cross-section are calculated. Properties of the pair production at various limits are discussed.

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...