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...

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...

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. We show that our problem is equivalent to joint diagonalization, however, unlike joint diagonalization, allows to explicitly preserve the properties of Laplacians. Our construction n...

In this paper, we use weakly commuting and weakly compatible conditions of self-mapping pairs, prove some new common fixed point theorems for three pairs of self-maps in the framework of generalized metric spaces. The results presented in this paper generalize the well known comparable results in the literature due to Abbas et al. [M. Abbas, T. Nazir, R. Saadati, Adv. Difference Equ., 2011 (201...

We consider MacKay’s renormalization operator for pairs of area-preserving maps, near the fixed point obtained in [17]. Of particular interest is the restriction R0 of this operator to pairs that commute and have a zero Calabi invariant. We prove that a suitable extension of R 0 is hyperbolic at the fixed point, with a single expanding direction. The pairs in this direction are presumably commu...

While classical ergodic theory deals largely with single ergodic transformations or flows (i.e. with actions of N,Z,R+ or R on measure spaces), many of the lattice models in statistical mechanics (such as dimer models) have multi-dimensional symmetry groups: they carry actions of Z or R with d > 1. However, the transition from Zor R-actions to multi-parameter ergodic theory presents considerabl...

Let f (z) = e 2ii z + z 2 , where is an irrational number of bounded type. According to Siegel, f is linearizable on a disk containing the origin. In this paper we show: the Hausdorr dimension of the Julia set J (f) is strictly less than two; and if is a quadratic irrational (such as the golden mean), then the Siegel disk for f is self-similar about the critical point. In the latter case, we al...

Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the results with the generalized Fibonacci chains and show that the well-known Fricke character I(x, y, z) = x 2 + y 2 + z 2 − 2xyz − 1 is not the only type of invariant that can occur. We discuss several physical applications...