In the last years, shoulder injuries have represented an increasing health problem in soccer players. The goalkeepers are more exposed to shoulder disorders than other field players. Injury prevention exercises for upper limbs were cited in few studies involving throwing athletes, but we know that goalkeepers need a specific program. The purpose of this study is to describe the development of an adapted Fédération Internationale de Football Association (FIFA) 11+ program, namely the FIFA 11+ shoulder, which targets the prevention of shoulder injuries in soccer goalkeepers. The FIFA 11+ shoulder program is structured into three parts: general warming-up exercises, exercises to improve strength and balance of the shoulder, elbow, wrist, and finger muscles, and advanced exercises for core stability and muscle control. The exercises were selected based on recommendations from studies demonstrating high electromyographic activity.

In the present work we apply the atomic approach to the single-impurity Anderson model (SIAM). A general formulation of this approach, that can be applied both to the impurity and to the lattice Anderson Hamiltonian, was developed in a previous work (Foglio et al 2009 arxiv: 0903.0139v2 [cond-mat.str-el]). The method starts from the cumulant expansion of the periodic Anderson model, employing the hybridization as a perturbation. The atomic Anderson limit is analytically solved and its sixteen eigenenergies and eigenstates are obtained. This atomic Anderson solution, which we call the AAS, has all the fundamental excitations that generate the Kondo effect, and in the atomic approach is employed as a 'seed' to generate the approximate solutions for finite U. The width of the conduction band is reduced to zero in the AAS, and we choose its position such that the Friedel sum rule is satisfied, close to the chemical potential mu. We perform a complete study of the density of states of the SIAM over the whole relevant range of parameters: the empty dot, intermediate valence, Kondo and magnetic regimes. In the Kondo regime we obtain a density of states that characterizes well the structure of the Kondo peak. To show the usefulness of the method we have calculated the conductance of a quantum dot, side-coupled to a conduction band.

We describe the Kondo resonance in quantum dots employing the atomic approach for the Anderson impurity. The starting point of this approach is the exact solution of the Anderson impurity in the zero-bandwidth limit, and we choose the level of the atomic conduction band so that the completeness relation be satisfied. There are two or more solutions close to the chemical potential that satisfy this condition at low temperatures, and we choose the one with minimum Helmholtz free energy, considering that this corresponds to the Kondo solution. At low temperatures we obtain a density of states that characterizes well the structure of the Kondo peak. The results obtained for both the localized density of states at the chemical potential and for dynamical properties (like the conductance) agree very well with those obtained by the numerical renormalization group formalism and by the slave boson mean field approach, respectively. This result is a consequence of the satisfaction of the Friedel sum rule by the atomic approach in the Kondo limit. As a simple application we calculate the conductance of a side-coupled quantum dot.

We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as difficult to calculate as the original GF, and the Atomic Approximation consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. This approximation has already been used for the case of infinite electronic repulsion U (Phys. Rev. B 62, 7882 (2000)), and here we extend the treatment to the case of finite U . The method can also be applied to the single impurity Anderson model (SIAM), and we give explicit expressions of the approximate GF both for the PAM and the SIAM.

We describe the Kondo resonance in quantum dots employing the atomic model. We calculate approximate Green's functions of the impurity Anderson model employing the exact solution of the system with a conduction band with zero width, and we use the completeness condition to choose the position of that band. At low temperatures, there are two solutions close to the chemical potential µ, satisfying this condition, and we choose the one with minimum Helmholtz free energy, considering that this corresponds to the Kondo solution. At high temperatures, this solution no longer exist, corresponding to the disappearance of the Kondo peak. We present curves of density of states that characterize the Kondo peak structure problem. As a simple application we calculate the conductance of a side-coupled quantum dot and we obtain good agreement with recent experimental results.Keywords: Electronic transport; Side-coupled quantum dot; Kondo resonance I. CONDUCTANCE OF A SIDE-COUPLED QUANTUM DOTThe Kondo effect explains the increased resistivity shown by a metal with magnetic impurities at low temperatures. The Kondo effect in quantum dots has been theoretically predicted since 1988 [1], and recent experiments confirmed its presence [2]. These systems can be modelled by the Anderson impurity model, and in this paper we apply the impurity atomic model to study the electronic transport through a quantum wire with a side-coupled quantum dot (QD). This system has been studied, from the theoretical point of view, [3,4] and has been recently studied experimentally [5,6].In Fig. 1 we present a pictorial view of a simple onedimensional quantum wire with a side-coupled Anderson impurity with infinite Coulomb repulsion U at site 0. The Hamiltonian of the system can be written aswhere the first term represents the noninteracting wire, characterized by free conduction electrons (c-electrons), the second describes the QD described by a localized f level E f ,σ , (we employ the f letter to indicate localized electrons at the impurity site) and the last one corresponds to the tunneling, where the hybridization V denotes the tunneling matrix element between the QD level and the site 0 of the quantum wire, and for simplicity we consider a constant hybridization V . We employ the Hubbard operators [7,8] to project out the double occupation state | f , 2 , from the local states on the impurity. As the X Hubbard operators do not satisfy the usual fermion commutation relations, the diagrammatic methods based on Wick's theorem are not applicable, and one has to use the product rules