The ACTN3 Gene and Differences between Playing Positions in Bone Mineral Content, Fat Mass and Lean Tissue Mass in the Arms, Legs and Trunk Of Rugby Union Football Players

Aim: The function of the present study was to identify differences between individual playing positions in bone mineral content, fat mass, and lean tissue mass, in the arms, trunk and legs of young adult Rugby Union football players who carried the ACTN3 gene. Subjects and methods: A cross-sectional case control study was carried out using a candidate gene approach (n=55). Individuals belonged to a homogeneous group of players relative to age, gender, ability, and ethnicity. Players were allocated to their preferred playing position. These were the front row (n=14), second and back rows (n=16), scrum and outside-half (n=11), and centres, wings and fullbacks (n=14). A 5 ml sample of saliva was obtained from each player and specimens stored at 4oC until buccal cell DNA extraction was carried out. Height was measured to the nearest 0.1 cm and body mass to the closest 0.1 kg. Dual-energy X-ray absorptiometry was measured using a Hologic QDR Discovery fan beam model. Statistical analyses were undertaken using ANOVA, ANCOVA and MANOVA. Results: The study sample comprised 22% RR, 60% RX, and 18% XX genotypes of the ACTN3 gene respectively. Players in the second and back rows were significantly taller than other positions. Body mass differences, were significantly greater in forwards than backs. There were non-significant differences between positions in adjusted bone mineral content or adjusted lean tissue mass. Adjusted fat mass reflected differences between left and right arms, but not left and right legs. Conclusion: At a developmental level of performance, an understanding and practical application of the structural, physiological and body composition characteristics of individual players, will facilitate personal and team accomplishment, efficiency of training and conditioning, and nurture the potential of young adult players

Positive Self-Adjoint Operator Extensions with Applications to Differential Operators

In this paper we consider extensions of positive operators. We study the connections between the von Neumann theory of extensions and characterisations of positive extensions via decompositions of the domain of the associated form. We apply the results to elliptic second-order differential operators and look in particular at examples of the Laplacian on a disc and the Aharanov-Bohm operator

A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

Hardy's inequality and curvature

A Hardy inequality of the form \int_{\tilde{\Omega}} |\nabla f({\bf{x}})|^p d {\bf{x}} \ge (\frac{p-1}{p})^p \int_{\tilde{\Omega}} \{1 + a(\delta, \partial \tilde{\Omega})(\x)\}\frac{|f({\bf{x}})|^p}{\delta({\bf{x}})^p} d{\bf{x}}, for all $f \in C_0^{\infty}({\tilde{\Omega}})$, is considered for $p\in (1,\infty)$, where ${\tilde{\Omega}}$ can be either $\Omega$ or $\mathbb{R}^n \setminus \Omega$ with $\Omega$ a domain in $\mathbb{R}^n$, $n \ge 2$, and $\delta({\bf{x}})$ is the distance from ${\bf{x}} \in {\tilde{\Omega}}$ to the boundary $\partial {\tilde{\Omega}}.$ The main emphasis is on determining the dependance of $a(\delta, \partial {\tilde{\Omega}})$ on the geometric properties of $\partial {\tilde{\Omega}}.$ A Hardy inequality is also established for any doubly connected domain $\Omega$ in $\mathbb{R}^2$ in terms of a uniformisation of $\Omega,$ that is, any conformal univalent map of $\Omega$ onto an annulus

A nonhomogeneous boundary value problem in mass transfer theory

We prove a uniqueness result of solutions for a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory. The results are obtained under very mild regularity assumptions both on the reference set $\Omega\subset\mathbf{R}^n$, and on the (possibly asymmetric) norm defined in $\Omega$. In the special case when $\Omega$ is endowed with the Euclidean metric, our results provide a complete description of the stationary solutions to the tray table problem in granular matter theory.Comment: 22 pages, 2 figure

Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $\Lambda$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/\pi+\pi/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $\Lambda$ and for nuclear charges less than $e^{-2}2/\pi$.Comment: 37 page