The power spectrum of the circular noise

The circular noise is important in connection to Mach's principle, and also as a possible probe of the Unruh effect. In this letter the power spectrum of the detector following the Trocheries-Takeno motion in the Minkowski vacuum is analytically obtained in the form of an infinite series. A mean distribution function and corresponding energy density are obtained for this particular detected noise. The analogous of a non constant temperature distribution is obtained. And in the end, a brief discussion about the equilibrium configuration is given.Comment: accepted for publication in GR

VELOCITY AND ACCURACY AS PERFORMANCE CRITERIA FOR THREE DIFFERENT SOCCER KICKING TECHNIQUES

Kicking velocity (KV) and kicking accuracy (KA) of 19 experienced male soccer players were examined for the full instep, the inner instep, and the side foot kick. Measurements were performed simultaneously by a radar gun (KV) and a newly introduced high-speed-video camera set-up (KA). Subjects had two different tasks: to kick as fast as possible (Max KV) and to kick as accurate as possible (Max KA) with each kicking technique. Six repetitive kicks were performed for each required condition. The full instep and the inner instep kick were faster compared to the side foot kick for both performance tasks. In contrast, the side foot kick was the more accurate technique compared to the inner instep and the full instep kick, also for both performance tasks. Kicking variability between and within subjects was generally low for KV and generally high for KA for all kicking. It is concluded that velocity control is easier to achieve than accuracy control for soccer kicks

Canonical heights and division polynomials

Number theory, Algebra and Geometr

Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with \cite{BKD}, a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic

Collective multipole expansions and the perturbation theory in the quantum three-body problem

The perturbation theory with respect to the potential energy of three particles is considered. The first-order correction to the continuum wave function of three free particles is derived. It is shown that the use of the collective multipole expansion of the free three-body Green function over the set of Wigner $D$-functions can reduce the dimensionality of perturbative matrix elements from twelve to six. The explicit expressions for the coefficients of the collective multipole expansion of the free Green function are derived. It is found that the $S$-wave multipole coefficient depends only upon three variables instead of six as higher multipoles do. The possible applications of the developed theory to the three-body molecular break-up processes are discussed.Comment: 20 pages, 2 figure

Tangential intersection of branches of motion

The branches of motion in the configuration space of a reconfigurable linkage can intersect in different ways leading to different types of singularities. In the vast majority of reported linkages whose configuration spaces contain multiple branches of motion the intersection happens transversally, allowing local methods, like the computation of its tangent cone, to identify different branches by means of their tangents. However, if these branches are of the same dimension and they intersect tangentially, it is not possible to identify them by means of the tangent cone at the singularity as the tangent spaces to the branches are the same. Although this possibility has been mentioned by a few researchers, whether linkages with this kind of tangent intersection of branches of motion exist is still an open question. In this paper, it is shown that the answer to this question is yes: A local method is proposed for the effective identification of branches of motion intersecting tangentially, and a method for the type synthesis of linkages that exhibit this particular type of singularity is presente

The theory of stellar winds

We present a brief overview of the theory of stellar winds with a strong emphasis on the radiation-driven outflows from massive stars. The resulting implications for the evolution and fate of massive stars are also discussed. Furthermore, we relate the effects of mass loss to the angular momentum evolution, which is particularly relevant for the production of long and soft gamma-ray bursts. Mass-loss rates are not only a function of the metallicity, but are also found to depend on temperature, particularly in the region of the bi-stability jump at 21 000 Kelvin. We highlight the role of the bi-stability jump for Luminous Blue Variable (LBV) stars, and discuss suggestions that LBVs might be direct progenitors of supernovae. We emphasize that radiation-driven wind studies rely heavily on the input opacity data and linelists, and that these are thus of fundamental importance to both the mass-loss predictions themselves, as well as to our overall understanding of the lives and deaths of massive stars.Comment: 6 pages, invited review Astrophysics and Space Science, Vol 336, Issue 1, pp. 163-167 (special HEDLA 2010 Issue