A paradox about an atom and a photon

In this article we propose a new relativistic paradox concerning the absorption of a photon by a hydrogen atom. We show that the actual cause of the paradox is one of the hypotheses of Bohr model; therefore, in order to solve the paradox, we have to move away from Bohr model. Our analysis is carried out only in the special relativistic framework, so we are not interested in giving a full quantum mechanical treatment of the problem. We derive some expressions for emission and absorption of photons by atoms, which are in perfect agreement with special relativity, although comparable to the classical Bohr formula with an excellent degree of approximation. Quite interestingly, these expressions are no more invariant under a global shift of energy levels, showing a breaking of classical "gauge invariance" of energy. We stress that, to the best of our knowledge, the present approach has never been considered in literature. At the end we will be able to solve the proposed paradox.Comment: 10 pages, no figures. PACS number: 03.30.+p, 32.30.-r, 32.80.-tp Keywords: relativistic paradox, photon emission, photon absorptio

From gene to therapy in spinal and bulbar muscular atrophy: Are we there yet?

Abnormal polyglutamine expansions in the androgen receptor (AR) cause a muscular condition, known as Kennedy's disease or spinal and bulbar muscular atrophy (SBMA). The disease is transmitted in an X-linked fashion and is clinically characterized by weakness, atrophy and fasciculations of the limb and bulbar muscles as a result of a toxic gain-of-function of the mutant protein. Notably, affected males also show signs of androgen insensitivity, such as gynaecomastia and reduced fertility. The characterization of the natural history of the disease, the increasing understanding of the mechanism of pathogenesis and the elucidation of the functions of normal and mutant AR have offered a momentum for developing a rational therapeutic strategy for this disease. In this special issue on androgens and AR functions, we will review the molecular, biochemical, and cellular mechanisms underlying the pathogenesis of SBMA. We will discuss recent advances on therapeutic approaches and opportunities for this yet incurable disease, ranging from androgen deprivation, to gene silencing, to an expanding repertoire of peripheral targets, including muscle. With the advancement of these strategies into the clinic, it can be reasonably anticipated that the landscape of treatment options for SBMA and other neuromuscular conditions will change rapidly in the near future

Branched covers of the sphere and the prime-degree conjecture

To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate surface cover" is an abstract branch datum, a priori not coming from a branched cover, but satisfying the Riemann-Hurwitz formula. The old Hurwitz problem asks which candidate surface covers are realizable by branched covers. It is now known that all candidate covers are realizable when the candidate covered surface has positive genus, but not all are when it is the 2-sphere. However a long-standing conjecture asserts that candidate covers with prime degree are realizable. To a candidate surface cover one can associate one Y -> X between 2-orbifolds, and in a previous paper we have completely analyzed the candidate surface covers such that either X is bad, spherical, or Euclidean, or both X and Y are rigid hyperbolic orbifolds, thus also providing strong supporting evidence for the prime-degree conjecture. In this paper, using a variety of different techniques, we continue this analysis, carrying it out completely for the case where X is hyperbolic and rigid and Y has a 2-dimensional Teichmueller space. We find many more realizable and non-realizable candidate covers, providing more support for the prime-degree conjecture.Comment: Some slips in the first version have been corrected, and a reference to the omitted proofs now fully available online has been added; 44 pages, 14 figure

Volume preserving flow by powers of symmetric polynomials in the principal curvatures

We study a volume preserving curvature flow of convex hypersurfaces, driven by a power of the $k$-th elementary symmetric polynomial in the principal curvatures. Unlike most of the previous works on related problems, we do not require assumptions on the curvature pinching of the initial datum. We prove that the solution exists for all times and that the speed remains bounded and converges to a constant in an integral norm. In the case of the volume preserving scalar curvature flow, we can prove that the hypersurfaces converge smoothly and exponentially fast to a round sphere.Comment: 17 page

Goodness of fit in models for mortality data

Mortality data on an aggregate level are characterized by very large sample sizes. For this reason, uninformative outcomes are evident in common Goodness-of-Fit measures. In this paper we propose a new measure that allows comparison of different mortality models even for large sample sizes. Particularly, we develop a measure which uses a null model specifically designed for mortality data. Several simulation studies and actual applications will demonstrate the performances of this new measure with special emphasis on demographic models and Pspline approach.Goodness of fit, P-splines, R2, Mortality

Spectral Efficiency of Random Time-Hopping CDMA

Traditionally paired with impulsive communications, Time-Hopping CDMA (TH-CDMA) is a multiple access technique that separates users in time by coding their transmissions into pulses occupying a subset of $N_\mathsf{s}$ chips out of the total $N$ included in a symbol period, in contrast with traditional Direct-Sequence CDMA (DS-CDMA) where $N_\mathsf{s}=N$. This work analyzes TH-CDMA with random spreading, by determining whether peculiar theoretical limits are identifiable, with both optimal and sub-optimal receiver structures, in particular in the archetypal case of sparse spreading, that is, $N_\mathsf{s}=1$. Results indicate that TH-CDMA has a fundamentally different behavior than DS-CDMA, where the crucial role played by energy concentration, typical of time-hopping, directly relates with its intrinsic "uneven" use of degrees of freedom.Comment: 26 pages, 13 figure

Trade and Competitiveness of the Mediterranean Countries on the Olive Oil Market

In the context of the establishment of a Mediterranean Free Trade Area, the paper analyses the structure and competitiveness of the Mediterranean basin countries in the olive oil trade and gives a preliminary explanation of the likely impact of the next liberalization process and challenges for the EU Mediterranean countries. The paper starts showing the level of integration of the international olive oil market and underlining the main factors affecting the process. Than, after a brief explanation of the methodology adopted, it analyses the main results achieved. Conclusions try to understand the impact of the competitive scenario showed by the empirical analysis on the Euromediterranean olive oil market following the trade liberalization.International Relations/Trade,

Motion by Curvature of Planar Networks

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional multiphase system where the energy is simply the sum of the lengths of the interfaces, in particular it is a possible model for the growth of grain boundaries. Moreover, the motion of these networks of curves is the simplest example of curvature flow for sets which are ``essentially'' non regular. As a first step, in this paper we study in detail the case of three curves in the plane concurring at a single triple junction and with the other ends fixed. We show some results about the existence, uniqueness and, in particular, the global regularity of the flow, following the line of analysis carried on in the last years for the evolution by mean curvature of smooth curves and hypersurfaces