Visualizing elements of Sha[3] in genus 2 jacobians

Mazur proved that any element xi of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in the sense that xi lies in the kernel of the natural homomorphism between the cohomology groups H^1(k,E) -> H^1(k,A). However, the abelian surface in Mazur's construction is almost never a jacobian of a genus 2 curve. In this paper we show that any element of order three in the Shafarevich-Tate group of an elliptic curve over a number field can be visualized in the jacobians of a genus 2 curve. Moreover, we describe how to get explicit models of the genus 2 curves involved.Comment: 12 page

3D printing dimensional calibration shape: Clebsch Cubic

3D printing and other layer manufacturing processes are challenged by dimensional accuracy. Several techniques are used to validate and calibrate dimensional accuracy through the complete building envelope. The validation process involves the growing and measuring of a shape with known parameters. The measured result is compared with the intended digital model. Processes with the risk of deformation after time or post processing may find this technique beneficial. We propose to use objects from algebraic geometry as test shapes. A cubic surface is given as the zero set of a 3rd degree polynomial with 3 variables. A class of cubics in real 3D space contains exactly 27 real lines. We provide a library for the computer algebra system Singular which, from 6 given points in the plane, constructs a cubic and the lines on it. A surface shape derived from a cubic offers simplicity to the dimensional comparison process, in that the straight lines and many other features can be analytically determined and easily measured using non-digital equipment. For example, the surface contains so-called Eckardt points, in each of which three of the lines intersect, and also other intersection points of pairs of lines. Distances between these intersection points can easily be measured, since the points are connected by straight lines. At all intersection points of lines, angles can be verified. Hence, many features distributed over the build volume are known analytically, and can be used for the validation process. Due to the thin shape geometry the material required to produce an algebraic surface is minimal. This paper is the first in a series that proposes the process chain to first define a cubic with a configuration of lines in a given print volume and then to develop the point cloud for the final manufacturing. Simple measuring techniques are recommended.Comment: 8 pages, 1 figure, 1 tabl

What is the probability that a random integral quadratic form in nn variables has an integral zero?

We show that the density of quadratic forms in $n$ variables over $\mathbb Z_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. When real quadratic forms in $n$ variables are distributed according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we determine explicitly the probability that a random such real quadratic form is isotropic (i.e., indefinite). As a consequence, for each $n$, we determine an exact expression for the probability that a random integral quadratic form in $n$ variables is isotropic (i.e., has a nontrivial zero over $\mathbb Z$), when these integral quadratic forms are chosen according to the GOE distribution. In particular, we find an exact expression for the probability that a random integral quaternary quadratic form has an integral zero; numerically, this probability is approximately $98.3\%$.Comment: 17 pages. This article supercedes arXiv:1311.554

Selmer Groups in Twist Families of Elliptic Curves

The aim of this article is to give some numerical data related to the order of the Selmer groups in twist families of elliptic curves. To do this we assume the Birch and Swinnerton-Dyer conjecture is true and we use a celebrated theorem of Waldspurger to get a fast algorithm to compute $$. Having an extensive amount of data we compare the distribution of the order of the Selmer groups by functions of type $\alpha \frac{(\log \log (X))^{1+\varepsilon}}{\log (X)}$ with $\varepsilon$ small. We discuss how the "best choice" of $\alpha$ is depending on the conductor of the chosen elliptic curves and the congruence classes of twist factors.Comment: to appear in Quaestiones Mathematicae. 16 page

Familial hypercholesterolemia in cardiac rehabilitation: a new field of interest

Familial hypercholesterolemia (FH) is a frequently undiagnosed genetic disease characterized by substantial elevations of low-density lipoprotein cholesterol (LDL-C). The prevalence of heterozygous FH (HeFH) in the general population is 1:500 inhabitants, while the prevalence of homozygous FH (HoFH) is 1:1,000,000. If FH is not identified and aggressively treated at an early age, affected individuals have a 20-fold increased lifetime risk of coronary heart disease compared with the general population. This narrative review provide a concise overview of recommendations for diagnosis and treatment of adults and children with FH, and discuss the utility of considering FH as a comorbidity at the entry of cardiac rehabilitation programme

A rare Giant Killian-Jamieson diverticulum in a 97-year-old female. Considerations and multidisciplinary treatments in a symptomatic patient

The purpose of this publication is to describe the clinical and imaging findings of rare symptomatic giant Killian-Jamieson diverticulum (KJD) detected in a 97-year-old female patient and discuss diagnostic and therapeutic protocols to be implemented. The clinical history began implementing anamnesis and physical examination, followed by laryngoscopy, esophagogastroduodenoscopy, sonographic examination and subsequently a double-contrast pharyngoesophagram evaluations, to our symptomatic old patient with results of typically KJD, with maximal dimension of 5 cm. The KJD was successfully treated with a surgical approach, esophagomyotomy in addition to a diverticulopexy; these techniques were used for adequate visualization of the tissue bridge of the diverticulum and protection of the surrounding tissue during dissection of the tissue bridge. Our patient has benefit from the operation immediately, with resolution of the disease. The follow-up (on-going), up to now, showed no recurrence of the pathological and no complications, making sure the authors of the efficacy of the surgical treatment. According to the authors the surgical treatment was the only procedure to cure the patients and, to date, our successful experience suggests that only surgical approach can be a safe and effective method for the treatment of symptomatic giant KJD, due to its close proximity to the recurrent laryngeal nerve and the concern of possible nerve injury

On the complexity of the boundary layer structure and aerosol vertical distribution in the coastal Mediterranean regions: a case study

The planetary boundary layer structure in the coastal areas, and particularly in complex orography regions such as the Mediterranean, is extremely intricate. In this study, we show the evolution of the planetary boundary layer based on in situ airborne measurements and ground-based remote sensing observations carried out during the MORE (Marine Ozone and Radiation Experiment) campaign in June 2010. The campaign was held in a rural coastal Mediterranean region in Southern Italy. The study focuses on the observations made on 17 June. Vertical profiles of meteorological parameters and aerosol size distribution were measured during two flights: in the morning and in the afternoon. Airborne observations were combined with ground-based LIDAR, SODAR, microwave and visible radiometer measurements, allowing a detailed description of the atmospheric vertical structure. The analysis was complemented with data from a regional atmospheric model run with horizontal resolutions of 12, 4 and 1 km, respectively; back-trajectories were calculated at these spatial resolutions. The observations show the simultaneous occurrence of dust transport, descent of mid-tropospheric air and sea breeze circulation on 17 June. Local pollution effects on the aerosol distribution, and a possible event of new particles formation were also observed. A large variability in the thermodynamical structure and aerosol distribution in the flight region, extending by approximately 30km along the coast, was found. Within this complex, environment-relevant differences in the back-trajectories calculated at different spatial resolutions are found, suggesting that the description of several dynamical processes, and in particular the sea breeze circulation, requires high-resolution meteorological analyses. The study also shows that the integration of different observational techniques is needed to describe these complex conditions; in particular, the availability of flights and their timing with respect to the occurring phenomena are crucial

Photoluminescence, photoabsorption and photoemission studies of hydrazone thin film used as hole transporting material in OLEDs

A fotoluminescência de filmes finos de 1-(3-metilfenil)-1,2,3,4-tetrahidroquinolina-6-carboxialdeído-1,1’-difenilhidrazona foi monitorada em função da irradiação com luz UV. A intensidade da emissão decresce exponencialmente com o tempo de exposição, sugerindo degradação das amostras. Com o objetivo de investigar os mecanismos de degradação e determinar a estrutura eletrônica desse material orgânico usado com sucesso como camada transportadora de buracos na fabricação de diodos orgânicos emissores de luz (OLEDs), foram empregadas as técnicas de fotoabsorção e de fotoemissão nas bordas 1s do carbono e do nitrogênio bem como na banda de valência. A influência da luz solar foi simulada usando radiação síncrotron não-monocromática. Após exposição, todos os espectros apresentam um decréscimo nos sinais de fotoabsorção e de fotoemissão, que é menos acentuado na borda do carbono, apresentando, entretanto, um decréscimo drástico na borda do nitrogênio e na região de valência. O estudo sugere que a perda de nitrogênio é a principal causa para a quebra do sistema π, levando, dessa forma, à falha do dispositivo fabricado com esse composto.Photoluminescence (PL) emission of 1-(3-methylphenyl)-1,2,3,4-tetrahydroquinoline-6-carboxyaldehyde-1,1’-diphenylhydrazone (MTCD) thin films was monitored as a function of UV irradiation, and it was found to decrease exponentially with the exposure time. In order to gain insight into the degradation mechanisms and evaluate the electronic structure of this organic material used with good results as hole transporting layer (HTL) in the fabrication of organic light emitting diodes (OLEDs), synchrotron radiation-based photoabsorption and photoemission techniques at the carbon and nitrogen 1s edges as well as at the valence band were employed. The influence of sunlight was simulated using non-monochromatized synchrotron radiation. After exposure all the spectra show a decrease of the photoabsorption and photoemission signals, however, while it is less accentuated at the carbon edge, at the nitrogen edge and at the valence region it decreases drastically. The loss of nitrogen is suggested to be the main step in the disruption of the π system, leading to the failure of the devices fabricated with this compound as hole transporting layer

Modular symbols and Hecke operators

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.Comment: 11 pp, 2 figures, uses psfrag.st

Adult cystic fibrosis care in the 21st century

Cystic fibrosis (CF) is the most common autosomal recessive inherited disease of Caucasian populations. As a result of a variety of diagnostic and therapeutic strategies there has been a dramatic increase in the life expectancy of patients with CF in the last decades and 50% of patients are now adults. This review will focus on the disease in adults and the provision of appropriate care. The complex care required to improve the survival and quality of life in the adult patients can best be provided in a dedicated adult cystic fibrosis unit. These units currently exist in many European countries, but more are needed in Italy