Line bundles for which a projectivized jet bundle is a product

We characterize the triples (X,L,H), consisting of holomorphic line bundles L and H on a complex projective manifold X, such that for some positive integer k, the k-th holomorphic jet bundle of L, J_k(L), is isomorphic to a direct sum H+...+H. Given the geometrical constrains imposed by a projectivized line bundle being a product of the base and a projective space it is natural to expect that this would happen only under very rare circumstances. It is shown, in fact, that X is either an Abelian variety or projective space. In the former case L\cong H is any line bundle of Chern class zero. In the later case for k a positive integer, L=O_{P^n}(q) with J_k(L)=H+...+H if and only if H=O_{P^n}(q-k) and either q\ge k or q\le -1.Comment: Latex file, 5 page

Wie entscheiden sich Schülerinnen für oder gegen eine HPV-Impfung?

Zusammenfassung: Hintergrund: 2007 wurde die HPV- ("human papilloma virus-")Impfung in der Schweiz eingeführt und in der Stadt Zürich mittels einer Impfaktion des Schulärztlichen Dienstes 2008 allen Schülerinnen zwischen 11 und 16Jahren gratis angeboten. Danach impft der Schulärztliche Dienst im Rahmen einer Schulärztlichen Untersuchung in der 6. Und 8. Klasse. Die HPV-Impfung ist in der Schweiz umstritten und wird nicht selten, v.a. von impfkritischen Eltern, als überflüssig kritisiert. Ziel: Das Ziel der vorgestellten Studie war zu ermitteln, wie 13- bis 15-jährige Schülerinnen die Entscheidung für oder gegen die Impfung treffen, und von welchen Akteuren sie in ihrer Entscheidungsfindung beeinflusst werden. Ergebnis: Der größte Einflussfaktor bei der Entscheidung für oder gegen die Impfung sind die Eltern, insbesondere die Mütter der Schülerinnen. Diese sind ihrerseits von Frauen- und Kinderärzten beeinflusst. Die Medien, die Lehrpersonen sowie die Peers spielen eine eher untergeordnete Rolle. Insgesamt zeigen viele Akteure eine impfkritische Einstellung, die aber nur teilweise ausgesprochen wird. Um eine bessere Akzeptanz zu erreichen, müsste deshalb ein ganzheitlicher Entscheidungsprozess in den Schulen angestrebt werden, der alle Akteure mit einbezieh

Linear Toric Fibrations

These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory

A Frobenius variant of Seshadri constants

We define and study a version of Seshadri constant for ample line bundles in positive characteristic. We prove that lower bounds for this constant imply the global generation or very ampleness of the corresponding adjoint line bundle. As a consequence, we deduce that the criterion for global generation and very ampleness of adjoint line bundles in terms of usual Seshadri constants holds also in positive characteristic.Comment: 16 page

Seismic vulnerability of above-ground storage tanks with unanchored support conditions for Na-tech risks based on Gaussian process regression

AbstractThis paper aims to investigate the seismic vulnerability of an existing unanchored steel storage tank ideally installed in a refinery in Sicily (Italy), along the lines of performance-based earthquake engineering. Tank performance is estimated by means of component-level fragility curves for specific limit states. The assessment is based on a framework that relies on a three-dimensional finite element (3D FE) model and a low-fidelity demand model based on Gaussian process regression, which allows for cheaper simulations. Moreover, to approximate the system response corresponding to the random variation of both peak ground acceleration and liquid filling level, a second-order design of experiments method is adopted. Hence, a parametric investigation is conducted on a specific existing unanchored steel storage tank. The relevant 3D FE model is validated with an experimental campaign carried out on a shaking table test. Special attention is paid to the base uplift due to significant inelastic deformations that occur at the baseplate close to the welded baseplate-to-wall connection, offering extensive information on both capacity and demand. As a result, the tank performance is estimated by means of component-level fragility curves for the aforementioned limit state which are derived through Monte Carlo simulations. The flexibility of the proposed framework allows fragility curves to be derived considering both deterministic and random filling levels. The comparison of the seismic vulnerability of the tank obtained with probabilistic and deterministic mechanical models demonstrates the conservatism of the latter. The same trend is also exhibited in terms of risk assessment

HISTORICAL EARTHEN WALLS: FROM KNOWLEDGE TO CONSCIOUS CONSERVATION

Abstract. Centuries-old earthen masonry presenting various stages of degradation, earthen walls that have been restored several times: these are the archeological phases of the city walls of Mascarell, on the Spanish Mediterranean coast. Founded in the first half of the 13th century, this town is the only complex in Castellon Province that preserves all its ancient walls, which were built entirely by means of the brick-faced rammed-earth technique (clay with bricks and lime). This article reports the first results of a research project conducted on the multiple information available on these artifacts: bibliographic, archival and iconographic sources and the results of direct material analysis, stratigraphic analysis and archeological analysis. The situation is complex, as these walls have undergone a long sequence of transformations, including interventions carried out since the 18th century and multiple restorations in the period 1942–2015. The research developed and refined architecture archeology tools in order to analyze the rammed-earth techniques adopted during restoration work (similar but not identical to the historical technique), to characterize the materials used in restoration, to evaluate their resistance to degradation over the years, to define a sort of 'critical evolutionary line' of rammed-earth restoration, and to conduct a cross-sectional study of this building technique from the Middle Ages to the present. Finally, we drafted some guidelines for future interventions for conservation and enhancement

A mathematical model for mechanotransduction at the early steps of suture formation

Growth and patterning of craniofacial sutures are subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron x-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (\emph{Polypterus bichir}) and a placoderm (\emph{Compagopiscis croucheri}), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion