On fundamental groups related to the Hirzebruch surface F_1

Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in C^2 or in CP^2. In this article, we show that these groups, for the Hirzebruch surface F_{1,(a,b)}, are almost-solvable. That is - they are an extension of a solvable group, which strengthen the conjecture on degeneratable surfaces.Comment: accepted for publication at "Sci. in China, ser. Math"; 22 pages, 11 figure

Trisecant Lemma for Non Equidimensional Varieties

The classic trisecant lemma states that if $X$ is an integral curve of \PP^3 then the variety of trisecants has dimension one, unless the curve is planar and has degree at least 3, in which case the variety of trisecants has dimension 2. In this paper, our purpose is first to present another derivation of this result and then to introduce a generalization to non-equidimensional varities. For the sake of clarity, we shall reformulate our first problem as follows. Let $Z$ be an equidimensional variety (maybe singular and/or reducible) of dimension $n$, other than a linear space, embedded into \PP^r, $r \geq n+1$. The variety of trisecant lines of $Z$, say $V_{1,3}(Z)$, has dimension strictly less than $2n$, unless $Z$ is included in a $(n+1)-$dimensional linear space and has degree at least 3, in which case $\dim(V_{1,3}(Z)) = 2n$. Then we inquire the more general case, where $Z$ is not required to be equidimensional. In that case, let $Z$ be a possibly singular variety of dimension $n$, that may be neither irreducible nor equidimensional, embedded into \PP^r, where $r \geq n+1$, and $Y$ a proper subvariety of dimension $k \geq 1$. Consider now $S$ being a component of maximal dimension of the closure of \{l \in \G(1,r) \vtl \exists p \in Y, q_1, q_2 \in Z \backslash Y, q_1,q_2,p \in l\}. We show that $S$ has dimension strictly less than $n+k$, unless the union of lines in $S$ has dimension $n+1$, in which case $dim(S) = n+k$. In the latter case, if the dimension of the space is stricly greater then $n+1$, the union of lines in $S$ cannot cover the whole space. This is the main result of our work. We also introduce some examples showing than our bound is strict

Assessing the UK policies for broadband adoption

Broadband technology has been introduced to the business community and the public as a rapid way of exploiting the Internet. The benefits of its use (fast reliable connections, and always on) have been widely realised and broadband diffusion is one of the items at the top of the agenda for technology related polices of governments worldwide. In this paper an examination of the impact of the UK government’s polices upon broadband adoption is undertaken. Based on institutional theory a consideration of the manipulation of supply push and demand pull forces in the diffusion of broadband is offered. Using primary and secondary data sources, an analysis of the specific institutional actions related to IT diffusion as pursued by the UK government in the case of broadband is provided. Bringing the time dimension into consideration it is revealed that the UK government has shifted its attention from supply push-only strategies to more interventional ones where the demand pull forces are also mobilised. It is believed that this research will assist in the extraction of the “success factors” in government intervention that support the diffusion of technology with a view to render favourable results if applied to other national settings

Developmental exposures to perfluorooctanesulfonic acid (PFOS) impact embryonic nutrition, pancreatic morphology, and adiposity in the zebrafish, \u3cem\u3eDanio rerio\u3c/em\u3e

Perfluorooctanesulfonic acid (PFOS) is a persistent environmental contaminant previously found in consumer surfactants and industrial fire-fighting foams. PFOS has been widely implicated in metabolic dysfunction across the lifespan, including diabetes and obesity. However, the contributions of the embryonic environment to metabolic disease remain uncharacterized. This study seeks to identify perturbations in embryonic metabolism, pancreas development, and adiposity due to developmental and subchronic PFOS exposures and their persistence into later larval and juvenile periods. Zebrafish embryos were exposed to 16 or 32 μM PFOS developmentally (1–5 days post fertilization; dpf) or subchronically (1–15 dpf). Embryonic fatty acid and macronutrient concentrations and expression of peroxisome proliferator-activated receptor (PPAR) isoforms were quantified in embryos. Pancreatic islet morphometry was assessed at 15 and 30 dpf, and adiposity and fish behavior were assessed at 15 dpf. Concentrations of lauric (C12:0) and myristic (C14:0) saturated fatty acids were increased by PFOS at 4 dpf, and PPAR gene expression was reduced. Incidence of aberrant islet morphologies, principal islet areas, and adiposity were increased in 15 dpf larvae and 30 dpf juvenile fish. Together, these data suggest that the embryonic period is a susceptible window of metabolic programming in response to PFOS exposures, and that these early exposures alone can have persisting effects later in the lifecourse