An analysis of China in eight fourth-grade geography textbooks

Thesis (Ed.M.)--Boston Universit

Exhibiting Sha[2] on hyperelliptic jacobians

We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves, with an emphasis on the theory and practice of visualisation. Especially for hyperelliptic curves, this often enables the computation of ranks of Jacobians, even when the 2-Selmer bound does not bound the rank sharply. This was previously only possible for a few special cases. For curves of genus 2, we also demonstrate a connection with degree 4 del Pezzo surfaces, and show how the Brauer-Manin obstruction on these surfaces can be used to compute members of the Shafarevich-Tate group of Jacobians. We derive an explicit parametrised infinite family of genus 2 curves whose Jacobians have nontrivial members of the Sharevich-Tate group. Finally we prove that under certain conditions, the visualisation dimension for order 2 cocycles of Jacobians of certain genus 2 curves is 4 rather than the general bound of 32

Towers of 2-covers of hyperelliptic curves

In this article, we give a way of constructing an unramified Galois cover of a hyperelliptic curve. The geometric Galois-group is an elementary abelian 2-group. The construction does not make use of the embedding of the curve in its Jacobian and it readily displays all subcovers. We show that the cover we construct is isomorphic to the pullback along the multiplication-by-2 map of an embedding of the curve in its Jacobian. We show that the constructed cover has an abundance of elliptic and hyperelliptic subcovers. This makes this cover especially suited for covering techniques employed for determining the rational points on curves. Especially the hyperelliptic subcovers give a chance for applying the method iteratively, thus creating towers of elementary abelian 2-covers of hyperelliptic curves. As an application, we determine the rational points on the genus 2 curve arising from the question whether the sum of the first n fourth powers can ever be a square. For this curve, a simple covering step fails, but a second step succeeds

N-covers of hyperelliptic curves

For a hyperelliptic curve C of genus g with a divisor class of order n=g+1, we shall consider an associated covering collection of curves D$_\delta$, each of genus g$^2$. We describe, up to isogeny, the Jacobian of each D$_\delta$ via a map from D$_\delta$ to C, and two independent maps from D$_\delta$ to a curve of genus g(g-1)/2. For some curves, this allows covering techniques that depend on arithmetic data of number fields of smaller degree than standard 2-coverings; we illustrate this by using 3-coverings to find all Q-rational points on a curve of genus 2 for which 2-covering techniques would be impractical

The importance of space, place and everyday life for the reintegration of prisoners and criminal desistance.

This thesis is a study of the impact of place on the choices and decisions of released prisoners to desist from offending. It takes as its starting point recent research evidence that large numbers of prisoners in the US and UK are drawn from specific urban neighbourhoods to which they return after release only to reoffend and be re-imprisoned. Rather than assume there is a direct equivalence between criminal behaviour and place, it investigates how place differences interact with individual differences to determine the pathways taken by prisoners over the life course. Thus, it assesses how both structural and agentic factors affect reoffending and/or criminal desistance in the places prisoners grow up, in prison, and the places to which they return after prison. As well as criminological literature, the study draws on a wide range of social scientific materials on the importance of space, place and everyday life. Most prominently, it refers to geographical, sociological and psychological analyses which have explored the reciprocal nature of people/place relationships. In particular, the perspective within human geography that `just as people construct places, places construct people' has informed the research design adopted for the study. This incorporates both a quantitative mapping exercise to show the geographical distribution of prisoners from Greater London and a qualitative account of the meanings, emotions and attitudes of a sample of prisoners towards the places they inhabit, and the influence these have on reoffending and/or criminal desistance. The main conclusions of the thesis are that most prisoners from Greater London are drawn from wards which are socially deprived. During childhood, a shared experience of specific places shapes criminal behaviour which is interpersonal and fundamentally experiential in nature. Then, having enjoyed the thrill and excitement of `crime as play', persistent offenders grow up to embrace `crime as a way of life'. Many prisoners profess an inclination to give up crime, but the different ways they respond to prison does not encourage them to `go straight'. Although the process of criminal desistance is not dependent on moving away from local criminogenic environments, it may be constrained by social characteristics and social relations in the places most prisoners return to after release. The thesis ends by discussing the implications of this life course perspective for prisoner reintegration policy

Canonical heights on the jacobians of curves of genus 2 and the infinite descent

We give an algorithm to compute the canonical height on a Jacobian of a curve of genus 2. The computations involve only working with the Kummer surface and so lengthy computations with divisors in the Jacobian are avoided. We use this height algorithm to give an algorithm to perform the infinite descent stage of computing the Mordell-Weil group. This last stage is performed by a lattice enlarging procedure

Enhanced 3-epi-25-hydroxyvitamin D3 signal leads to overestimation of its concentration and amplifies interference in 25-hydroxyvitamin D LC-MS/MS assays

Background 3-epi-25-hydroxyvitamin D3 (3-epi-25OHD3) interferes in most liquid chromatography-tandem mass spectrometry (LC-MS/MS) assays for 25-hydroxyvitamin D (25OHD). The clinical significance of this is unclear, with concentrations from undetectable to 230 nmol/L reported. Many studies have quantified 3-epi-25OHD3 based on 25OHD3 calibrators or other indirect methods, and we speculated that this contributes to the observed variability in reported 3-epi-25OHD3 concentrations. Methods We compared continuous MS/MS infusions of 3-epi-25OHD3 and 25OHD3 solutions, spiked both analytes into the same serum matrix and analysed patient samples to assess the effect of three different quantitation methods on 3-epi-25OHD3 concentration. Experiments were performed on an LC-MS/MS system using a phenyl column which does not resolve 3-epi-25OHD3, and a modified method utilizing a Zorbax SB-CN column that chromatographically resolves 3-epi-25OHD3 from 25OHD3. Results A greater 3-epi-25OHD3 signal, compared with 25OHD3, was observed during equimolar post-column continuous infusion of analyte solutions, and following analysis of a serum pool spiked with both analytes. 3-epi-25OHD3 signal enhancement was dependent on mobile phase composition. Compared with 3-epi-25OHD3 calibrators, indirect quantitation methods resulted in up to 10 times as many samples having 3-epi-25OHD3 concentrations ≥ 10 nmol/L, and an approximately fourfold increase in the maximum observed 3-epi-25OHD3 concentration to 95 nmol/L. Conclusions Enhanced 3-epi-25OHD3 signal leads to overestimation of its concentrations in the indirect quantitation methods used in many previous studies. The enhanced signal may contribute to greater interference in some 25OHD LC-MS/MS assays than others. We highlight that equimolar responses cannot be assumed in LC-MS/MS systems, even if two molecules are structurally similar

Disk M Dwarf Luminosity Function From HST Star Counts

We study a sample of 257 Galactic disk M dwarfs (8<M_V<18.5) found in images obtained using HST. These include 192 stars in 22 fields imaged with the repaired WFC2 with mean limiting mag I=23.7 and 65 stars in 162 fields imaged with the pre-repair Planetary Camera with mean limiting mag V=21.3. We find that the disk luminosity function (LF) drops sharply for M_V>12 (M<0.25 \ms), decreasing by a factor \gsim 3 by M_V~14 (M~0.14\ms). This decrease in the LF is in good agreement with the ground-based photometric study of nearby stars by Stobie et al. (1989), and in mild conflict with the most recent LF measurements based on local parallax stars by Reid et al. (1995). The local LF of the faint Galactic disk stars can be transformed into a local mass function using an empirical mass-M_V relation. The mass function can be represented analytically over the mass range 0.1\ms<M<1.6\ms by \log(\phi)=-1.35-1.34\log(M/\ms)-1.85 [\log(M/\ms)]^2 where \phi is the number density per logarithmic unit of mass. The total column density of M stars is only \Sigma_M=11.8\pm 1.8\ms\pc^{-2}, implying a total `observed' disk column density of \Sigma_\obs~=39\ms\pc^{-2}, lower than previously believed, and also lower than all estimates with which we are familiar of the dynamically inferred mass of the disk. The measured scale length for the M-star disk is 3.0\pm 0.4 kpc. The optical depth to microlensing toward the LMC by the observed stars in the Milky Way disk is \tau~1x10^{-8}, compared to the observed optical depth found in ongoing experiments \tau_\obs~ 10^{-7}. The M-stars show evidence for a population with characteristics intermediate between thin disk and spheroid populations. Approximating what may be a continuum of populations by two separate component, we find characteristic exponential scale heights of ~210 pc and ~740 pc.Comment: 30 pages, uuencoded postscript, includes 3 figures, 2 table

The Digital Flynn Effect: Complexity of Posts on Social Media Increases over Time

Parents and teachers often express concern about the extensive use of social media by youngsters. Some of them see emoticons, undecipherable initialisms and loose grammar typical for social media as evidence of language degradation. In this paper, we use a simple measure of text complexity to investigate how the complexity of public posts on a popular social networking site changes over time. We analyze a unique dataset that contains texts posted by 942, 336 users from a large European city across nine years. We show that the chosen complexity measure is correlated with the academic performance of users: users from high-performing schools produce more complex texts than users from low-performing schools. We also find that complexity of posts increases with age. Finally, we demonstrate that overall language complexity of posts on the social networking site is constantly increasing. We call this phenomenon the digital Flynn effect. Our results may suggest that the worries about language degradation are not warranted