Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
535
result(s) for
"Dyer, Peter"
Sort by:
The boy in the biscuit tin
When Ibby goes to stay with her aunt, she discovers her troublesome boy cousins can do real magic.
Book
Curves of Small Genus on Certain K3 Surfaces
Recent workers [1, 3] have proved density theorems about the rational points on K3 surfaces of the form
$$
V:\\;X_0^4+cX_1^4=X_2^4+cX_3^4
$$
for certain non-zero values of c. Their arguments depend on the presence of at least two pencils of curves of genus 1 on V. Unfortunately the values of c for which the argument works are constrained by the need to exhibit explicitly a rational point on V which satisfies certain extra conditions; these in particular require it to lie outside the four obvious rational lines on V. It is therefore natural to ask whether there are other curves of genus 0 or 1 defined over Q on V. In the case c = 1 there are known to be infinitely many such curves (see [2]), and for general rational c the quadratic form Q on the Néron–Severi group whose value is the self-intersection number takes the values 0 and -2 infinitely often. Naively one might expect the case c = 1 to be typical; but this is not so. The main object of this paper is to prove the following result.
Journal Article
The effect of twisting on the 2-Selmer group
Let Γ be an elliptic curve defined over Q, all of whose 2-division points are rational, and let Γb be its quadratic twist by b. Subject to a mild additional condition on Γ, we find the limit of the probability distribution of the dimension of the 2-Selmer group of Γb as the number of prime factors of b increases; and we show that this distribution depends only on whether the 2-Selmer group of Γ has odd or even dimension.
Journal Article
Common Themes and Uncertainties in Management of Secondary Polycythaemia: An International Clinician Survey of Practice
Introduction Secondary and idiopathic polycythaemia is far more common than polycythaemia vera. Whilst venesection for polycythaemia vera has a robust evidence base, the data supporting this treatment for secondary and/or idiopathic polycythaemia are limited to small single‐arm studies showing transient improvement in symptoms or physiologic endpoints. As a result the British Society for Haematology Guideline for the management of specific situations in polycythaemia vera and secondary erythrocytosis suggests considering venesection in patients with hypoxic lung disease with Hct > 0.56 or to a target Hct < 0.55 in those with idiopathic polycythaemia. We hypothesised that this paucity of evidence results in widespread variation in management of secondary polycythaemia. Methods To assess attitudes and practice in the treatment of secondary and idiopathic polycythaemia we designed an international clinician survey to evaluate current practice and define the point of clinical equipoise at which clinicians would be content to enter patients into a randomised venesection study. This survey was distributed using the wide‐reaching HaemSTAR research network. Results A total of 123 clinicians responded, of which 90 were experienced senior clinicians. 62% reported not routinely offering regular venesection whereas 38% of respondents did. Those considering venesection rose to ∼2/3 of respondents in specific circumstances such as polycythaemia‐related symptoms, previous arterial or unprovoked venous thrombosis. Respondents were more likely to offer venesection to patients with idiopathic‐ compared to androgen‐ or hypoxia‐driven polycythaemia. Of those who would venesect, most would use a threshold Hct ≥ 0.55, with a target Hct < 0.55 but there was significant variability. Conclusions Our survey showed considerable variability in venesection practice for patients with secondary or idiopathic polycythaemia, probably reflecting the paucity of the evidence base. There was widespread support for a trial of venesection vs observation in secondary polycythaemia and this survey has helped to define the threshold Hct at which clinical equipoise exists.
Journal Article
Presidential address
The Presidential and Valedictory addresses published here were given at the British Dental Conference & Exhibition 2017 in Manchester on the 25 May 2017.
Journal Article
Cubic surfaces over finite fields
Let V be a nonsingular cubic surface defined over the finite field Fq. It is well known that the number of points on V satisfies #V(Fq) = q2 + nq + 1 where −2 ≤ n ≤ 7 and that n = 6 is impossible; see for example [1], Table 1. Serre has asked if these bounds are best possible for each q. In this paper I shall show that this is so, with three exceptions:
Journal Article