Subgroups of direct products of limit groups

If $G_1,...,G_n$ are limit groups and $S\subset G_1\times...\times G_n$ is of type \FP_n(\mathbb Q) then $S$ contains a subgroup of finite index that is itself a direct product of at most $n$ limit groups. This settles a question of Sela.Comment: 20 pages, no figures. Final version. Accepted by the Annals of Mathematic

On the finite presentation of subdirect products and the nature of residually free groups

We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,...,\Gamma_n$ are finitely presented and $S<\Gamma_1\times...\times\Gamma_n$ projects to a subgroup of finite index in each $\Gamma_i\times\Gamma_j$, then $S$ is finitely presentable, indeed there is an algorithm that will construct a finite presentation for $S$. We use the VSP criterion to characterise the finitely presented residually free groups. We prove that the class of such groups is recursively enumerable. We describe an algorithm that, given a finite presentation of a residually free group, constructs a canonical embedding into a direct product of finitely many limit groups. We solve the (multiple) conjugacy problem and membership problem for finitely presentable subgroups of residually free groups. We also prove that there is an algorithm that, given a finite generating set for such a subgroup, will construct a finite presentation. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups that are neither ${\rm{FP}}_\infty$ nor of Stallings-Bieri typeComment: 44 pages. To appear in American Journal of Mathematics. This is a substantial rewrite of our previous Arxiv article 0809.3704, taking into account subsequent developments, advice of colleagues and referee's comment

Arterial occlusion: a radiological study of a series of patients with peripheral, arterial disease

An unselected series of 546 patients, on whom 946 arteriograms were performed is considered.1250 complete arterial occlusions were found. The incidence was 2.3 per patient, both in men and in women.It is suggested that the sex distribution of peripheral vascular disease in a population is more accurately indicated by the findings in gangrene and pregangrene where there are 2.3 and 2 men, respectively to 1 woman, than by those in intermittent claudication where the sex ratio is 4.8 men to 1 woman,Aortographic evidence is presented to suggest that aortic occlusion may originate directly in the aorta itself, in women, more commonly than previously believed.On the symptomatic side occlusion in the femoro -popliteal segment alone occurs in only 43.5% of the occluded symptomatic limbs in men, and in only 34.6% of those in women.Femoro-popliteal occlusion with leg artery occlusion occurs in 43.2% of the occluded symptomatic limbs in men, and in 40.7% of those in women.Leg artery occlusion alone occurs in 13.3% of the occluded symptomatic limbs in men, and in 24.7% of those in women.On the asymptomatic side femoro-popliteal artery occlusion alone occurs in 19.8% of the occluded limbs of men and in 9.7% in women. Femoro -popliteal occlusions with associated leg artery occlusion occurs in 20.7% of the occluded asymptomatic limbs in men, and in 25.8% of those in women. Leg artery occlusion alone occurs in 59.5% of the occluded asymptomatic limbs in men and in 64.5% of those in women.The patterns of occlusion in the lower limbs are recorded. The commonest pattern is occlusion of the superficial femoral artery alone, in both women and men. Second most common is occlusion of the anterior tibial artery alone in men, and of the posterior tibial artery alone in women,The occlusion patterns in men and women are considered in intermittent claudication, gangrene and pregangrene.Patients with complete occlusion in the aortoiliac group are younger than those with complete occlusion in the femoro-popliteal group.The patients with complete occlusion in the femoro-popliteal group are older than those without complete occlusion. In the aortoiliac group those with complete occlusion are younger than those without,The incidence of leg artery occlusion is the same in the symptomatic and asymptomatic limbs in intermittent claudication.It is suggested that there is evidence that the first artery to show complete occlusion in the lower limb tends to be a leg artery.The incidence of complete occlusion is higher in limbs in patients with unilateral symptoms, than in those with bilateral symptoms.The peak incidence of occlusion in the femoro-popliteal segment in women is more proximal in the adductor canal than in men.The femoro-popliteal occlusions in the limbs with leg artery occlusion are longer than in those without, and show a greater tendency to popliteal artery involvement.The occlusions in the symptomatic and asymptomatic limbs are considered. They are, very broadly, similar in their histographic appearances

Intermolecular N-H...O=C hydrogen bonding in the crystal structure of 6-amino-1,3-dimethyluracil

The 6-amino- 1,3-dimethyluracil molecule [6-amino- 1,3- dimethyl-2,4(1H,3H)-pyrimidinedione], C6H9N302 (I), lies on a crystallographic mirror plane and participates in an extensive two-dimensional hydrogen-bonding network in the solid state. Each molecule is involved in N-- H...O=C hydrogen bonding involving the amino and carbonyl gr. oups, with O...N separations of 2.894 (3) and 2.904 (3) A

Ariel - Volume 11 Number 2

Executive Editors Ellen Feldman Leonardo S. Nasca, Jr. Business .Managers Barbara L. Davies Martin B. Getzow News Editor Aaron D. Bleznak Features Editor Hugh A. Gelabert CAHS Editor Joan M. Greco Editorial Page Editor Samuel Markind Photography Editor Leonardo S. Nasca, Jr. Sports Editor Paul F. Mansfiel

Scottish theme towns: have new identities enhanced development?

Three small towns in southwest Scotland have recently been branded as distinct theme towns, based on books, artists and food. This is an attempt to make them more attractive to visitors and thereby improve their economy. The objective of this research is to establish whether the new identities possessed by the towns have enhanced their development. It is argued, using data reviewing the past decade, that they have all developed, albeit at different rates, in terms of the economy and culture. Moreover, it is maintained that social capital has been enhanced and is a factor whose importance has been under-appreciated by planners and observers of this type of process. The relevance of the new identity to the pre-branding identity is also seen as a factor in successful development and ideas of authenticity and heritage are brought to bear on the relationship

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts

Multi-color Optical and NIR Light Curves of 64 Stripped-Envelope Core-Collapse Supernovae

We present a densely-sampled, homogeneous set of light curves of 64 low redshift (z < 0.05) stripped-envelope supernovae (SN of type IIb, Ib, Ic and Ic-bl). These data were obtained between 2001 and 2009 at the Fred L. Whipple Observatory (FLWO) on Mt. Hopkins in Arizona, with the optical FLWO 1.2-m and the near-infrared PAIRITEL 1.3-m telescopes. Our dataset consists of 4543 optical photometric measurements on 61 SN, including a combination of UBVRI, UBVr'i', and u'BVr'i', and 2142 JHKs near-infrared measurements on 25 SN. This sample constitutes the most extensive multi-color data set of stripped-envelope SN to date. Our photometry is based on template-subtracted images to eliminate any potential host galaxy light contamination. This work presents these photometric data, compares them with data in the literature, and estimates basic statistical quantities: date of maximum, color, and photometric properties. We identify promising color trends that may permit the identification of stripped-envelope SN subtypes from their photometry alone. Many of these SN were observed spectroscopically by the CfA SN group, and the spectra are presented in a companion paper (Modjaz et al. 2014). A thorough exploration that combines the CfA photometry and spectroscopy of stripped-envelope core-collapse SN will be presented in a follow-up paper.Comment: 26 pages, 17 figures, 8 tables. Revised version resubmitted to ApJ Supplements after referee report. Additional online material is available through http://cosmo.nyu.edu/SNYU