Experimenting with infinite groups, I

A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. Since free groups are residually nilpotent, they are parafree. Nonfree parafree groups abound and they all have many properties in common with free groups. Finitely presented parafree groups have solvable word problems, but little is known about the conjugacy and isomorphism problems. The conjugacy problem plays an important part in determining whether an automorphism is inner, which we term the inner automorphism problem. We will attack these and other problems about parafree groups experimentally, in a series of papers, of which this is the first and which is concerned with the isomorphism problem. The approach that we take here is to distinguish some parafree groups by computing the number of epimorphisms onto selected finite groups. It turns out, rather unexpectedly, that an understanding of the quotients of certain groups leads to some new results about equations in free and relatively free groups. We touch on this only lightly here but will discuss this in more depth in a future paper.

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Promising results of a cooperative group phase II trial of preoperative chemoradiation for locally advanced rectal cancer (TROG 9801)

PURPOSE: This article reports the overall survival, failure-free survival, local failure, and late radiation toxicity of a phase II trial of preoperative radiotherapy with continuous infusion 5-fluorouracil for rectal cancer after a minimum 3.5 years of follow-up. METHODS: Eligible patients were those with newly diagnosed localized adenocarcinoma of the rectum, within 12 cm of the anal verge, staged T3-T4 and deemed suitable for curative resection. Radiotherapy (50.4 Gy in 28 fractions in five weeks and three days) was given with continuous infusion 5-fluorouracil throughout the course of radiotherapy. RESULTS: A total of 82 patients were accrued in 13 months. The median follow-up time was 4.1 (range, 2.3-4.5) years. There were 55 males (67 percent) and the median age was 59 (range, 27-87) years. Patients were staged pretreatment as T3 (89 percent) and resectable T4 (11 percent). Endorectal ultrasound was performed in 70 percent and magnetic resonance imaging in another 5 percent. The four-year overall and failure-free survival rates were 82 percent (95 percent Cl: 72-89) and 69 percent (95 percent Cl: 58-78), respectively. The cumulative incidence of local failure at four years was 3.9 percent (95 percent CI: 1.3-11). Risk of failures, local and distant, has not reached a plateau phase. CONCLUSION: This regimen can be delivered safely and without leading to a significant increase in late toxicity. It provides excellent local control and favorable overall survival. There is a need for longer follow-up than has commonly been used for the proper evaluation of failures after an effective regimen of preoperative chemoradiation.

Fracture load and marginal fit of shrinkage-free ZrSiO4 all-ceramic crowns after chewing simulation

The aim of this in vitro study was to evaluate the fracture load and marginal accuracy of crowns made from a shrinkage-free ZrSiO4 ceramic cemented with glass-ionomer or composite cement after chewing simulation. Thirty-two human mandibular molars were randomly divided into two groups. All teeth were prepared for and restored with shrinkage-free ZrSiO4 ceramic crowns (Everest HPC (R), KaVo). The crowns of group A (N = 16) were luted to the teeth using KetacCem (R) and group B (N = 16) were adhesively cemented using Panavia (R) 21EX. Measurements of the marginal accuracy before and after cementation were made using replicas and an image analysis system. All specimens were exposed to 1.2 million cycles of thermo-mechanical fatigue in a chewing simulator. Surviving specimens were subsequently loaded until fracture in a static testing device. Fracture loads (N) were recorded. All specimens survived chewing simulation. The mean fracture loads (+/- s.d.) were Group A, 1622 N (+/- 433); group B, 1957 N (+/- 806). There was no significant difference between the two groups (P > 0.05). The marginal gap values before cementation were (mean +/- s.d.): Group A, 32.7 mu m (+/- 6.8); group B, 33.0 mu m (+/- 6.7).The mean marginal gap values after cementation were (+/- s.d.): Group A, 44.6 mu m (+/- 6.7); group B, 46.6 mu m (+/- 7.7). The marginal openings were significantly higher after cementation for both groups (P < 0.05). All test groups demonstrated fracture load and marginal accuracy values within the range of clinical acceptability.

Whole brain irradiation following surgery or radiosurgery for solitary brain metastases: Mature results of a prematurely closed randomized Trans-Tasman Radiation Oncology Group trial (TROG 98.05)

We evaluated the effect of adjuvant whole brain irradiation (WBI) after surgery or radiosurgery for solitary brain metastases in a Phase III multicentre trial with randomization to 30-36 Gy WBI or observation. The study was closed early due to slow accrual after 19 patients (WBI 10, observation 9). There was no difference in CNS failure-free survival or overall survival between the arms. There was a trend to reduced CNS relapse with WBI (30% versus 78%, P = 0.12). Limited analysis of quality of life and neurocognitive function data revealed no evidence of difference between the arms. Our results are not inconsistent with two larger randomized trials and support the use of upfront WBI to decrease brain recurrence in this setting. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

No more free beer tomorrow? Economic policy and outcomes in Australia and New Zealand since 1984

There are no controlled experiments in macroeconomic policy, nor in systematic programs of microeconomic reform, but a comparison between New Zealand and Australia over the period since 1984 provides as close an approach to such an experiment as is ever likely to be possible. From quite similar starting points the two countries pursued liberal reform programs that differed sharply, mainly as a result of exogenous differences in constitutional structures and the personal styles of the central actors. Australia followed a more cautious, piecemeal, consensus-based approach, whereas New Zealand, in contrast, adopted a radical, rapid, 'purist' platform. The NZ reform package was generally seen by contemporary commentators as representing a 'textbook' model for best practice reform. However, Australia since 1984 has performed much better than New Zealand, whose per capita GDP growth indeed ranked at or near the bottom of the OECD. In this paper, we assess a variety of explanations for the divergences in policies and outcomes.