On exponential growth rates for free groups

Let Fp be a free group of rank p ¸ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p¡1. We show that the exponential growth rate ¿ of a group G with respect to a p-element generating set X is 2p¡1 if and only if G is free on X; otherwise ¿ 2p¡1.59

Environmental changes and violent conflict

This letter reviews the scientific literature on whether and how environmental changes affect the risk of violent conflict. The available evidence from qualitative case studies indicates that environmental stress can contribute to violent conflict in some specific cases. Results from quantitative large-N studies, however, strongly suggest that we should be careful in drawing general conclusions. Those large-N studies that we regard as the most sophisticated ones obtain results that are not robust to alternative model specifications and, thus, have been debated. This suggests that environmental changes may, under specific circumstances, increase the risk of violent conflict, but not necessarily in a systematic way and unconditionally. Hence there is, to date, no scientific consensus on the impact of environmental changes on violent conflict. This letter also highlights the most important challenges for further research on the subject. One of the key issues is that the effects of environmental changes on violent conflict are likely to be contingent on a set of economic and political conditions that determine adaptation capacity. In the authors' view, the most important indirect effects are likely to lead from environmental changes via economic performance and migration to violent conflict. © 2012 IOP Publishing Ltd

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Evaluation of shear bond strength of two resin-based composites and glass ionomer cement to pure tricalcium silicate-based cement (Biodentine®)

Objectives: Tricalcium silicate is the major constituent phase in mineral trioxide aggregate (MTA). It is thus postulated that pure tricalcium silicate can replace the Portland cement component of MTA. The aim of this study was to evaluate bond strength of methacrylate-based (MB) composites, silorane-based (SB) composites, and glass ionomer cement (GIC) to Biodentine® and mineral trioxide aggregate (MTA). Material and Methods: Acrylic blocks (n=90, 2 mm high, 5 mm diameter central hole) were prepared. In 45 of the samples, the holes were fully filled with Biodentine® and in the other 45 samples, the holes were fully filled with MTA. The Biodentine® and the MTA samples were randomly divided into 3 subgroups of 15 specimens each: Group-1: MB composite; Group-2: SB composite; and Group-3: GIC. For the shear bond strength (SBS) test, each block was secured in a universal testing machine. Results: The highest (17.7±6.2 MPa) and the lowest (5.8±3.2 MPa) bond strength values were recorded for the MB composite-Biodentine® and the GIC-MTA, respectively. Although the MB composite showed significantly higher bond strength to Biodentine (17.7±6.2) than it did to MTA (8.9±5.7) (p<0.001), the SB composite (SB and MTA=7.4±3.3; SB and Biodentine®=8.0±3,6) and GIC (GIC and MTA=5.8±3.2; GIC and Biodentine=6.7±2.6) showed similar bond strength performance with MTA compared with Biodentine (p=0.73 and p=0.38, respectively). Conclusions: The new pure tricalcium-based pulp capping, repair, and endodontic material showed higher shear bond scores compared to MTA when used with the MB composite