An alternative proof that the Fibonacci group F(2,9) is infinite

This note contains a report of a proof by computer that the Fibonacci group F(2,9) is automatic. The automatic structure can be used to solve the word problem in the group. Furthermore, it can be seen directly from the word-acceptor that the group generators have infinite order, which of course implies that the group itself is infinite.Comment: LaTex, 3 pages, no figures. To appear in Experimental Mathematic

Finitely generated soluble groups and their subgroups

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.Comment: 16 page

Solving the word problem in real time

The paper is devoted to the study of groups whose word problem can be solved by a Turing machine which operates in real time. A recent result of the first author for word hyperbolic groups is extended to prove that under certain conditions the generalised Dehn algorithms of Cannon, Goodman and Shapiro, which clearly run in linear time, can be programmed on real-time Turing machines. It follows that word-hyperbolic groups, finitely generated nilpotent groups and geometrically finite hyperbolic groups all have real-time word problems

Prediction and analysis of long-term variability of temperature and salinity in the Irish Sea

The variability of temperature and salinity in the Irish Sea over the 40 year period 1960 - 1999 is investigated using a free-running fine-resolution local area model. The skill of the model to represent observed temperature and salinity variability is assessed using conductivity-temperature-depth survey data ( 3397 profiles) and a long time series of measurements from Cypris station (southwest of Isle of Man). This clearly demonstrates that the model can reproduce the observed seasonal and longer-term cycles in temperature, with mean and RMS errors of - 0.01 degrees C and 0.78 degrees C. Particularly apparent is the long-term warming trend at Cypris station and throughout the model domain. Model estimates of salinity are less accurate and are generally too saline (mean and RMS errors are 0.79 and 0.98 practical salinity units). Inaccuracies are likely to arise from boundary conditions and forcing (riverine and surface). However, while absolute values are not particularly well represented, the model reproduces many of the trends in the salinity variability observed at Cypris station, suggesting that the dominant physical processes in the Irish Sea, with timescales up to similar to 3 years, are well represented. The model is also used to investigate the variability in temperature stratification. While stratification is confined to approximately the same geographical area in each year of the simulation, there is significant variability in the timing of the onset and breakdown of stratification and in the peak surface to bed temperature difference. Together, these results suggest that a local area model with limited boundary conditions may be sufficiently accurate for climatic investigation of some (locally forced) parameter

On real-time word problems

It is proved that the word problem of the direct product of two free groups of rank 2 can be recognised by a 2-tape real-time but not by a 1-tape real-time Turing machine. It is also proved that the Baumslag–Solitar groups B(1,r) have the 5-tape real-time word problem for all r != 0

Hurricane María: An Agroecological Turning Point for Puerto Rico?

When Hurricane María tore through Puerto Rico on September 20, 2017, it left 17 dead, 11,000 seeking shelter, and the island’s 3.4 million people without power, water, or fresh food supplies.i It also ripped off the democratic veneer of the US’ “commonwealth,” revealing the structural vulnerability of an island that has been colonized for over half a millennium. Disasters tend to unmask both unsustainable practices and inequitable relations of power. But they can also unleash the power of solidarity and self-governance as communities—abandoned by their governments and preyed upon by disaster capitalists—come together in unexpected ways. In the aftermath of Puerto Rico’s worst social, economic and environmental catastrophe, the Puerto Rican food sovereignty movement is using agroecology to reconstruct the island’s beleaguered food system