The Quantum Galilei Group

The quantum Galilei group $G_{\varkappa}$ is defined. The bicrossproduct structure of $G_{\varkappa}$ and the corresponding Lie algebra is revealed. The projective representations for the two-dimensional quantum Galilei group are constructed.Comment: AMSTe

Fundamental solution method applied to time evolution of two energy level systems: exact and adiabatic limit results

A method of fundamental solutions has been used to investigate transitions in two energy level systems with no level crossing in a real time. Compact formulas for transition probabilities have been found in their exact form as well as in their adiabatic limit. No interference effects resulting from many level complex crossings as announced by Joye, Mileti and Pfister (Phys. Rev. {\bf A44} 4280 (1991)) have been detected in either case. It is argued that these results of this work are incorrect. However, some effects of Berry's phases are confirmed.Comment: LaTeX2e, 23 pages, 8 EPS figures. Style correcte

Failure of classical elasticity in auxetic foams

A recent derivation [P.H. Mott and C.M. Roland, Phys. Rev. B 80, 132104 (2009).] of the bounds on Poisson's ratio, v, for linearly elastic materials showed that the conventional lower limit, -1, is wrong, and that v cannot be less than 0.2 for classical elasticity to be valid. This is a significant result, since it is precisely for materials having small values of v that direct measurements are not feasible, so that v must be calculated from other elastic constants. Herein we measure directly Poisson's ratio for four materials, two for which the more restrictive bounds on v apply, and two having values below this limit of 0.2. We find that while the measured v for the former are equivalent to values calculated from the shear and tensile moduli, for two auxetic materials (v < 0), the equations of classical elasticity give inaccurate values of v. This is experimental corroboration that the correct lower limit on Poisson's ratio is 0.2 in order for classical elasticity to apply.Comment: 9 pages, 2 figure

Quadratic integrals of motion for the systems of identical particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.Comment: 6 pages, no figure

Application of Fuzzy Cognitive Mapping in Livelihood Vulnerability Analysis

Feedback mechanisms are important in the analysis of vulnerability and resilience of social-ecological systems, as well as in the analysis of livelihoods, but how to evaluate systems with direct feedbacks has been a great challenge. We applied fuzzy cognitive mapping, a tool that allows analysis of both direct and indirect feedbacks and can be used to explore the vulnerabilities of livelihoods to identified hazards. We studied characteristics and drivers of rural livelihoods in the Great Limpopo Transfrontier Conservation Area in southern Africa to assess the vulnerability of inhabitants to the different hazards they face. The process involved four steps: (1) surveys and interviews to identify the major livelihood types; (2) description of specific livelihood types in a system format using fuzzy cognitive maps (FCMs), a semi-quantitative tool that models systems based on people’s knowledge; (3) linking variables and drivers in FCMs by attaching weights; and (4) defining and applying scenarios to visualize the effects of drought and changing park boundaries on cash and household food security. FCMs successfully gave information concerning the nature (increase or decrease) and magnitude by which a livelihood system changed under different scenarios. However, they did not explain the recovery path in relation to time and pattern (e.g., how long it takes for cattle to return to desired numbers after a drought). Using FCMs revealed that issues of policy, such as changing situations at borders, can strongly aggravate effects of climate change such as drought. FCMs revealed hidden knowledge and gave insights that improved the understanding of the complexity of livelihood systems in a way that is better appreciated by stakeholders

Exploring the variability among smallholder farms in the banana-based farming systems in Bukoba district, Northwest Tanzania

A study was conducted in the high and low rainfall zones in the banana-based farming system in Bukoba district, Tanzania, to explore the variability among household characteristics and farm productivity. Approaches used included a participatory rural appraisal, rapid system characterization, surveys and detailed farm monitoring in two villages, one from each zone in 2005 through 2006. Based on a wealth-ranking, four household resource groups with decreasing wealth were identified: Resource group 1 > Resource group 2 > Resource group 3 > Resource group 4, distinguished by domestic assets, livestock ownership and labour relations. Through principal component analysis using additional variables defined by research team, three Functional Resource Groups from among the four Resource groups at each rainfall zone were identified distinguished by: soil fertility management, food security and farm and off-farm income as important indicators of variability. Further detailed monitoring over 14 months (from March, 2006 through May, 2007) in at least three households from each functional resource group showed that N, P and K balances among land use types and farms were driven by levels of organic inputs used and were also related to wealth and dependence on off-farm activities. However, all households were net food buyers, implying food insecurity. In addition, off-farm activities and off-farm income were important livelihood survival strategie