On sequences of projections of the cubic lattice

In this paper we study sequences of lattices which are, up to similarity, projections of $\mathbb{Z}^{n+1}$ onto a hyperplane $\bm{v}^{\perp}$, with $\bm{v} \in \mathbb{Z}^{n+1}$ and converge to a target lattice $\Lambda$ which is equivalent to an integer lattice. We show a sufficient condition to construct sequences converging at rate $O(1/ |\bm{v}|^{2/n})$ and exhibit explicit constructions for some important families of lattices.Comment: 16 pages, 5 figure

The Limits of Bioenergy : A Complex Systems Approach to Land Use Dynamics and Constraints

This thesis aims to use a novel methodology to obtain an understanding of the potential limits of bioenergy by using a complex systems approach for assessing land use dynamics and constraints. Although bioenergy is classified as a renewable energy source, land is a finite resource and its expansion limited. The anthropogenic demands on land result from a combination of multiple provisioning services. These include global food consumption, dietary preference, crop and livestock yields, land use integration, wastes and residues, and bioenergy yields and forms, as well as the allocation of surplus land for forestry and energy crops, and the potential role of negative emission technologies. Thus, bioenergy is just one part of a complex land-use system. The general hypothesis is that there are fundamental limits to the overall scale and rate of the sustainable expansion of bioenergy, which can be assessed by means of combinations of empirical data, mapping tools and complex systems models. To this end, a novel methodological approach is proposed, which is based on a combination of two original models. The first one is termed the Global Calculator Land Use Change Model (GCLUC), developed as part of the Global Calculator Project, in which land is freely allocated worldwide and food security is assumed a priority. The second considers land for dedicated energy crops as a delimited reserve, by integrating Hubbert’s curve principles (originally proposed for peak oil assessments) in agro-ecological zoning schemes (as recently done for sugarcane ethanol in Brazil), resulting in a new model here termed green-Hubbert. The results show ranges of bioenergy potentials and expansion rates in the context of different land use futures. The potential public policies necessary to support sustainable bioenergy are also discussed. Finally, the conclusions show that, indeed, there are fundamental limits to bioenergy, and these limits are dynamic over time.Open Acces

Assessing the climate impacts of Chinese dietary choices using a telecoupled global food trade and local land use framework

Global emissions trajectories developed to meet the 2⁰C temperature target are likely to rely on the widespread deployment of negative emissions technologies and/or the implementation of substantial terrestrial carbon sinks. Such technologies include afforestation, carbon capture and storage (CCS) and bioenergy with carbon capture and storage (BECCS), but mitigation options for agriculture appear limited. For example, using the Global Calculator tool (http://www.globalcalculator.org/), under a 2⁰C pathway, the ‘forests and other land use’ sector is projected to become a major carbon sink, reaching -15 GtCO2e yr-1 by 2050, compared to fossil emissions of 21 GtCO2e yr-1. At the same time, rates of agricultural emissions remain static at about 6 GtCO2e yr-1, despite increasing demands for crop and livestock production to meet the forecast dietary demands of the growing and increasingly wealthy global population. Emissions in the Global Calculator are sensitive to the assumed global diet, and particularly to the level and type of meat consumption, which in turn drive global land use patterns and agricultural emissions. Here we assess the potential to use a modified down-scaled Global Calculator methodology embedded within the telecoupled global food trade framework, to estimate the agricultural emissions and terrestrial carbon stock impacts in China and Brazil, arising from a plausible range of dietary choices in China. These dietary choices are linked via telecoupling mechanisms to Brazilian crop production (e.g. Brazilian soy for Chinese animal feed provision) and drive land and global market dynamics. ‘Spill-over’ impacts will also be assessed using the EU and Malawi as case studies

A Note On Quadrangular Embedding Of Abelian Cayley Graphs

The genus graphs have been studied by many authors, but just a few results concerning in special cases: Planar, Toroidal, Complete, Bipartite and Cartesian Product of Bipartite. We present here a general lower bound for the genus of a abelian Cayley graph and construct a family of circulant graphs which reach this bound.17333134

Народна педагогіка в педагогічній спадщині Василя Сухомлинського

У статті автором відображено народознавчий аспект діяльності В. О.Сухомлинського, виокремлено прогресивні ідеї навчання й виховання дітей та молоді в сучасній національній школі