The Covering Radius and a Discrete Surface Area for Non-Hollow Simplices

We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of d/2 in dimension d, achieved by the “standard terminal simplices” and direct sums of them. We prove this conjecture up to dimension three and show it to be equivalent to the conjecture of González-Merino and Schymura (Discrete Comput. Geom. 58(3), 663–685 (2017)) that the d-th covering minimum of the standard terminal n-simplex equals d/2, for every $$n\ge d$$ n ≥ d . We also show that these two conjectures would follow from a discrete analog for lattice simplices of Hadwiger’s formula bounding the covering radius of a convex body in terms of the ratio of surface area versus volume. To this end, we introduce a new notion of discrete surface area of non-hollow simplices. We prove our discrete analog in dimension two and give strong evidence for its validity in arbitrary dimension.

Vertical forest: green open space alternative in urban area development

Addressing environmental problems in urban areas, the Law No. 26 of 2007 has mandated local governments to preserve Green Open Space (GOS) covering minimum 30% of its area. However, some local governments barely meet this obligation due to high price of lands and budget constraints. Meanwhile, an innovation in the form of vertical forest started to be applied in developed countries may be adopted to overcome the limited land constraint for developing GOS. This study was conducted to determine the opportunities for implementing vertical forest as an alternative solution for the constraints. In addition, it also aims to find out the possibility of its application for spatial planning policies so that it supports the national sustainable development goal. This study is an explorative research with qualitative method. The study concluded that vertical forest essentially is suitable to be implemented as an alternative solution to limited land for the GOS development. From the policy perspective, the development of vertical forest can encourage the competitiveness of the green city program. Therefore, the government need to design incentive policies for local governments and the private sectors to develop vertical forest. It is also necessary to adjust GOS developing regulation to become more accommodating so that vertical forest can be recognized as part of GOS.

EVALUATION OF SPATIAL JUSTICE IN ACCESSIBILITY OF URBAN FACILITIES: A CASE STUDY OF ACCESSIBILITY OF PUBLIC PARKS IN DISTRICT # 11 OF TEHRAN, IRAN

The green spaces and urban parks play a critical role to improve the quality of life of citizens. In order to meet the principles of the justice-based city and spatial justice in the distribution of public services, it is necessary to evaluate the accessibility to parks in different locations and pay more attention to the places with a low level of accessibility. This study evaluates the spatial justice or inequalities in accessibility to urban parks in District # 11 of Tehran, Iran using a set of spatial indices and GIS tools. Indices used in this study are Covering, Minimum distance, Average distance, Proximity, Two-step floating catchment area and Gravity-based two-step floating catchment area. The results indicate that the level of accessibility to mini and neighborhood parks are almost similar and below the average level. The slight differences in the results are related to the differences in the assumptions and logics of methods. Moreover, the results show that the Coverage, 2SFCA and GB2SFCA (with inappropriate distance decay coefficient) methods face limitations when the accessibility for the community parks are calculated. For example, the Coverage method does not take into account the area of the park for measuring the accessibility level, in turn, this leads to inaccurate results. Overall, the findings show better accessibility to community parks than mini and neighborhood parks. This implies that the municipalities need to increase the number of local mini and neighborhood parks across the city.

Dairy welfare in Hungary and in the United Kingdom vs. National and European Union legislation

Dairy industries in Eastern and Western Europe have different history, heritage, but the same aim to produce cheap, high quantity of good quality milk with the care of dairy welfare. Member countries of European Union had choice to either implement minimum standards provided by the European Commission, like in Hungary, or to create their own legislation also covering minimum standards, like in the Great Britain. British, Hungarian and European Union legislation was compared with dairy welfare measures taken on 53 farms in the UK and on 27 farms in Hungary. Among 13 welfare measures observed 8 were found to be statistically different (p<0.05. p<0.01 or p<0.001) between countries. Fewer cows were reported with dirty hind limbs, hock hair losses, non hock injuries, being dull or with greater flight distance on Hungarian farms than in the UK. There were fewer cows with dirty udders, being fat or lame in the UK in comparison to Hungarian farms. Cheaper bedding materials in Hungary are thought to be the major factors cows are found cleaner. More farm workers per one animal make more attention is paid for providing cattle with suitable conditions for resting what also might impact shorter flight distance. In the Great Britain cleaner udders might be related to modern husbandry systems providing cleaner conditions. Education is also thought to be playing a great role in lower proportion of cows being lame, with digestion problems and mastitis in the UK in comparison to Hungary.

A Comparison of Labour Standards in the United States and Canada

This article introduces a methodology for measuring differences in the labour standards between the United States and Canada, taking into account variations by state and province. This methodology is then used to analyze differences in the two countries on ten labour standards. The results indicate that six standards are higher in Canada than in the United States: paid time off, unemployment/employment Insurance, workers' compensation, collective bargaining, unjust discharge and advance notice of plant closings/large scale layoffs. Standards covering minimum wages, overtime and occupational safety and health are higher in the United States than in Canada. There is no difference in the two countries in standards covering employment discrimination/employment equity. The results suggest that overall, although there are exceptions, labour standards are higher in Canada than the United States.