Solutions to polynomial congruences in well shaped sets

We use a generalization of Vinogradov's mean value theorem of S. Parsell, S. Prendiville and T. Wooley and ideas of W. Schmidt to give nontrivial bounds for the number of solutions to polynomial congruences, for arbitrary polynomials, when the solutions lie in a very general class of sets, including all convex sets

Cyberpsychology and Human Factors

The online environment has become a significant focus of the everyday behaviour and activities of individuals and organisations in contemporary society. The increasing mediation of communication has led to concerns about the potential risks and associated negative experiences which can occur to users, particularly children and young people. This is related to the emergence of the online environment as a location for criminal and abusive behaviour (e.g., harassment, sexual exploitation, fraud, hacking, malware). One of the key aspects of understanding online victimisation and engagement in criminal behaviours is the characteristics of online communication that are related to the affordances of the technologies, services and applications which constitute digital environments. The aim of this paper is to examine the influence of these characteristics on individual and group behaviour, as well as the associated opportunities for victimisation and criminal behaviour. These issues are of relevance for those involved in the design and implementation of technologies and services, as the ability to assess their potential use in this way can enhance strategies for improving the security of systems and users. It can also inform educational strategies for increasing user understanding of potential informational, privacy and personal risks, and associated steps to improve their security and privacy. Each of the main characteristics of mediated communication is examined, as well as their potential impact on individual and group behaviour, and associated opportunities for victimisation and offending. The article ends by considering the importance of recognising these issues when designing and implementing new technologies, services and applications

Testing the role of radiation in determining tropical cloud top temperature

Tropical anvil clouds that detrain near the mixing barrier near 13km in the tropics have a strong effect on the longwave and shortwave energy budgets of Earth. A cloud-resolving model is used to test the Fixed Anvil Temperature (FAT) Hypothesis proposed by Hartmann and Larson (2002). Results show that the radiative cooling, primarily due to water vapor, is the strongest control of the anvil cloud detrainment temperature. Water vapor concentrations are largely controlled by temperature, so, following the FAT hypothesis, the cloud detrainment should follow a fixed temperature. The results also show, however, that ozone contributes a significant heating rate in the upper tropical troposphere. If ozone is fixed as a function of pressure as the SST is warmed, anvil clouds warm and their fractional coverage decreases. The presence of a fixed ozone profile in our model can be thought of as a pressure dependent contribution to stability that inhibits convection from rising to the level of diminished water vapor cooling. This suggests that to model the response of tropical anvil clouds to climate change, one must also predict ozone in the upper tropical troposphere and TTL region, where ozone concentrations are also influenced by convection, forming a strong interaction between ozone and cold clouds in the tropics. Broader implications of the influence of the TTL on the detrainment temperature of tropical anvils include the modification of the longwave cloud radiative effect and the net radiative energy budget effect of tropical deep convective systems