On Solutions and Higher Moments for the Linear Boltzmann Equation with Infinite-Range Forces

This paper considers an integral form of the linear, space-inhomogeneousBoltzmann equation with infinite-range forces in the collisionterm, and with periodic boundary conditions. The existence ofa measure solution is proved in the case of hard-potential forcesincluding kth power forces with k 5. The solution conservesmass and has bounded energy. Also, higher moments of the solutionremain globally bounded in time, if they exist initially. Inthe course of the proof, some collision estimates for the velocitiesare obtained.     

Quantum states of hydrogen transfer and vibration in malonaldehyde

New ab initio results on the 21D potential energy surface of malonaldehyde and a quantum mechanical treatment of the hydrogen transfer motion and its interaction with all vibrations are presented. An explicit approximate reaction path, close to the minimum energy path but matching the reactive normal mode near equilibrium, allows one to predict the ground state tunnelling frequency even when using small basis sets. With a barrier of 1144 cm^?1 (3.27kcal mol-¹) the tunnelling splitting is predicted to be 22.0cm^?1 for the parent species and 3.8 cm^?1 for the species deuterated in the hydrogen bond, in good agreement with the observed values 21.6 and 2.9 cm^?1, respectively. Predicted energy levels for excited states of the hydrogen transfer motion and for the non-reactive vibrations suggest a re-examination of the vibrational spectra and an extension of the number of vibrational factors in the basis set to improve the results for the vibrationally excited states.     

PLANNING MARINE PROTECTED AREAS: A MULTIPLE USE GAME

Abstract The EU Marine Strategy Directive (MSD) has a regional focus in its implementation. The directive obliges countries to take multiple uses and the marine strategies of neighboring countries into account when formulating marine strategies and when designating marine protected areas (MPAs). We use game theoretical analysis both to find the optimal size of MPAs with multiple uses by multiple countries and to investigate the influences of multiple uses on cooperation. To this end, we develop a model in which two specific uses, fisheries and nature conservation, by multiple countries are considered in a strategic framework. The results of the paper suggest that EU marine policy such as the MSD and the coming Maritime Policy may help to secure the highest possible benefits from these MPAs if these policies induce cooperation among countries, but only if policies force countries to consider all possible benefits of MPAs. In fact cooperation on a single issue may give a worse outcome than the noncooperative equilibrium. The results also indicate that cooperation may be hard to achieve because of defector incentives, and therefore policy measures should be strict in enforcing cooperation on all possible uses of MPAs.     

Existence Theorems for the Linear, Space-inhomogeneous Transport Equation

This paper studies existence problems in L¹ for the linear,space-inhomogeneous Boltzmann equation with periodic or (perfectly)absorbing boundary conditions under realistic assumptions onthe cross-sections. By an iteration technique, solutions arefirst constructed to an integral equation variant of the transportequation in the case of bounded impact parameters and an L¹type of cross-sections. They are then used to study the existenceof solutions of a measure form of the transport equation inthe case of unbounded impact parameters. These solutions conservemass. Estimates of their higher moments are also given. In particularthe results hold for inverse kth-power forces with 3 < k 5.