Classification of Torus Fibrations Over S2S^2 Up to Fibre Sum Stabilisation

We study torus fibrations over the 2-sphere and Hurwitz equivalence of their monodromies. We show that, if two torus fibrations over $S^2$ have the same type of singularities, then their global monodromies are Hurwitz equivalent after performing direct sums with certain torus Lefschetz fibrations. The additional torus Lefschetz fibration is universal when the type of singularities is "simple".Comment: 42

A tool to evaluate sustainability of pavement maintenance projects.

Pavement maintenance activities are widely regarded to be critical elements during pavement life cycle, different maintenance techniques have been used to restore or extend the service lives of pavements. However, the existing maintenance practices on pavement system have problems that impair the economic benefits, disturb the natural environment, and somewhat ignore the needs from stakeholders. To minimize these negative impacts, sustainability is an ideal way because it addresses the problems under Triple Bottom Line (TBL, refers to economy, environment, and society). Sustainability analysis within transportation or pavement industry has been studied in different countries, but the concept of sustainable pavement maintenance is relatively new and has not been defined well yet. In this research, the concept of sustainable pavement maintenance has been proposed and defined to help benefit the current pavement industry. Rating tool has its advantages measuring sustainability activities. There are many rating tools designed for sustainable infrastructure, transportation, or pavement, but maintenance has its own characteristics and yet never had its own rating tool. To link the theoretical concept of sustainable pavement maintenance with actual projects, a sustainability rating tool for pavement maintenance (Pavement Sustainability Index for Maintenance, PSIM) has been developed by a so-called 5-step methodology. Step one and two are to determine the rating categories and indicators; step three is to determine the priority of each category by the Analytic Hierarchy Process (AHP); step four is to determine points distribution under each indicator by reviewing the sustainability practices of 8 State DOTs; final step is to propose the certification methodology according to the Pavement Sustainability Index (PSI) earned by the maintenance project. To prove the usability value of PSIM, four common maintenance activities have been discussed as case studies, including rejuvenation, utility cut restoration (UCR), overlay, as well as mill and overlay. The projects selected were located in or adjacent to Louisville, KY. Among the nine projects being evaluated by PSIM framework, UCR projects were not sustainable; rejuvenation project, overlay projects, and one of the mill and overlay projects earned one PSIM star; two PSIM stars were awarded to two of the mill and overlay projects