Geodesics on a K3 surface near the orbifold limit

This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi–Yau metrics due to Kobayashi. As an application, we study stable closed geodesics. We use the metric estimates to show how there are generally restrictions on the existence of such geodesics. We also show how there can exist stable, closed geodesics in some highly symmetric circumstances due to hyperkähler identities

Implications of ridesourcing and self-driving vehicles on the need for regulation in unscheduled passenger transport

One of the major recent developments in passenger transport is the arrival of large scale ridesourcing services, such as Uber and Lyft. These actors have challenged the definitions of what private and commercial transport is, by utilizing fleets of private cars and app-technology. Ridesourcing services pose several challenges to the existing transport framework. They exist in-between commercial and private activities, are partly outside the control of governments, and partly in direct contradiction with the current regulations. This paper also looks at how ridesourcing and autonomous vehicles may reshape the market for unscheduled passenger transport. This paper combines the use of literature on regulation and the economic properties of the markets for unscheduled passenger transport with scenario analyses to look into how ridesourcing and automated vehicles affect the markets in unscheduled passenger transport. The main findings are that as underlying economic mechanisms that points towards situations that calls for regulation are similar regardless of how the services are offered, the need for regulation will remain. However, as the market properties of the market segments are different, and a shift in the relative importance of the different market segments are likely, the possible and suitable points of regulation will change.Institute of Transport and Logistics Studies. Faculty of Economics and Business. The University of Sydne

Martian Lava Tube Exploration Using Jumping Legged Robots: A Concept Study

In recent years, robotic exploration has become increasingly important in planetary exploration. One area of particular interest for exploration is Martian lava tubes, which have several distinct features of interest. First, it is theorized that they contain more easily accessible resources such as water ice, needed for in-situ utilization on Mars. Second, lava tubes of significant size can provide radiation and impact shelter for possible future human missions to Mars. Third, lava tubes may offer a protected and preserved view into Mars' geological and possible biological past. However, exploration of these lava tubes poses significant challenges due to their sheer size, geometric complexity, uneven terrain, steep slopes, collapsed sections, significant obstacles, and unstable surfaces. Such challenges may hinder traditional wheeled rover exploration. To overcome these challenges, legged robots and particularly jumping systems have been proposed as potential solutions. Jumping legged robots utilize legs to both walk and jump. This allows them to traverse uneven terrain and steep slopes more easily compared to wheeled or tracked systems. In the context of Martian lava tube exploration, jumping legged robots would be particularly useful due to their ability to jump over big boulders, gaps, and obstacles, as well as to descend and climb steep slopes. This would allow them to explore and map such caves, and possibly collect samples from areas that may otherwise be inaccessible. This paper presents the specifications, design, capabilities, and possible mission profiles for state-of-the-art legged robots tailored to space exploration. Additionally, it presents the design, capabilities, and possible mission profiles of a new jumping legged robot for Martian lava tube exploration that is being developed at the Norwegian University of Science and Technology.Comment: 74rd International Astronautical Congress (IAC

Long-time existence of Yamabe flow on singular spaces with positive Yamabe constant

In this work we establish long-time existence of the normalized Yamabe flow with positive Yamabe constant on a class of manifolds that includes spaces with incomplete cone-edge singularities. We formulate our results axiomatically, so that our results extend to general stratified spaces as well, provided certain parabolic Schauder estimates hold. The central analytic tool is a parabolic Moser iteration, which yields uniform upper and lower bounds on both the solution and the scalar curvature.Comment: 36 pages

Statistical modelling of conidial discharge of entomophthoralean fungi using a newly discovered Pandora species

Entomophthoralean fungi are insect pathogenic fungi and are characterized by their active discharge of infective conidia that infect insects. Our aim was to study the effects of temperature on the discharge and to characterize the variation in the associated temporal pattern of a newly discovered Pandora species with focus on peak location and shape of the discharge. Mycelia were incubated at various temperatures in darkness, and conidial discharge was measured over time. We used a novel modification of a statistical model (pavpop), that simultaneously estimates phase and amplitude effects, into a setting of generalized linear models. This model is used to test hypotheses of peak location and discharge of conidia. The statistical analysis showed that high temperature leads to an early and fast decreasing peak, whereas there were no significant differences in total number of discharged conidia. Using the proposed model we also quantified the biological variation in the timing of the peak location at a fixed temperature.Comment: 23 pages including supplementary materia

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