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Abstract.In this note we are concerned with the behavior of geodesies in Euclidean «-space with a smooth obstacle. Our principal result is that if the obstacle is locally analytic, that is, locally of the form xn = f(xx, ... , xn_x) for a real analytic function /, then a geodesic can have, in any segment of finite arc length, only a finite number of distinct switch points, points on the boundary that bound a segment not touching the boundary.This result is certainly false that for a C°° boundary. Indeed, even in E , where our result is obvious for analytic boundaries, we can construct a C°°b oundary so that the closure of the set of switch points is of positive measure.We denote by M the closure of the complement of the obstacle in Euclidean space En and by S the boundary of the obstacle. Thus M is an «-dimensional Riemannian manifold-with-boundary embedded in En and S is its boundary surface.A geodesic on a Riemannian manifold-with-boundary, M, is defined to be a locally shortest path in M. In our context the geodesies are easy to visualize; in E the geodesic is the path of a stretched string with the boundary considered as the surface of an obstacle around which the string must bend or into which the string must plunge and end. In [ABB1, ABB2] the properties of these geodesies are explored in the general setting of a Riemannian manifold-with-boundary.We describe briefly the elementary properties of the geodesies in M. A geodesic contacting the boundary in a segment is a geodesic of the boundary; a geodesic segment not touching the boundary is a straight line segment. A segment on the boundary joins a segment in the ambient space in a differentiable join. We call the endpoints on the boundary S of a segment not touching the boundary switch points. Cluster points of switch points, necessarily points at which the geodesic contacts the boundary, we call intermittent points or chatter points. As we will see, even for a C°° surface we can have sets of positive measure of such chatter points, and so it is reassuring to observe that the acceleration of a geodesic at a chatter point is 0. Indeed, acceleration is well defined and bounded everywhere except at the necessarily countable set of switch points; where it is defined, acceleration is normal and outward-pointing

Background: Cooperation among university units is considered a cornerstone for the promotion of students' health. The underlying mechanisms of health-promoting networks at universities have rarely been examined so far. Shedding light on partnerships is generally limited to the naming of allied actors in a network.Objectives and Methods: In this study, we used network analysis intending to visualize and describe the positions and characteristics of the network actors, and examine organizational relationships to determine the characteristics of the complete network.Results: The network analysis at hand provides in-depth insights into university structures promoting students' health comprising 33 organizational units and hundreds of ties. Both cooperation and communication network show a flat, non-hierarchical structure, which is reflected by its low centralization indices (39–43%) and short average distances (1.43–1.47) with low standard deviations (0.499–0.507), small diameter (3), and the non-existence of subgroups. Density lies between 0.53 and 0.57. According to the respondents, the University Sports Center is considered the most important actor in the context of students' health. Presidium and Institute of Sport and Sports Science play an integral role in terms of network functionality.Conclusion: In the health-promoting network, numerous opportunities for further integration and interaction of actors exist. Indications for transferring results to other universities are discussed. Network analysis enables universities to profoundly analyze their health-promoting structures, which is the basis for sustained network governance and development.