$4+1$-Moulton Configuration and Positive Mass Deformation

For given $k$ bodies of collinear central configuration of Newtonian $k$-body problem, we ask whether one can add another body on the line without changing the configuration and motion of the initial bodies so that the total $k+1$ bodies provide a central configuration. The case $k=4$ is analyzed. We study the inverse problem of five bodies and obtain a global explicit formula. Then using the formula we find there are five possible positions of the added body and for each case the mass of the added body is zero. We further consider to deform the position of the added body without changing the positions of the initial four bodies so that the total five bodies are in a state of central configuration and the mass of the added body becomes positive. For each solution above, we find such a deformation of the position of the added body in an explicit manner starting from the solution.

Central configurations in the spatial n-body problem for $$n=5,6$$ with equal masses

We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for $$n=5$$ n = 5 and 6, with equal masses. For each central configuration, we give a full list of its Euclidean symmetries. For all masses sufficiently close to the equal masses case, we give an exact count of configurations in the planar case for $$n=4,5,6,7$$ n = 4 , 5 , 6 , 7 and in the spatial case for $$n=4,5,6$$ n = 4 , 5 , 6 .

Central configurations in planar n-body problem with equal masses for $$n=5,6,7$$

We give a computer-assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for $$n=5,6,7$$ n = 5 , 6 , 7 with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For $$n=8,9,10$$ n = 8 , 9 , 10 , we establish the existence of central configurations without any reflectional symmetry.

Increasing Windows security by hardening PC configurations

Over 8000 Windows PCs are actively used on the CERN site for tasks ranging from controlling the accelerator facilities to processing invoices. PCs are managed through CERN's Computer Management Framework and Group Policies, with configurations deployed based on machine sets and a lot of autonomy left to the end-users. While the generic central configuration works well for the majority of the users, a specific hardened PC configuration is now provided for users who require stronger resilience against external attacks. This paper describes the technical choices and configurations involved and discusses the effectiveness of the hardened PC approach.