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1. CMB Online first

Alhowaity, Sawsan; Diacu, Florin; Pérez-Chavela, Ernesto
Relative equilibria in curved restricted $4$-body problems
We consider the curved $4$-body problems on spheres and hyperbolic spheres. After obtaining a criterion for the existence of quadrilateral configurations on the equator of the sphere, we study two restricted $4$-body problems, one in which two masses are negligible, and another in which only one mass is negligible. In the former we prove the evidence square-like relative equilibria, whereas in the latter we discuss the existence of kite-shaped relative equilibria.

Keywords:$N$-body problem, relative equilibria, celestial mechanics
Categories:70F10, 37N05

2. CMB 1998 (vol 41 pp. 151)

Fuchs, Laszlo; Lee, Sang Bum
Equivalent presentations of modules over Prüfer domains
If $F$ and $F^\prime$ are free $R$-modules, then $M \cong F/H$ and $M \cong F^\prime/H^\prime$ are viewed as equivalent presentations of the $R$-module $M$ if there is an isomorphism $F \to F^\prime$ which carries the submodule $H$ onto $H^\prime$. We study when presentations of modules of projective dimension $1$ over Pr\"ufer domains of finite character are necessarily equivalent.


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