We show that the Cantor-Bendixon rank of limit groups is finite as well as that of limit groups of linear groups. Let T be an universal theory. In what follows this will be just the universal theory of some linear group. If T has at most countably many finitely generated models, then one can associate to each finitely generated model M of T an ordinal rank, denoted Rk(M), as defined in [2]. We ...

In this paper we prove that the level sets of the first non–constant eigenfunction of the Neumann Laplacian on a convex planar domain have only finitely many connected components. This problem is motivated, in part, by the “hot spots” conjecture of J. Rauch. ∗Supported in part by NSF Grant # 9700585-DMS

We characterize the zero-temperature limits of minimal free energy states for interacting corpora – that is, for objects with finitely many degrees of freedom, such as articulated rods. These limits are measures supported on zero-level-sets of the interaction potential. We describe a selection mechanism for the limits that is mediated by evanescent entropic contributions. MSC 2000 classificatio...

We study generalized multisets (multisets that allow possible negative multiplicities) both in the Zermelo-Fraenkel framework and in the finitely supported mathematics. We extend the notion of generalized multiset over a finite alphabet, and we replace it by the notion of algebraically finitely supported generalized multiset over a possibly infinite alphabet. We analyze the correspondence betwe...

We characterize the high intensity limits of minimal free energy states for interacting corpora – that is, for objects with finitely many degrees of freedom, such as articulated rods. These limits are measures supported on zero-level-sets of the interaction potential. We describe a selection mechanism for the limits that is mediated by evanescent entropic contributions. MSC 2000 classification ...

We characterize the zero-temperature limits of minimal free energy states for interacting corpora – that is, for objects with finitely many degrees of freedom, such as articulated rods. These limits are measures supported on zero-level-sets of the interaction potential. We describe a selection mechanism for the limits that is mediated by evanescent entropic contributions.