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We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type D n , with specific emphasis on the case of number fields and p -adic fields. This includes the forms associated to quadratic spaces, all of their inner and outer forms as well as the Spin groups, their simply connected covers. In particular, in this work, we handle all (simply connected) outer forms of D 4 . [ABSTRACT FROM AUTHOR]

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla-Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well. [ABSTRACT FROM AUTHOR]

A k-container of a graph G is a set of k internally disjoint paths between two distinct vertices. A k-container of G is a k*-container if it contains all vertices of G. A graph G is k*-connected if there exists a k*-container between any two distinct vertices, and a bipartite graph G is k*-laceable if there exists a k*-container between any two vertices from different partite sets of G. A k-connected graph (respectively, bipartite graph) G is super spanning connected (respectively, laceable) if G is r*-connected ( r*-laceable) for any r with 1 ≤ r ≤ k. This paper shows that the two-dimensional torus (m, n), m, n ≥ 3, is super spanning connected if at least one of m and n is odd and super spanning laceable if both m and n are even. Furthermore, the super spanning connectivity and spanning laceability of tori with faulty elements have been discussed. [ABSTRACT FROM AUTHOR]

In this paper, we report the dynamical behaviors of a four-dimensional autonomous system, that is, the modified canonical Chua's circuit. An interesting transition of three-tori-period-3 doubling-chaos is observed when the circuit parameters are varied in the range of our choice. Furthermore, the detailed numerical studies of the system behavior with supporting PSPICE simulations and hardware experiments are also presented here. [ABSTRACT FROM AUTHOR]