When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

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The addition of a topologically massive term to an admittedly nonunitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its non-unitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? The electromagnetic models remain unitary after the topological augmentation but, surprisingly enoug...

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in four dimensions. The topological Chern Simons terms have played an important role in several physical models. For instance, they appear in the eleven dimensio...

We study the boundary conditions in topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as complexified gauge invariant boundary conditions which lead to supergroup WZW models. We propose that the low-energy effective field theories on the two-dimensi...

Many examples exist of one-dimensional systems that are topologically conjugate to the shift operator on Σ2 and are thus chaotic. Most of these examples which have invariant Cantor subsets, have Cantor subsets of measure zero. In this paper we outline the formulation of a C map on a closed interval that has an invariant Cantor subset of positive Lebesgue measure. We also survey techniques used ...

In 1967 Furstenberg proved that every infinite closed subset of T = R/Z simultaneously invariant under multiplication by 2 and by 3 is equal to T (cf. [8]), which motivated the still unresolved question whether this scarcity of invariant sets is paralleled by a corresponding scarcity of invariant probability measures: is Lebesgue measure the only nonatomic probability measure on T which is inva...