We prove a non conventional pointwise convergence theorem for a nilsystem, and give an explicit formula for the limit.

M. NILS PETERSON,∗ MARKUS J. PETERSON,† AND TARLA RAI PETERSON‡ ∗Center for Systems Integration and Sustainability, Michigan State University, 13 Natural Resources Building, East Lansing, MI 48824-1222, U.S.A., email [email protected] †Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, TX 77843-2258, U.S.A. ‡Department of Communication, Program in Peace & Confl...

Every commutative nil-semigroup of index 2 can be imbedded into such a semigroup without irreducible elements.

In this paper, we study biharmonic maps into Sol and Nil spaces, two model spaces of Thurston's 3-dimensional geometries. We characterize non-geodesic biharmonic curves in Sol space and prove that there exists no non-geodesic biharmonic helix in Sol space. We also show that a linear map from a Eu-clidean space into Sol or Nil space is biharmonic if and only if it is a harmonic map, and give a c...

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transf...

Nitric oxide (NO) is suggested to play a role in liver injury elicited by acetaminophen (APAP). Hepatic microcirculatory dysfunction also is reported to contribute to the development of the injury. As a result, the role of NO in hepatic microcirculatory alterations in response to APAP was examined in mice by in vivo microscopy. A selective inducible NO synthase (iNOS) inhibitor,l-N6-(1-iminoeth...

We revisit the problem of electron transport in clean and disordered zigzag graphene nanoribbons, and expose numerous hitherto unknown peculiar properties of these systems at zero energy, where both sublattices decouple because of chiral symmetry. For clean ribbons, we give a quantitative description of the unusual power-law dispersion of the central energy bands and of its main consequences, i...

The Newtonian divided-di¤erence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil...