Bulk neutrinos as an alternative cause of the gallium and reactor anti-neutrino anomalies

We consider an alternative explanation for the deficit of nu(e) in Ga solar neutrino calibration experiments and of the (nu) over bar (e) in short-baseline reactor experiments by a model where neutrinos can oscillate into sterile Kaluza-Klein modes that can propagate in compactified submicrometer flat extra dimensions. We have analyzed the results of the gallium radioactive source experiments and 19 reactor experiments with baseline shorter than 100 m, and showed that these data can be fit into this scenario. The values of the lightest neutrino mass and of the size of the largest extra dimension that are compatible with these experiments are mostly not excluded by other neutrino oscillation experiments.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.