A note on the cone restriction conjecture in the cylindrically symmetric case

In this note, we present two arguments showing that the classical \textit{linear adjoint cone restriction conjecture} holds for the class of functions supported on the cone and invariant under the spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the second follows from a strengthening version of the Hausdorff-Young inequality and the H\"older inequality in the Lorentz spaces.Comment: 9 pages, no figures. Referee's suggestions and comments incorporated; to appear the Proceedings of the AM

Degeneracy in Studying the Supranuclear Equation of State and Modified Gravity with Neutron Stars

It is generally acknowledged that an extrapolation in physics from a well-known scale to an unknown scale is perilous. This prevents us from using laboratory experience to gain precise information for the supranuclear matter inside neutron stars (NSs). With operating and upcoming astronomical facilities, NSs' equation of state (EOS) is expected to be determined at a new level in the near future, under the assumption that general relativity (GR) is the correct theory for gravitation. While GR is a reasonable working assumption yet still an extrapolation, there could be a large uncertainty due to the not-so-well-tested strong gravitational field inside NSs. Here we review some recent theoretical efforts towards a better understanding of the degeneracy between the supranuclear EOS and alternative gravity theories.Comment: 11 pages, 6 figure

Gauge mediation with heavy doublet superparticles

It is challenging for supersymmetry if the 125 GeV Higgs boson is confirmed by the LHC. In the case of small squark mixing it is inevitable to introduce heavy top squarks to lift the Higgs mass that is hard to be produced by the LHC. Here we consider the possibility that in gauge mediation the superparticles belonging to SU(2) doublets are much heavier than those do not carry the SU(2) quantum numbers. Under the assumption not only the Higgs mass can be large enough but also there are light right handed top squarks below the TeV scale that can be observed in future.Comment: 10pages, no figures, accepted for publication in Phys. Rev.