Decay and asymptotics for □u = F(u)

Sequential Shrinkage U - Statistics : General Asymptotics

For general estimable parameters in a nonparametric setup, shrinkage (Stein-rule) and preliminary test estimator versions of U-statistics are considered for the (multi-parameter) minimum risk sequential estimation problem. In the usual fashion, allowing the cost per unit sample to be small, an asymptotic model is framed, and in this setup, the asymptotic distributional risks of these versions o...

Asymptotics for the Moment Convergence of U-Statistics in LIL

Anomalous U(1) Symmetry and Proton Decay

Recently, a new mechanism, which explains why three gauge coupling constants meet at a scale in the minimal supersymmetric standard model, has been proposed in a scenario of grand unified theories (GUT) with anomalous U(1)A gauge symmetry. It is non-trivial that although there are a lot of superheavy fields whose mass scales are below the unification scale, the mechanism explains the fact by us...

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for ut = ∆φ(u)

We investigate the long time asymptotics in L+(R) for solutions of general nonlinear diffusion equations ut = ∆φ(u). We describe, for the first time, the intermediate asymptotics for a very large class of non-homogeneous nonlinearities φ for which long time asymptotics cannot be characterized by self-similar solutions. Scaling the solutions by their own second moment (temperature in the kinetic...

Eigenvalue Asymptotics and Exponential Decay of Eigenfunctions for Schrödinger Operators with Magnetic Fields

We consider the Schrödinger operator with magnetic field, H = ( 1 i ∇−a (x)) + V (x) in R. Assuming that V ≥ 0 and |curla |+ V + 1 is locally in certain reverse Hölder class, we study the eigenvalue asymptotics and exponential decay of eigenfunctions. Introduction Consider the Schrödinger operator with magnetic field H = H( ⇀ a , V ) = ( 1 i ∇−a (x) )2 + V (x) in R, n ≥ 3, (0.1) where i = √ −1,...