We investigate connections between certain dispersive estimates of a (pseudo)differential operator of real principal type and the number of nonvanishing curvatures of its characteristic manifold. More precisely, we obtain sharp thresholds for the range of Lebesgue exponents depending on the specific geometry.

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivariate dispersive ordering of GOSs from one sample and Khaledi-Kochar multivar...

a. In Quarterly Progress Report No. 84 (pages 225-226) we described a state-variable formulation for the estimation and detection problem when the signal is a sample function from a nonstationary process that has passed through a dispersive medium. Work has continued in this area and we are attempting to find effective solution procedures for the equations that result. The state of current prog...

In this paper we establish dispersive estimates for solutions to the linear Schrödinger equation in three dimension 1 i ∂ t ψ − △ψ + V ψ = 0, ψ(s) = f (0.1) where V (t, x) is a time-dependent potential that satisfies the conditions sup t V (t, ·)

Under the frame of the (2+1)-dimensional zero curvature equation and Tu model, the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.

This paper presents novel pilot signal design algorithms for efficient symbol time offset estimation in an OFDM system. Evenly spaced pilot signals in the frequency-domain have large correlation in the time-domain, and the ML function of the symbol time offset estimator induces an inaccurate value of time offset. Novel pilot signal design algorithms—Sine Algorithm, Shift Algorithm, and Sine and...

In this note we announce dispersive estimates for Fourier integrals with parameter-dependent phase functions in terms of geometric quantities of associated families of Fresnel surfaces. The results are based on a multidimensional van der Corput lemma due to the first author. Applications to dispersive estimates for hyperbolic systems and scalar higher order hyperbolic equations are also discussed.

In these notes we discuss some recent developments in the study of global solutions to dispersive equations, especially for low regularity data.

We review our recent analysis of ππ scattering data in terms of Roy equations and Forward Dispersion Relations, and present some preliminary results in terms of a new set of oncesubtracted coupled equations for partial waves. The first analysis consists of independent fits to the different ππ channels that satisfies rather well the dispersive representation. In the second analysis we constrain ...