In this paper we study the initial-value problem associated with dispersion generalized-Benjamin-Ono-Zakharov-Kuznetsov equation,ut+Dxa+1∂xu+uxyy+uux=0,a∈(0,1). More specifically, persistence property of solution in weighted anisotropic Sobolev spacesH(1+a)s,2s(R2)∩L2((x2r1+y2r2)dxdy), for appropriate s, r1 and r2. By establishing unique continuation properties also show that our results are sh...

In this Letter, the problem of estimating the timedifference-of-arrival between signals received at two spatially separated sensors is addressed. By taking discrete Fourier transform of the sensor outputs, time delay estimation corresponds to finding the frequency of a noisy sinusoid with time-varying amplitude. The generalized weighted linear predictor is utilized to estimate the time delay an...

OBJECTIVE The aim of this study was to identify the principal determinants that are longitudinally associated with the performance of social roles in the first 3 years following a diagnosis of multiple sclerosis. DESIGN Inception cohort with 5 measurements over 3 years. PATIENTS A total of 156 patients recently diagnosed with multiple sclerosis. METHOD Performance of social roles was meas...

© 2011 Hing Cheung So and Hongqing Liu 27 This paper addresses estimating the frequency of a cisoid in the presence of white Gaussian noise, which has numerous applications in communications, radar, sonar, and instrumentation and measurement. Due to the nonlinear nature of the frequency estimation problem, there is threshold effect, that is, large error estimates or outliers will occur at suffi...

In this paper we develop basic elements of Malliavin calculus on a weighted L2( ). This class of generalized Wiener functionals is a Hilbert space. It turns out to be substantially smaller than the space of Hida distributions while large enough to accommodate solutions of bilinear stochastic PDE's. As an example, we consider a stochastic advectiondi usion equation driven by space-time white noi...

In this paper, we are interested in some aspects of the biharmonic equation in the half-space R+ , with N ≥ 2. We study the regularity of generalized solutions in weighted Sobolev spaces, then we consider the question of singular boundary conditions. To finish, we envisage other sorts of boundary conditions.

We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a general bulk growth model by means of a continuum Master equation for the evolution of the bulk density field. This general model just considers an arbitrary addition of particles (though it can be easily generalized to consider subtraction) with no other physical...

Coagulation of charged particles was studied using the mean-field Smoluchowski equation. The coagulation equation was generalized for the case of a conserved system of charged particles. It was shown that runaway cluster growth (gelation) solutions exist if the charge-dipole (induced) interaction of clusters is included. When clusters are in thermal equilibrium with the ambient gas, the charge-...

In this article we derive a Li–Yau-type gradient estimate for generalized weighted parabolic heat equation with potential on Riemannian manifold evolving by geometric flow. As an application, Harnack-type inequality is also derived in the end.

We introduce a family of generalized Jacobi polynomials/functions with indexes α,β ∈ R which are mutually orthogonal with respect to the corresponding Jacobi weights and which inherit selected important properties of the classical Jacobi polynomials. We establish their basic approximation properties in suitably weighted Sobolev spaces. As an example of their applications, we show that the gener...