This paper extends the partially linear varying coefficient model to contain time trend and nonstationary variables as regressors. We use the profile likelihood method to estimate both time trend coefficient in the linear component and the functional coefficients in the nonlinear component and establish their asymptotic distributions. Monte Carlo simulations are shown to investigate the finite ...

We determine an exact asymptotic expression of the blow-up time t(coll) for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point in d=3. We show that t(coll) = t(*) (eta- eta(c) )(-1/2) with t(*) =0.917 677 02..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta(c) is the critical...

We study in the whole space Rn the behaviour of solutions to the Boussinesq equations at large distances. Therefore, we investigate the solvability of these equations in weighted L∞-spaces and determine the asymptotic profile for sufficiently fast decaying initial data. For n = 2, 3 we are able to construct initial data such that the velocity exhibits an interesting concentration-diffusion phen...

Random increasing k-trees represent an interesting, useful class of strongly dependent graphs for which analytic-combinatorial tools can be successfully applied. We study in this paper a notion called connectivity-profile and derive asymptotic estimates for it; some interesting consequences will also be given.

Context. New observational means such as the space missions CoRoT and Kepler and ground-based networks are and will be collecting stellar pulsation data with unprecedented accuracy. A significant fraction of the stars in which pulsations are observed are rotating rapidly. Aims. Our aim is to characterise pulsation modes in rapidly rotating stellar models so as to be able to interpret asteroseis...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

Using the method of matched asymptotic expansion we construct the mobifity relation describing the vortex dynamics in the conservative Ginzburg-Landau equation with a spatially varying supercriticality parameter. For a particular case of a circularly symmetric supercriticality profile, we present the equations of vortex dynamics in a Hamiltonian form, and demonstrate the dynamic confinement of ...

Gu and Zhu [16] have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on Sn+1 (n ≥ 2). In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit.

We present a systematic study of singular vortex solutions of the critical and supercritical two-dimensional nonlinear Schrödinger equation. In particular, we study the critical power for collapse and the asymptotic blowup profile of singular vortices. c © 2008 Elsevier B.V. All rights reserved. PACS: 42.65.Jx; 42.65.-k