In this paper, we consider the local existence of solutions to Euler equations with linear damping under the assumption of physical vacuum boundary condition. By using the transformation introduced in Lin and Yang (Methods Appl. Anal. 7 (3) (2000) 495) to capture the singularity of the boundary, we prove a local existence theorem on a perturbation of a planar wave solution by using LittlewoodPaley theory and justifies the transformation introduced in Liu and Yang (2000) in a rigorous setting.

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The paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudopartiallikelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the profile pseudopartiallikelihood, whereas the varyingcoefficient functions are considered as nuisance parameters that are profiled out of the likelihood. It is shown that the estimators of the parameters are root <i>n</i> consistent and the estimators of the nonparametric coefficient functions achieve optimal convergence rates. Asymptotic normality is obtained for the estimators of the finite parameters and varyingcoefficient functions. Consistent estimators of the asymptotic variances are derived and empirically tested, which facilitate inference for the model. We prove that the varyingcoefficient functions can be estimated as well as if the

We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection amplitude and show that there is an infinite ladder of resonances; analyzing the resonance pole trajectories, we show that half of them turn into true embedded eigenvalues provided the flux through the loop is an integer or half-integer multiple of the flux unit hc/e. We also describe a general method to solve the scattering problem on graphs of which the present model is a simple particular case. Finally, we discuss ways in which a state localized initially at the loop decays.

We construct the boundary phase space in D-dimensional Einstein gravity with a generic given co-dimension one null surface N as the boundary. The associated boundary symmetry algebra is a semi-direct sum of diffeomorphisms of \mathcal{N} and Weyl rescalings. It is generated by D towers of surface charges that are generic functions over \mathcal{N}. These surface charges can be rendered integrable for appropriate slicings of the phase space, provided there is no graviton flux through \mathcal{N}. In one particular slicing of this type, the charge algebra is the direct sum of the Heisenberg algebra and diffeomorphisms of the transverse space, \mathcal{N}_v for any fixed value of the advanced time v. Finally, we introduce null surface expansion- and spin-memories, and discuss associated memory effects that encode the passage of gravitational waves through \mathcal{N}, imprinted in a change of the surface charges.