This paper concerns the inviscid, heat-conductive and resistive compressible MHD system in a horizontally periodic flat strip domain. The global well-posedness of the problem around an equilibrium with the positive constant density and temperature and a uniform non-horizontal magnetic field is established, and the solution decays to the equilibrium almost exponentially. Our result reveals the strong stabilizing effect of the transversal magnetic field and resistivity as the global well-posedness of compressible inviscid heat-conductive flows in multi-D is unknown.

On the basis of a well-established binomial structure and the so-called Poisson-Lindley distribution, a new two-parameter discrete distribution is introduced. Its properties are studied from both the theoretical and practical sides. For the theory, we discuss the moments, survival and hazard rate functions, mode and quantile function. The statistical inference on the model parameters is investigated by the maximum likelihood, moments, proportions, least square, and weighted least square estimations. A simulation study is conducted to observe the performance of the bias and mean square error of the obtained estimates. Then, applications to two practical data sets are given. Finally, we construct a new flexible count data regression model called the binomial-Poisson Lindley regression model with two practical examples in the medical area.

In this work, we aim to show how to solve the continuous-time and continuous-space Krause model by using high-order finite difference (FD) schemes. Since the considered model admits solutions with $δ$-singularities, the FD method cannot be applied directly. To deal with the annoying $δ$-singularities, we propose to lift the solution space by introducing a splitting method, such that the $δ$-singularities in one spatial direction become step functions with discontinuities. Thus the traditional shock-capturing FD schemes can be applied directly. In particular, we focus on the two-dimensional case and apply a fifth-order weighted nonlinear compact scheme (WCNS) to illustrate the validity of the proposed method. Some technical details for implementation are also presented. Numerical results show that the proposed method can capture $δ$-singularities well, and the obtained number of delta peaks agrees with the theoretical prediction in the literature.

We consider the global well-posedness of three dimensional incompressible inhomogeneous Navier-Stokes equation with different viscous coefficients in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared with the initial data and the initial density is close enough to a positive constant, we prove the global well-posedness of this system. This result extends the previous results in [9, 11] for the classical Navier-Stokes system.

Few studies focus on the application of functional data to the field of design-based survey sampling. In this paper, the scalar-on-function regression model-assisted method is proposed to estimate the finite population means with auxiliary functional data information. The functional principal component method is used for the estimation of functional linear regression model. Our proposed functional linear regression model-assisted (FLR-assisted) estimator is asymptotically design-unbiased, consistent under mild conditions. Simulation experiments and real data analysis show that the FLR-assisted estimators are more efficient than the Horvitz-Thompson estimators under different sampling designs.

In this paper, we mainly investigate three topics on the renormalization group (RG) method to singularly perturbed problems: 1) We will present an explicit strategy of RG procedure to get the approximate solution up to any order. 2) We will refer that the RG procedure can, in fact, be used to get the normal form of differential dynamical systems. 3) We will also present the approximating center manifolds of the perturbed systems, and investigate the long time asymptotic behavior by means of RG formula.