ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES

In this paper,we study the controllability of compressible Navier-Stokes equations with density dependent viscosities.For when the shear viscosityμis a positive constant and the bulk viscosityλis a function of the density,it is proven that the system is exactly locally controllable to a constant target trajectory by using boundary control functions.

On the first negative Hecke eigenvalue of an automorphic representation of GL_(2)(A_(Q))

Letπbe a self-dual irreducible cuspidal automorphic representation of GL_(2)(A_(Q))with trivial central character.Its Hecke eigenvalue λπ(n)is a real multiplicative function in n.We show that λπ(n)<0 for some n<<Q^(2/5)_(π),where Qπdenotes(a special value of)the analytic conductor.The value 2/5 is the first explicit exponent for Hecke-Maass newforms.

IMPULSE NOISE REMOVAL BY L1 WEIGHTED NUCLEAR NORM MINIMIZATION

In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.

Unified Variable Selection for Varying Coefficient Models with Longitudinal Data

Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data.The proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant coefficients.It is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient models.Under regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients.The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically normal.Finally,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis.The results show that the proposed method performs better than the existing competitor.

A novel energy functional minimization model for speckle noise removal

In this paper, a novel energy functional minimization model is proposed for ultrasound images denoising. A controllable regularized term and the variational method are employed in the process of speckle noise. This model not only improves the plasticity of the model, but also improves the effect and efficiency of noise removal. The new model has different diffusion performance in different regions. At the same time, the diffusion performance is related to the parameters introduced by the proposed model. Numerical simulation results show that different parameters have different denoising effects, and the proposed model for speckle noise removal is superior to traditional models.

A NONLOCAL KRONECKER-BASIS-REPRESENTATION METHOD FOR LOW-DOSE CT SINOGRAM RECOVERY

Low-dose computed tomography(LDCT)contains the mixed noise of Poisson and Gaus-sian,which makes the image reconstruction a challenging task.In order to describe the statistical characteristics of the mixed noise,we adopt the sinogram preprocessing as a stan-dard maximum a posteriori(MAP).Based on the fact that the sinogram of LDCT has non-local self-similarity property,it exhibits low-rank characteristics.The conventional way of solving the low-rank problem is implemented in matrix forms,and ignores the correlations among similar patch groups.To avoid this issue,we make use of a nonlocal Kronecker-Basis-Representation(KBR)method to depict the low-rank problem.A new denoising model,which consists of the sinogram preprocessing for data fidelity and the nonlocal KBR term,is developed in this work.The proposed denoising model can better illustrate the generative mechanism of the mixed noise and the prior knowledge of the LDCT.Nu-merical results show that the proposed denoising model outperforms the state-of-the-art algorithms in terms of peak-signal-to-noise ratio(PSNR),feature similarity(FSIM),and normalized mean square error(NMSE).