Various Methods for Constructing Auto-Bcklund Transformations for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painleve expansion method, extendedvariable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painleve expansion method and extended variable-coetfficient balancing-act method is testified.

Study of numerical errors in direct numerical simulation and large eddy simulation

By comparing the energy spectrum and total kinetic energy, the effects of numerical errors （which arise from aliasing and discretization errors）, subgrid-scale （SGS） models, and their interactions on direct numerical simulation （DNS） and large eddy simulation （LES） are investigated, The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Pade compact difference schemes are studied. The truncated Navier-Stokes （TNS） equation model with Pade discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.

Truncated Fractional-Order Total Variation Model for Image Restoration

Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,the Grunwald–Letnikov fractional-order derivative is usually used,where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator.In this paper,a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation(tFoTV)model is proposed for image restoration.Hopefully,first any boundary condition can be used in the numerical experiments.Second,the accuracy of the reconstructed images by the tFoTV model can be improved.The alternating directional method of multiplier is applied to solve the tFoTV model.Its convergence is also analyzed briefly.In the numerical experiments,we apply the tFoTV model to recover images that are corrupted by blur and noise.The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio(PSNR)than the full fractional-order variation and total variation models.From the numerical results,we can also see that the tFoTV model is comparable with the total generalized variation(TGV)model in accuracy.In addition,we can roughly fix a fractional order according to the structure of the image,and therefore,there is only one parameter left to determine in the tFoTV model,while there are always two parameters to be fixed in TGV model.

ASYMPTOTIC NORMALITY OF THE NEAREST NEIGHBOR HAZARD ESTIMATES

The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar results for the n.n. hazard estimate have not been shown in the literature. In this paper, we develop a different approach to deal with the n.n. type estimator. For a mixed censorship-truneation model, we show that, under mild conditions, the n. n. estimate can be approximated by an estimate formed with a proper fixed bandwidth sequence and derive the asymptotic normality as a consequence.