线性模型中部分根方估计的优良性

在均方误差矩阵(MSE-M)准则和在Pitman Closeness(PC)准则下,比较了部分根方估计相对于最小二乘估计的优良性.     

Waveform Design for Multi-Target Detection Based on Two-Stage Information Criterion

Parameter estimation accuracy and average sample number (ASN) reduction are important to improving target detection performance in sequential hypothesis tests. Multiple-input multiple-output (MIMO) radar can balance between parameter estimation accuracy and ASN reduction through waveform diversity. In this study, we propose a waveform design method based on a two-stage information criterion to improve multi-target detection performance. In the first stage, the waveform is designed to estimate the target parameters based on the criterion of single-hypothesis mutual information (MI) maximization under the constraint of the signal-to-noise ratio (SNR). In the second stage, the objective function is designed based on the criterion of MI minimization and Kullback–Leibler divergence (KLD) maximization between multi-hypothesis posterior probabilities, and the waveform is chosen from the waveform library of the first-stage parameter estimation. Furthermore, an adaptive waveform design algorithm framework for multi-target detection is proposed. The simulation results reveal that the waveform design based on the two-stage information criterion can rapidly detect the target direction. In addition, the waveform design based on the criterion of dual-hypothesis MI minimization can improve the parameter estimation performance, whereas the design based on the criterion of dual-hypothesis KLD maximization can improve the target detection performance.     

Complete permutation polynomials with the form (xpm−x+δ)s+axpm+bx over Fpn

In this paper, several classes of complete permutation polynomials with the form ${(x^{p^m}-x+\delta )}^s+a{x}^{p^m}+bx$ over ${\mathbb{F}}_{p^n}$ are proposed by the AGW criterion and determining the number of solutions of some equations. Our results also enrich constructions of known permutation polynomials.     

Oscillation result for half‐linear dynamic equations on timescales and its consequences

We study oscillatory properties of half‐linear dynamic equations on timescales. Via the combination of the Riccati technique and an averaging method, we find the domain of oscillation for many equations. The presented main result is not the conversion of a known result from the theory of differential or difference equations, ie, we obtain new results for the timescales (for differential equations) and (for difference equations). Half‐linear equations generalize linear equations (in fact, they coincide with certain one‐dimensional PDEs with p‐Laplacian), but the main result is new also for linear differential and difference equations. The corresponding corollaries and examples are given as well.     

On the blow‐up criterion of 3D Navier‐Stokes equation in

In this paper, we prove two results about the blow‐up criterion of the three‐dimensional incompressible Navier‐Stokes equation in the Sobolev space . The first one improves the result of Cortissoz et al. The second deals with the relationship of the blow up in and some critical spaces. Fourier analysis and standard techniques are used.     

Components reduction regularity results for the Navier–Stokes equations in general dimensions

We consider the Cauchy problem of the Navier–Stokes equations in arbitrary dimensions, and establish several new components reduction regularity criteria.