Boundedness of Solutions for a Class of Second-Order Periodic Systems

In this paper we study the following second-order periodic system: x′′+V′(x)+p(x,t)=0, where V(x) has a singularity. Under some assumptions on the V(x) and p(x,t) by Ortega’ small twist theorem, we obtain the existence of quasi-periodic solutions and boundedness of all the solutions

Quality analysis of commercial samples of Ziziphi spinosae semen (suanzaoren) by means of chromatographic fingerprinting assisted by principal component analysis

Due to the scarcity of resources of Ziziphi spinosae semen (ZSS), many inferior goods and even adulterants are generally found in medicine markets. To strengthen the quality control, HPLC fingerprint common pattern established in this paper showed three main bioactive compounds in one chromatogram simultaneously. Principal component analysis based on DAD signals could discriminate adulterants and inferiorities. Principal component analysis indicated that all samples could be mainly regrouped into two main clusters according to the first principal component (PC1, redefined as Vicenin II) and the second principal component (PC2, redefined as zizyphusine). PC1 and PC2 could explain 91.42% of the variance. Content of zizyphusine fluctuated more greatly than that of spinosin, and this result was also confirmed by the HPTLC result. Samples with low content of jujubosides and two common adulterants could not be used equivalently with authenticated ones in clinic, while one reference standard extract could substitute the crude drug in pharmaceutical production. Giving special consideration to the well-known bioactive saponins but with low response by end absorption, a fast and cheap HPTLC method for quality control of ZSS was developed and the result obtained was commensurate well with that of HPLC analysis. Samples having similar fingerprints to HPTLC common pattern targeting at saponins could be regarded as authenticated ones. This work provided a faster and cheaper way for quality control of ZSS and laid foundation for establishing a more effective quality control method for ZSS. Keywords: Adulterant, Common pattern, Principal component analysis, Quality control, Ziziphi spinosae seme

LASAR High-resolution 3D Imaging Algorithm Based on Sparse Bayesian Regularization

Linear Array Synthetic Aperture Radar (LASAR) is a novel and promising radar imaging technique. It is difficult to achieve high-resolution LASAR three-dimensional (3D) imaging using the traditional imaging methods based on match filter, because of limitations by the sizes of the linear array antenna and the platform. In this paper, by exploiting the prior distribution of the LASAR echoes and the observed scene, an LASAR high-resolution 3D algorithm based on sparse Bayesian regularization is proposed. The algorithm first combines the Bayesian principle and maximum likelihood estimation theory, and then a sparse Bayesian minimum cost function is constructed for LASAR target recovery. Second, using an iterative regularization reconstruction method, high-resolution imaging of LASAR sparse targets is achieved by solving a joint-norms optimization problem. In addition, for the problem of a large amount of sparse Bayesian regularization imaging, combined with the position prediction fast imaging idea, the threshold segmentation algorithm is used to extract the strong target of sparse coarse imaging, and then the algorithm operation efficiency is improved. Simulation and experiment results are presented to confirm the effectiveness of the algorithm

Precise and Robust Ship Detection for High-Resolution SAR Imagery Based on HR-SDNet

Ship detection in high-resolution synthetic aperture radar (SAR) imagery is a challenging problem in the case of complex environments, especially inshore and offshore scenes. Nowadays, the existing methods of SAR ship detection mainly use low-resolution representations obtained by classification networks or recover high-resolution representations from low-resolution representations in SAR images. As the representation learning is characterized by low resolution and the huge loss of resolution makes it difficult to obtain accurate prediction results in spatial accuracy; therefore, these networks are not suitable to ship detection of region-level. In this paper, a novel ship detection method based on a high-resolution ship detection network (HR-SDNet) for high-resolution SAR imagery is proposed. The HR-SDNet adopts a novel high-resolution feature pyramid network (HRFPN) to take full advantage of the feature maps of high-resolution and low-resolution convolutions for SAR image ship detection. In this scheme, the HRFPN connects high-to-low resolution subnetworks in parallel and can maintain high resolution. Next, the Soft Non-Maximum Suppression (Soft-NMS) is used to improve the performance of the NMS, thereby improving the detection performance of the dense ships. Then, we introduce the Microsoft Common Objects in Context (COCO) evaluation metrics, which provides not only the higher quality evaluation metrics average precision (AP) for more accurate bounding box regression, but also the evaluation metrics for small, medium and large targets, so as to precisely evaluate the detection performance of our method. Finally, the experimental results on the SAR ship detection dataset (SSDD) and TerraSAR-X high-resolution images reveal that (1) our approach based on the HRFPN has superior detection performance for both inshore and offshore scenes of the high-resolution SAR imagery, which achieves nearly 4.3% performance gains compared to feature pyramid network (FPN) in inshore scenes, thus proving its effectiveness; (2) compared with the existing algorithms, our approach is more accurate and robust for ship detection of high-resolution SAR imagery, especially inshore and offshore scenes; (3) with the Soft-NMS algorithm, our network performs better, which achieves nearly 1% performance gains in terms of AP; (4) the COCO evaluation metrics are effective for SAR image ship detection; (5) the displayed thresholds within a certain range have a significant impact on the robustness of ship detectors