Falconer distance problem on Riemannian manifolds with constant sectional curvature

For $d$ even, we prove that on a $d$-dimensional Riemannian manifold with constant sectional curvature, the distance set of a Borel set $E$ has positive Lebesgue measure if the Hausdorff dimension of $E$ is greater than $\frac d2+\frac14.$Comment: 18 page

Microlocal decoupling inequalities and the distance problem on Riemannian manifolds

We study the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. Key new ingredients include a family of refined microlocal decoupling inequalities, which are related to the work of Beltran-Hickman-Sogge on Wolff-type inequalities, and an analog of Orponen's radial projection lemma which has proved quite useful in recent work on distance sets.Comment: 36 pages, 2 figures, Referee's suggestions incorporate

Improved local smoothing estimate for the wave equation in higher dimensions

In this paper, we establish the sharp $k$-broad estimate for a class of phase functions satisfying the homogeneous convex conditions. As an application, we obtain improved local smoothing estimates for the half-wave operator in dimensions $n\ge3$. As a byproduct, we also generalize the restriction estimates of Ou--Wang to a broader class of phase functions.Comment: 32 pages, 3 figures, Referees' suggestions incorporated. To appear in J. Func. Ana

Visualization of out-of-plane spin generation in mirror symmetry broken Co

Generating out-of-plane spins in sputtered materials holds immense potential for achieving field-free spin-orbit torque switching in practical applications and mass production. In this work, we present the detection of out-of-plane spins from single-layer ferromagnetic Co layers, which are visualized through helicity-dependent photomapping techniques. Our experiments have shown that out-of-plane spin generation is dependent on the magnetization direction, current density, and Co thickness. Our findings indicate that amorphous sputtered Co can be a promising candidate as an out-of-plane spin source material for industrial massive production.Comment: 5 figure

Boundary-semantic collaborative guidance network with dual-stream feedback mechanism for salient object detection in optical remote sensing imagery

With the increasing application of deep learning in various domains, salient object detection in optical remote sensing images (ORSI-SOD) has attracted significant attention. However, most existing ORSI-SOD methods predominantly rely on local information from low-level features to infer salient boundary cues and supervise them using boundary ground truth, but fail to sufficiently optimize and protect the local information, and almost all approaches ignore the potential advantages offered by the last layer of the decoder to maintain the integrity of saliency maps. To address these issues, we propose a novel method named boundary-semantic collaborative guidance network (BSCGNet) with dual-stream feedback mechanism. First, we propose a boundary protection calibration (BPC) module, which effectively reduces the loss of edge position information during forward propagation and suppresses noise in low-level features without relying on boundary ground truth. Second, based on the BPC module, a dual feature feedback complementary (DFFC) module is proposed, which aggregates boundary-semantic dual features and provides effective feedback to coordinate features across different layers, thereby enhancing cross-scale knowledge communication. Finally, to obtain more complete saliency maps, we consider the uniqueness of the last layer of the decoder for the first time and propose the adaptive feedback refinement (AFR) module, which further refines feature representation and eliminates differences between features through a unique feedback mechanism. Extensive experiments on three benchmark datasets demonstrate that BSCGNet exhibits distinct advantages in challenging scenarios and outperforms the 17 state-of-the-art (SOTA) approaches proposed in recent years. Codes and results have been released on GitHub: https://github.com/YUHsss/BSCGNet.Comment: Accepted by TGR

Estimation of flow direction in meandering compound channels

YesThe flow in the main channel of a meandering compound channel does not occur in the ridge direction because of the effect of the upstream floodplain flows. This study proposes a model for estimating the flow direction in the depth-averaged two-dimensional domain (depth-averaged flow angles) between the entrance and the apex sections. Detailed velocity measurements were performed in the region between the meander entrance section and apex section in a large-scale meandering compound channel. The vertical size of the secondary current cell is highly related to the depth-averaged flow angle; thus, the means of the local flow angles above the secondary current cell and within the cell are separately discussed. The experimental measurements indicate that the mean local flow angle above the cell is equal to the section angle, whereas the mean local flow angle within the cell is equal to zero. The proposed model is validated using published data from five sources. Good agreement is obtained between the predictions and measurements, indicating that the proposed model can accurately estimate the depth-averaged flow direction in the meandering compound channels. Finally, the limitations and application ranges of the model are discussed.National Key Research and Development Program of China (No. 2016YFC0402302), the National Natural Science Foundation of China (Nos. 51539007 and 51609160