arXiv subjects

Hua Zhu

Publications and source records attributed to Hua Zhu.

16 recordsLinked to original sources

arXiv2026

MAD-LEO: A Maneuver-Annotated Orbital Dataset for LEO Satellites with Tiered Multi-Source Evidence

With the rapid development of aerospace technology and the large-scale deployment of low Earth orbit (LEO) constellations, the risk of orbital collisions has increased, creating a growing demand for reliable observations of satellite maneuvers. However, public datasets containing real maneuver records remain scarce. We present MAD-LEO, a Maneuver-Annotated orbital Dataset for LEO satellites. The mission-reported subset contains 1,134 maneuver events from eleven geodetic and altimetry satellites spanning 1992 to 2026, with labels taken directly from mission-published maneuver histories. Each event is checked against two-line element (TLE) data, precise orbit products, and satellite laser ranging (SLR) observations, with evidence tiers assigned according to data availability. The operational subset pairs operator-published ephemerides for 6,785 Starlink satellites with cataloged TLE records over a continuous 107-hour period. Technical validation across seven machine-readable experiment suites confirms the cross-source consistency of the labels and the evidence products.

astro-ph.EP↗

arXiv2026

Liouville theorem for a class of p-Laplace type equations on manifolds

We study a class of $p$-Laplace equations $$\Delta_p u-\lambda u^{p-1}+ u^{q-1}=0$$ on a closed $n$-dimensional Riemannian manifold $(M,g)$ with $\operatorname{Ric}\geqslant(n-1)g$. For $1 2$ and $p 0$; aside from the constant solution, the equation admits a positive nonconstant solution. This answers V\'eron's problem raised in \cite{Ver92}.

math.AP↗

arXiv2026

Liouville Theorem for $(p,q)$-Laplace Equations

We employ the vector field method to establish a Liouville-type theorem for a class of $(p,q)$-Laplace equations in the Euclidean space $\mathbb{R}^n$. By modifying the exponents in the differential identity, we prove nonexistence in the subcritical range $p-1<\alpha<q^*-1$, where $q^*=nq/(n-q)$. The approach relies on constructing a suitable differential identity, carrying out precise integral estimates with cutoff functions, and combining sign control and decay of the cutoff errors.

math.AP↗

arXiv2025

Classification of positive solutions to a class of Laplace equations with a gradient term

In this paper, we investigate positive solutions to a class of Laplace equations with a gradient term on a complete, connected, and noncompact Riemannian manifold $(M^n,g)$ with nonnegative Ricci curvature, namely \[-\Delta u = f(u)|\nabla u|^q\quad\text{in }~M^n,\] where $n\geqslant 3$, $q>0,$ and $f$ is a positive continuous function. We prove some Liouville theorems employing a key differential identity derived via the invariant tensor technique. In particular, for $f(u)=u^{\frac{2-q}{n-2}(n+\frac{q}{1-q})-1}$ is the second critical case in dimension $n=3,4,5$, without any additional conditions, such as integrable conditions on $u$, we show the rigidity for the ambient manifold and classification result of positive solutions. To our knowledge, this is the first rigidity result for equations with gradient terms in the second critical case. Moreover, this result confirms that all solutions must be of the form found in \cite{BV-GH-V2019}.

math.AP↗

arXiv2025

SpaceTrack-TimeSeries: Time Series Dataset towards Satellite Orbit Analysis

With the rapid advancement of aerospace technology and the large-scale deployment of low Earth orbit (LEO) satellite constellations, the challenges facing astronomical observations and deep space exploration have become increasingly pronounced. As a result, the demand for high-precision orbital data on space objects-along with comprehensive analyses of satellite positioning, constellation configurations, and deep space satellite dynamics-has grown more urgent. However, there remains a notable lack of publicly accessible, real-world datasets to support research in areas such as space object maneuver behavior prediction and collision risk assessment. This study seeks to address this gap by collecting and curating a representative dataset of maneuvering behavior from Starlink satellites. The dataset integrates Two-Line Element (TLE) catalog data with corresponding high-precision ephemeris data, thereby enabling a more realistic and multidimensional modeling of space object behavior. It provides valuable insights into practical deployment of maneuver detection methods and the evaluation of collision risks in increasingly congested orbital environments.

astro-ph.EP↗

arXiv2025

Neumann Problems for Elliptic and Parabolic Sum Hessian Equations

This paper studies the Neumann boundary value problem for sum Hessian equations. We first derive a priori $C^2$ estimates for $(k-1)$-admissible solutions in almost convex and uniformly $(k-1)$-convex domains, and prove the existence of admissible solutions via the method of continuity. Furthermore, we obtain existence results for the classical Neumann problem in uniformly convex domains. Finally, we extend these results to the corresponding parabolic problems.

math.AP↗

arXiv2024

The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions

In this paper, we primarily study the Pogorelov-type $C^2$ estimates for $(k-1)$-convex solutions of the sum Hessian equation under the assumption of semi-convexity, and apply these estimates to obtain a rigidity theorem for global solutions satisfying the corresponding conditions. Furthermore, we investigate the Pogorelov estimates and rigidity theorems for solutions to the parabolic versions under similar conditions. These results extend the works of \cite{He-Sheng-Xiang-Zhang-2022-CCM} and \cite{Liu-Ren-2023-JFA}.

math.AP↗

arXiv2024

Two-dimensional Kagome Materials: Theoretical Insights, Experimental Realizations, and Electronic Structures

In recent years, kagome materials have attracted significant attention due to their rich emergent phenomena arising from the quantum interplay of geometry, topology, spin, and correlations. However, in the search for kagome materials, it has been found that bulk compounds with electronic properties related to the kagome lattice are relatively scarce, primarily due to the hybridization of kagome layers with adjacent layers. Therefore, researchers have shown increasing interest in the discovery and construction of two-dimensional (2D) kagome materials, aiming to achieve clean kagome bands near the Fermi level in monolayer or few-layer systems. Substantial advancements have already been made in this area. In this review, we summarize the current progress in the construction and development of 2D kagome materials. We begin by introducing the geometric and electronic structures of the kagome lattice model and its variants, followed by discussions on the experimental realizations and electronic structure characterizations of 2D kagome materials. Finally, we provide an outlook on the future developments of 2D kagome materials.

cond-mat.mtrl-sci↗

arXiv2024

Mask-Enhanced Segment Anything Model for Tumor Lesion Semantic Segmentation

Tumor lesion segmentation on CT or MRI images plays a critical role in cancer diagnosis and treatment planning. Considering the inherent differences in tumor lesion segmentation data across various medical imaging modalities and equipment, integrating medical knowledge into the Segment Anything Model (SAM) presents promising capability due to its versatility and generalization potential. Recent studies have attempted to enhance SAM with medical expertise by pre-training on large-scale medical segmentation datasets. However, challenges still exist in 3D tumor lesion segmentation owing to tumor complexity and the imbalance in foreground and background regions. Therefore, we introduce Mask-Enhanced SAM (M-SAM), an innovative architecture tailored for 3D tumor lesion segmentation. We propose a novel Mask-Enhanced Adapter (MEA) within M-SAM that enriches the semantic information of medical images with positional data from coarse segmentation masks, facilitating the generation of more precise segmentation masks. Furthermore, an iterative refinement scheme is implemented in M-SAM to refine the segmentation masks progressively, leading to improved performance. Extensive experiments on seven tumor lesion segmentation datasets indicate that our M-SAM not only achieves high segmentation accuracy but also exhibits robust generalization. The code is available at https://github.com/nanase1025/M-SAM.

eess.IV↗

arXiv2022

Maximal estimates for the bilinear Riesz means on Heisenberg groups

In this article, we investigate the maximal bilinear Riesz means $S^{\alpha }_{*}$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{\alpha }_{*}$ is bounded from $L^{p_{1}}\times L^{p_{2}}$ into $% L^{p}$ for $2\leq p_{1}, p_{2}\leq \infty $ and $1/p=1/p_{1}+1/p_{2}$ when $% \alpha $ is large than a suitable smoothness index $\alpha (p_{1},p_{2})$. For obtaining a lower index $\alpha (p_{1},p_{2})$, we define two important auxiliary operators and investigate their $L^{p}$ estimates,which play a key role in our proof.

math.FA↗

arXiv2022

Riesz means and bilinear Riesz means on M\'{e}tivier groups

In this paper, we investigate the $L^{p}$-boundedness of the Riesz means and the $L^{p_{1}}\times L^{p_{2}}\rightarrow L^{p}$ boundedness of the bilinear Riesz means on M\'{e}tivier groups. M\'{e}tivier groups are generalization of Heisenberg groups and general H-type groups. Because general M\'{e}tivier groups only satisfy the non-degeneracy condition and have high-dimensional centre, we have to use different methods and techniques from those on Heisenberg groups and H-type groups.

math.FA↗

arXiv2019

A Review of Visual Trackers and Analysis of its Application to Mobile Robot

Computer vision has received a significant attention in recent year, which is one of the important parts for robots to obtain information about the external environment. Visual trackers can provide the necessary physical and environmental parameters for the mobile robot, and their performance is related to the actual application of the robot. This study provides a comprehensive survey on visual trackers. Following a brief introduction, we first analyzed the basic framework and difficulties of visual trackers. Then the structure of generative and discriminative methods is introduced, and summarized the feature descriptors, modeling methods, and learning methods which be used in tracker. Later we reviewed and evaluated the state-of-the-art progress on discriminative trackers from three directions: correlation filter, deep learning and convolutional features. Finally, we analyzed the research direction of visual tracker used in mobile robot, as well as outlined the future trends for visual tracker on mobile robot.

cs.CV↗

arXiv2019

Tracking system of Mine Patrol Robot for Low Illumination Environment

Computer vision has received a significant attention in recent years, which is one of the important parts for robots to apperceive external environment. Discriminative Correlation Filter (DCF) based trackers gained more popularity due to their efficiency, however, tracking in low-illumination environments is a challenging problem, not yet successfully addressed in the literature. In this work, we tackle the problems by introducing Low-Illumination Long-term Correlation Tracker (LLCT). First, fused features only including HOG and Color Names are employed to boost the tracking efficiency. Second, we used the standard PCA to reduction scheme in the translation and scale estimation phase for accelerating. Third, we learned a long-term correlation filter to keep the long-term memory ability. Finally, update memory templates with interval updates, then re-match existing and initial templates every few frames to maintain template accuracy. The extensive experiments on popular Object Tracking Benchmark OTB-50 datasets have demonstrated that the proposed tracker outperforms the state-of-the-art trackers significantly achieves a high real-time (33FPS) performance. In addition, the proposed approach can be integrated easily in robot system and the running speed performed well. The experimental results show that the novel tracker performance in low-illumination environment is better than that of general trackers.

cs.CV↗

arXiv2014

Voting for Deceptive Opinion Spam Detection

Consumers' purchase decisions are increasingly influenced by user-generated online reviews. Accordingly, there has been growing concern about the potential for posting deceptive opinion spam fictitious reviews that have been deliberately written to sound authentic, to deceive the readers. Existing approaches mainly focus on developing automatic supervised learning based methods to help users identify deceptive opinion spams. This work, we used the LSI and Sprinkled LSI technique to reduce the dimension for deception detection. We make our contribution to demonstrate what LSI is capturing in latent semantic space and reveal how deceptive opinions can be recognized automatically from truthful opinions. Finally, we proposed a voting scheme which integrates different approaches to further improve the classification performance.

cs.CL↗

arXiv2014

Riesz transform characterization of weighted Hardy spaces associated to Schr\"{o}dinger operators

In this paper, we characterize the weighted local Hardy spaces $h^p_\rho(\omega)$ related to the critical radius function $\rho$ and weights $\omega\in A_{1}^{\rho,\,\infty}(\mathbb{R}^{n})$ by localized Riesz transforms $\widehat{R}_j$, in addition, we give a characterization of weighted Hardy spaces $H^{1}_{\cal L}(\omega)$ via Riesz tranforms associated to Schr\"{o}dinger operator $\cal L$, where $\L=-\Delta+V$ is a Schr\"{o}dinger operator on $\mathbb{R}^{n}$ ($n\ge 3$) and $V$ is a nonnegative function satisfying the reverse H\"older inequality.

math.FA↗

arXiv2014

Weighted local Hardy spaces associated to Schr\"{o}dinger operators

In this paper, we characterize the weighted local Hardy spaces $h^p_\rho(\omega)$ related to the critical radius function $\rho$ and weights $\omega\in A_{\infty}^{\rho,\,\infty}(\mathbb{R}^{n})$ which locally behave as Muckenhoupt's weights and actually include them, by the local vertical maximal function, the local nontangential maximal function and the atomic decomposition. By the atomic characterization, we also prove the existence of finite atomic decompositions associated with $h^{p}_{\rho}(\omega)$. Furthermore, we establish boundedness in $h^p_\rho(\omega)$ of quasi- Banach-valued sublinear operators. As their applications, we establish the equivalence of the weighted local Hardy space $h^1_\rho(\omega)$ and the weighted Hardy space $H^1_{\cal L}(\omega)$ associated to Schr\"{o}dinger operators $\cal L$ with $\omega \in A_1^{\rho,\infty}(\mathbb{R}^{n})$

math.CA↗