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Qianyun Li

Publications and source records attributed to Qianyun Li.

7 recordsLinked to original sources
arXiv2026

Hardy-Littlewood type phenomena and the Girela-Peláez conjecture for the Möbius invariant Laplacian operator

The purpose of this paper is twofold. First, we investigate the Hardy-Littlewood type phenomena for Dirichlet solutions to the Möbius invariant Laplace equation on the unit ball in $\mathbb{R}^n$. Our work extends and improves several key results due to Pavlovć [Rev. Mat. Iberoam. 23: 831-845, 2007] and Chen et al. [J. Geom. Anal. 34: 23 pp, 2024]. In particular, we give a complete answer to a question raised by Makoto Masumoto. Second, motivated by Aikawa's work, we study the boundedness of the operator norm of $P_α$, where $P_α[φ]$ is the Dirichlet solution of such equation for the boundary data $φ$. By using alternative proof techniques, we obtain an equivalent characterization of the boundedness of the operator norm of $P_α$. Finally, we show that the Girela-Peláez conjecture holds positively for more general classes of functions induced by the Möbius invariant Laplacian operator.

math.FA↗
arXiv2026

Riesz--Fejér type Inequalities for $α$-Harmonic Functions in the Unit Ball

In this paper, we establish Riesz--Fejér type inequalities for the $α$-harmonic functions $f=P_α[f^*]$ in $\mathbb B^n$, where $f^*\in L^{p}(\mathbb{S}^{n-1})$ and $1 -1$, we prove the existence of a constant $\mathcal{C}_{n,p,α}$ such that $\int_{-1}^{1} |f(rη)|^p(1-r^2)^{n-2}\,dr \leq \mathcal{C}_{n,p,α} \int_{\mathbb S^{n-1}}|f^*(ξ)|^p\,dσ(ξ)$. Moreover, in the range $α>\max\left\{ -\frac{n-1}{p},\,n-2-\frac{2(n-1)}{p} \right\}$, we determine the sharp constant explicitly. The result generalize and extend the corresponding results of Ahmed et al. (J. Math. Anal. Appl., 563:13, 2026), Hu et al. (Anal. Math. 51:15, 2025) and Long (arXiv: 2410.12137).

math.CV↗
arXiv2025

LongCat-Flash Technical Report

We introduce LongCat-Flash, a 560-billion-parameter Mixture-of-Experts (MoE) language model designed for both computational efficiency and advanced agentic capabilities. Stemming from the need for scalable efficiency, LongCat-Flash adopts two novel designs: (a) Zero-computation Experts, which enables dynamic computational budget allocation and activates 18.6B-31.3B (27B on average) per token depending on contextual demands, optimizing resource usage. (b) Shortcut-connected MoE, which enlarges the computation-communication overlap window, demonstrating notable gains in inference efficiency and throughput compared to models of a comparable scale. We develop a comprehensive scaling framework for large models that combines hyperparameter transfer, model-growth initialization, a multi-pronged stability suite, and deterministic computation to achieve stable and reproducible training. Notably, leveraging the synergy among scalable architectural design and infrastructure efforts, we complete model training on more than 20 trillion tokens within 30 days, while achieving over 100 tokens per second (TPS) for inference at a cost of \$0.70 per million output tokens. To cultivate LongCat-Flash towards agentic intelligence, we conduct a large-scale pre-training on optimized mixtures, followed by targeted mid- and post-training on reasoning, code, and instructions, with further augmentation from synthetic data and tool use tasks. Comprehensive evaluations demonstrate that, as a non-thinking foundation model, LongCat-Flash delivers highly competitive performance among other leading models, with exceptional strengths in agentic tasks. The model checkpoint of LongCat-Flash is open-sourced to foster community research. LongCat Chat: https://longcat.ai Hugging Face: https://huggingface.co/meituan-longcat GitHub: https://github.com/meituan-longcat

cs.CL↗
arXiv2025

Schwarz-Pick type lemma and Landau type theorem for $α$-harmonic mappings

The aim of this paper is twofold. First, we obtain a Schwarz-Pick type lemma for the $α$-harmonic mapping $u=P_α[ϕ]$, where $ϕ\in L^{p}(\mathbb{S}^{n-1},\mathbb{R} )$ and $p\in[1,\infty]$. We get an explicit form of the sharp function $\mathbf{C}_{α, q}(x)$ in the inequality $|\nabla u(x)| \leq \mathbf{C}_{α, q}(x)\|ϕ\|_{L^p(\mathbb{S}^{n-1}, \mathbb{ R} )}$. Second, we prove a Landau type theorem for $u=P_α[ϕ]$, where $ϕ\in L^{\infty}(\mathbb{S}^{n-1},\mathbb{R}^{n})$. These results generalize and extend the corresponding results due to Kalaj (Complex Anal. Oper. Theory, 2024) and Khalfallah et al. (Mediterr. J. Math., 2021).

math.AP↗
arXiv2023

CASSPR: Cross Attention Single Scan Place Recognition

Place recognition based on point clouds (LiDAR) is an important component for autonomous robots or self-driving vehicles. Current SOTA performance is achieved on accumulated LiDAR submaps using either point-based or voxel-based structures. While voxel-based approaches nicely integrate spatial context across multiple scales, they do not exhibit the local precision of point-based methods. As a result, existing methods struggle with fine-grained matching of subtle geometric features in sparse single-shot Li- DAR scans. To overcome these limitations, we propose CASSPR as a method to fuse point-based and voxel-based approaches using cross attention transformers. CASSPR leverages a sparse voxel branch for extracting and aggregating information at lower resolution and a point-wise branch for obtaining fine-grained local information. CASSPR uses queries from one branch to try to match structures in the other branch, ensuring that both extract self-contained descriptors of the point cloud (rather than one branch dominating), but using both to inform the output global descriptor of the point cloud. Extensive experiments show that CASSPR surpasses the state-of-the-art by a large margin on several datasets (Oxford RobotCar, TUM, USyd). For instance, it achieves AR@1 of 85.6% on the TUM dataset, surpassing the strongest prior model by ~15%. Our code is publicly available.

cs.CV↗
arXiv2022

Identification of the anomalous fast bulk events in a p-type point contact germanium detector

The ultralow detection threshold, ultralow intrinsic background, and excellent energy resolution of p-type point-contact germanium detector are important for rare-event searches, in particular for the detection of direct dark matter interactions, coherent elastic neutrino-nucleus scattering, and neutrinoless double beta decay. Anomalous bulk events with an extremely fast rise time are observed in the CDEX-1B detector. We report a method of extracting fast bulk events from bulk events using a pulse shape simulation and reconstructed source experiment signature. Calibration data and the distribution of X-rays generated by intrinsic radioactivity verified that the fast bulk experienced a single hit near the passivation layer. The performance of this germanium detector indicates that it is capable of single-hit bulk spatial resolution and thus provides a background removal technique.

physics.ins-det↗