Explanipedia

Sharp microlocal Kakeya--Nikodym estimates for eigenfunctions with applications Open

Chuanwei Gao, Shukun Wu, Yakun Xi · 2025

We extend the microlocal Kakeya--Nikodym bounds for eigenfunctions of Blair--Sogge to a larger range of exponents, which is optimal in odd dimensions. On manifolds of constant sectional curvature we introduce a new anisotropic variant of t…

A Smart Rehabilitation Glove Based on Shape-Memory Alloys for Stroke Recovery Open

Yutong Xie, S P Sun, Yiwen Liu, Fei Xiao, Weijie Li , et al. · 2025

Stroke-induced hand dysfunction substantially impairs patients’ quality of life, creating an urgent need for portable, adaptive rehabilitation devices. This study introduces a smart rehabilitation glove actuated by shape-memory alloy (SMA)…

Restriction and decoupling estimates for the hyperbolic paraboloid in $\mathbb{R}^3$ Open

Ciprian Demeter, Shukun Wu · 2025

We prove bilinear $\ell^2$-decoupling and refined bilinear decoupling inequalities for the truncated hyperbolic paraboloid in $\mathbb{R}^3$. As an application, we prove the associated restriction estimate in the range $p>22/7$, matching a…

On local smoothing estimates for wave equations Open

Shengwen Gan, Shukun Wu · 2025

We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in 3+1 dimensions and obtained improved estimates in higher dimensions. This is achieved by deriving local smoothing estimates for certain Fourier …

Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities Open

Hong Wang, Shukun Wu · 2024

We propose to study the restriction conjecture using decoupling theorems and two-ends Furstenberg inequalities. Specifically, we pose a two-ends Furstenberg conjecture, which implies the restriction conjecture. As evidence, we prove this c…

A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin Open

Jacob B. Fiedler, Guo-Dong Hong, Donggeun Ryou, Shukun Wu · 2024

This article is a study guide for ``On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" by Orponen and Shmerkin. We begin by introducing Furstenberg set problem and exceptional set of projections and pro…

A weighted decoupling inequality and its application to the maximal Bochner-Riesz problem Open

Shengwen Gan, Shukun Wu · 2024

We prove some weighted $L^p\ell^p$-decoupling estimates when $p=2n/(n-1)$. As an application, we give a result beyond the real interpolation exponents for the maximal Bochner-Riesz operator in $\mathbb{R}^3$. We also make an improvement in…

A bilinear estimate in $\mathbb{F}_p$ Open

Necef Kavrut, Shukun Wu · 2024

We improve an $L^2\times L^2\to L^2$ estimate for a certain bilinear operator in the finite field of size $p$, where $p$ is a prime sufficiently large. Our method carefully picks the variables to apply the Cauchy-Schwarz inequality. As a c…

Channel and Spatial Relation-Propagation Network for RGB-Thermal Semantic Segmentation Open

Zikun Zhou, Shukun Wu, Zhu Guoqing, Hongpeng Wang, Zhenyu He · 2023

RGB-Thermal (RGB-T) semantic segmentation has shown great potential in handling low-light conditions where RGB-based segmentation is hindered by poor RGB imaging quality. The key to RGB-T semantic segmentation is to effectively leverage th…

Control Input Inference of Mobile Agents under Unknown Objective Open

Chendi Qu, Jianping He, Xiaoming Duan, Shukun Wu · 2023

Trajectory and control secrecy is an important issue in robotics security. This paper proposes a novel algorithm for the control input inference of a mobile agent without knowing its control objective. Specifically, the algorithm first est…

Control Input Inference of Mobile Agents under Unknown Objective Open

Chendi Qu, Jianping He, Xiaoming Duan, Shukun Wu · 2023

Trajectory and control secrecy is an important issue in robotics security. This paper proposes a novel algorithm for the control input inference of a mobile agent without knowing its control objective. Specifically, the algorithm first est…

New bounds for Stein's square functions in higher dimensions Open

Shengwen Gan, Changkeun Oh, Shukun Wu · 2021

We improve the $L^p(\mathbb{R}^n)$ bounds on Stein's square function to the best-known range of the Fourier restriction problem when $n\geq4$. Applications including certain local smoothing estimates are also discussed.

New bounds for Stein's square function in $\mathbb{R}^3$ Open

Shengwen Gan, Yifan Jing, Shukun Wu · 2021

We prove new $L^p(\mathbb{R}^3)$ bounds on Stein's square function for $p\geq3.25$. As an application, it improves the maximal Bochner-Riesz conjecture to the same range of $p$.

The Bochner-Riesz problem: an old approach revisited Open

Shaoming Guo, Changkeun Oh, Hong Wang, Shukun Wu, Zhang Ruixiang · 2021

We show that the recent techniques developed to study the Fourier restriction problem apply equally well to the Bochner-Riesz problem. This is achieved via applying a pseudo-conformal transformation and a two-parameter induction-on-scales …

A note on the largest sum-free sets of integers Open

Yifan Jing, Shukun Wu · 2020

Given $A$ a set of $N$ positive integers, an old question in additive combinatorics asks that whether $A$ contains a sum-free subset of size at least $N/3+ω(N)$ for some increasing unbounded function $ω$. The question is generally attacked…

A Canny operator road edge detection method based on color features Open

Shigang Wang, Shukun Wu, Xuesong Wang, Zhenglin Li · 2020

The road edge detection method, proposed by us, highlights the morphological and color features of the road in the image. The method performs color space conversion and color feature screening on color images containing road information, a…

Research on improved sharpening algorithm based on closed operation and binarization Open

Xuesong Wang, Shigang Wang, Yifeng Guo, Shukun Wu, Kene Li · 2020

In this paper, binarization and closed operation are used to improve traditional sharpening algorithms. Aiming at the problem that traditional sharpening algorithm tends to sharpen noise when processing pictures. First of all, this paper e…

On the Bochner-Riesz operator in $\mathbb{R}^3$ Open

Shukun Wu · 2020

We improve the Bochner-Riesz conjecture in $\mathbb{R}^3$ to $\max\{p,p/(p-1)\}\geq3.25$.

Refined Strichartz estimates and Maximal Schr\"odinger operator Open

Shukun Wu · 2020

The largest $(k, \ell)$-sum-free subsets Open

Yifan Jing, Shukun Wu · 2020

Let $\mathscr{M}_{(2,1)}(N)$ be the infimum of the largest sum-free subset of any set of $N$ positive integers. An old conjecture in additive combinatorics asserts that there is a constant $c=c(2,1)$ and a function $ω(N)\to\infty$ as $N\to…

New estimates of maximal Bochner-Riesz operator in the plane Open

Xiao‐Chun Li, Shukun Wu · 2019

We prove some new $L^p$ estimates for maximal Bochner-Riesz operator in the plane.

Machining Strategy and Key Problems for 3D Structure of Micro-EDM by Fix-length Compensation Method with Tubular Electrodes Open

Jingyu Pei, Yebin Liu, Yietian Zhu, Lenan Zhang, Xiaoshun Zhuang , et al. · 2018

Micro-EDM milling is an effective machining process for three-dimension micro-cavity of high hardness materials. Fix-length compensation method is an efficient compensation method for cavity milling by improving single layer thickness. A t…

Research on the Equivalent Plane Machining with Fix-length Compensation Method in Micro-EDM Open

Jingyu Pei, Zhaowei Zhou, Lenan Zhang, Xiaoshun Zhuang, Shukun Wu , et al. · 2016

Micro-EDM milling is an effective machining process for three-dimension (3D) micro-cavity of high hardness materials. Because of the sharp wear of the electrode, fix-length compensation method is proposed, thus results in a cone-shaped ele…

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