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In this paper, we prove that the \(L^p(\mathbb {R}^d)\) norm of the maximal truncated Riesz transform in terms of the \(L^p(\mathbb {R}^d)\) norm of Riesz transform is dimension-free for any \(2\le p<...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On several bi-Hamiltonian systems
双哈密顿系统 齐次Hamitionan算子 相容三元组
2023/11/13
Recently, based on the classification of the second and third order homogeneous Hamitionan operators Lorenzoni and his collaborators classified compatible trios of two-component homogeneous Hamiltonia...
浙大宁波理工学院计算机与数据工程学院苏德矿教授
浙大宁波理工学院计算机与数据工程学院 苏德矿 教授 微积分
2023/6/30
苏德矿，浙江大学理学院数学系教授，浙江省精品课程《微积分》课程负责人、浙江大学公共数学基础课教学指导委员会副主任，浙江大学微积分课程负责人，浙江省高校高等数学教学研究会常务理事兼秘书长，清华大学萧树铁教授主持的前国家教委“面向21世纪教学内容和课程体系改革”研究课题组成员。
Let T=(V,A) be a tournament with a nonnegative integral weight w(e) on each arc e. A subset F of arcs is called a feedback arc set (FAS) if T\F contains no cycles (directed). A collection F of FASs (w...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singular integral and geometry
奇异积分 几何 谐波分析
2023/5/8
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Extensions of Projection Theorem in Banach Spaces
投影定理 巴拿赫空间 扩展
2023/5/4
In this talk, we first recall classic projection theorem for closed convex subsets in a Hilbert space. Then we introduce two extensions of the projection theorem in the Banach space where one is estab...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the preservation of second integrals by RK methods
RK方法 保存 第二积分
2023/4/25
One can elucidate integrability properties of ODEs by knowing the existence of second integrals. However, little is known about how they are preserved, if at all, under numerical methods. In this talk...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Weak multisymplectic spectral integrators with a resolution of Gibbs phenomenon
吉布斯现象 分辨率 弱多辛谱 积分器
2023/4/28
We will report our recent work on weak multisymplectic spectral integrators for a wide range of nonsmooth Hamiltonian partial differential equations, which appear in quite a few physical applications ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation
斯托克斯现象 等单向变形方程 黎曼-希尔伯特问题 显式解 单场方程 可积性
2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: An introduction
斯托克斯现象 等单向变形方程 斯托克斯矩阵
2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strong approximation and integral quadratic forms over affine curves
仿射曲线 强近似 积分二次形式
2023/5/9
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
Conference "Integrable Systems and Their Applications", Sept. 12-16, 2022
Conference Integrable Systems Applications
2022/9/14
The purpose of the conference is to establish international contacts for the subsequent involvement of world experts in cooperation with Russian scientists in the field of geometry and topology, dynam...
增广拉格朗日方法可以近似求解最小约束违背凸优化问题
拉格朗日方法 近似求解 最小约束 违背凸优化问题
2023/1/5
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer...
国家天元数学西北中心于2022年6月21日至29日成功举办“孤立子和可积系统前沿理论讲习班”第三期活动。本期活动的主题是“Riemann-Hilbert方法与可积系统整体解的存在性”，活动邀请复旦大学范恩贵教授做主讲人，进行了连续七次的系列课程，详细讲授了Riemann-Hilbert方法在证明导数薛定谔方程整体解存在性中的深刻应用，阐述了可积系统理论在非线性偏微分方程适定性理论中取得的最新进展。...