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The finite-time stabilization problem is considered for a class of multi-input multi-output nonlinear systems composed of several different subsystems that are coupled with unknown nonlinearities, pos...
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<...
As a specific type of shape gradient descent algorithm, shape gradient flow is widely used for shape optimization problems constrained by partial differential equations. In this approach, the constrai...
斜多项式稀疏矩阵乘法     斜多项式  稀疏矩阵  乘法       2023/12/13
Based on the observation that \mathbb{Q}^{(p-1) \times (p-1)} is isomorphic to a quotient skew polynomial ring, we propose a new deterministic algorithm for (p-1)\times(p-1) matrix multiplication over...
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...
Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize the convergence fact...
We prove a sharp quantitative version of the p-Sobolev inequality for any 1
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...
本文研究了二维多边形区域上的Stokes方程Dirichlet边界控制问题。其中目标泛函中的控制变量正则化项包含两类情形:基于L^2范数的正则化和能量空间范数正则化。我们证明了优化问题的适定性,给出了一阶最优性条件,得到了解的正则性结果,提出了求解两类问题的有限元离散格式,并对能量空间方法证明了有限元误差估计。考虑Stokes方程Dirichlet边界控制问题能量空间正则化方法的出发点来源于我们的...
Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theor...
We deal with the 3D Navier–Stokes equation in a smooth simply connected bounded domain, with controls on a non-empty open part of the boundary and a Navier slip-with-friction boundary condition on the...
幂级数, 随处可见,在复分析、组合理论、代数几何等领域扮演着重要角色。在复分析中,多变元幂级数收敛域的几何结构开启了多复变研究的序幕。在组合理论中,序列的生成函数就是幂级数,其算术与代数性质可以揭示序列的内在结构。在代数几何中,幂级数被用于理解代数簇在奇点处的几何结构。 幂级数的算术理论始于Fatou,Eisenstein,Polya,Szego等人的工作,其中最著名的定理是Szego定理与Pol...
In this paper, the authors prove the global existence and the large time decay estimate of solutions to Prandtl system with small initial data, which is analytical in the tangential variable. The key ...
对α阶(1<α<2)右侧Caputo分数阶导数引入新变量以降低函数阶数,采用L2-1插值方法,得到了高阶插值格式。为了进一步改善L2-1方法在区间[tN-1,b]上由L1插值带来的非一致O(Δt4-α)阶精度,增加约束条件,使整体区间均利用L2插值得到一致的O(Δt4-α)精度的高阶插值格式,并分别证明了二者的截断误差。
应用矩阵论和代数图论,分析l步信息脉冲牵引控制的多智能体一致性问题。把具有单个脉冲控制器的多智能体的一致性系统推广到只对一个智能体实施l步信息脉冲牵引控制的系统。在通讯拓扑是无向连通图的情况下,给出使多智能体达到一致性的一个充分条件。选择恰当的l有助于减少使多智能体系统达到一致性所需的脉冲次数。最后,仿真实例验证了理论结果。

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