检索结果-内蒙古大学图书馆

An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations

引用

Science China mathematics 2021年第11期64卷 2579-2602页

作者： Shuo Zhang LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

This paper presents a nonconforming finite element scheme for the planar biharmonic equation,which applies piecewise cubic polynomials(P_(3))and possesses O(h^(2))convergence rate for smooth solutions in the energy norm on general shape-regular *** Dirichlet and Navier type boundary value problems are *** basis for the scheme is a piecewise cubic polynomial space,which can approximate the H^(4) functions with O(h^(2))accuracy in the broken H^(2) ***,a discrete strengthened Miranda-Talenti estimate(▽^(2)_(h)·,▽^(2)_(h)·)=(Δh·,Δh·),which is usually not true for nonconforming finite element spaces,is *** finite element space does not correspond to a finite element defined with Ciarlet’s triple;however,it admits a set of locally supported basis functions and can thus be implemented by the usual *** notion of the finite element Stokes complex plays an important role in the analysis as well as the construction of the basis functions.

关键词： biharmonic equation optimal cubic finite element scheme general triangulation discretized Stokes complex discrete strengthened Miranda-Talenti estimate

来源：评论

学校读者我要写书评

暂无评论

Two-Stage Submodular Maximization Under Knapsack Problem

引用

Tsinghua Science and Technology 2024年第6期29卷 1703-1708页

作者： Zhicheng Liu Jing Jin Donglei Du Xiaoyan Zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China College of Taizhou Nanjing Normal UniversityTaizhou 225300China Faculty of Management University of New BrunswickFrederictonE3B 5A3Canada School of Mathematical Science Institute of Mathematicsand Ministry of Education Key Laboratory of NSLSCSNanjing Normal UniversityNanjing 210023China

Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial *** this paper,we consider knapsack *** this problem,we give n articles and m categories,and the goal is to select a subset of articles that can maximize the function F(S).Function F(S)consists of m monotone submodular functions fj,j=1,2,…,m,and each fj measures the similarity of each article in category *** present a constant-approximation algorithm for this problem.

关键词： submodular function knapsack constraint matroid

来源：评论

学校读者我要写书评

暂无评论

On the convergence of stochastic gradient descent with bandwidth-based step size

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2023年第1期24卷 1990-2038页

作者： Xiaoyu Wang Ya-xiang Yuan Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China and University of Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We first propose a general step-size framework for the stochastic gradient descent(SGD) method: bandwidth-based step sizes that are allowed to vary within a banded region. The framework provides efficient and flexible step size selection in optimization, including cyclical and non-monotonic step sizes (e.g., triangular policy and cosine with restart), for which theoretical guarantees are rare. We provide state-of-the-art convergence guarantees for SGD under mild conditions and allow a large constant step size at the beginning of training. Moreover, we investigate the error bounds of SGD under the bandwidth step size where the boundary functions are in the same order and different orders, respectively. Finally, we propose a 1/t up-down policy and design novel non-monotonic step sizes. Numerical experiments demonstrate these bandwidth-based step sizes' efficiency and significant potential in training regularized logistic regression and several large-scale neural network tasks.

关键词： stochastic gradient descent bandwidth-based step size non-asymptotic convergence non-monotonic step size machine learning

来源：评论

学校读者我要写书评

暂无评论

A Dynamical Variable-separation Method for Parameter-dependent Dynamical Systems

arXiv

引用

arXiv 2025年

作者： Chen, Liang Chen, Yaru Li, Qiuqi Zhou, Tao School of Mathematics Hunan University Changsha410082 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively enriching each term in the reduced basis functions via a greedy algorithm. This enables us to reformulate the problem to two decoupled evolution equations at each enrichment step, of which one is a parameter-independent partial differential equation and the other one is a parameter-dependent ordinary differential equation. These equations are directly derived from the original dynamical system and the previously separate representation terms. Moreover, the computational process of the proposed method can be split into an offline stage, in which the reduced basis functions are constructed, and an online stage, in which the efficient low-rank representation of the solution is employed. The proposed dynamical Variable-separation method is capable of offering reduced computational complexity and enhanced efficiency compared to many existing low-rank separation techniques. Finally, we present various numerical results for linear/nonlinear parameter-dependent dynamical systems to demonstrate the effectiveness of the proposed *** Codes 35R60, 37M99, 65P99 Copyright © 2025, The Authors. All rights reserved.

关键词： Ordinary differential equations

来源：评论

学校读者我要写书评

暂无评论

Optimally arranged TiO_(2)@MoS_(2) heterostructures with effectively induced built-in electric field for high-performance lithium-sulfur batteries

引用

Journal of Energy Chemistry 2023年第8期83卷 496-508,I0012页

作者： Jeongyoub Lee Changhoon Choi Jung Been Park Seungho Yu Jinho Ha Hyungsoo Lee Gyumin Jang Young Sun Park Juwon Yun Hayoung Im Subin Moon Soobin Lee Jung-Il Choi Dong-Wan Kim Jooho Moon Department of Materials Science and Engineering Yonsei UniversitySeoul 03722Republic of Korea School of Civil Environmental and Architectural EngineeringKorea UniversitySeoul 02841Republic of Korea Energy Storage Research Center Korea Institute of Science and Technology(KIST)Seoul 02792Republic of Korea School of Mathematics and Computing(Computational Science and Engineering) Yonsei UniversitySeoul 03722Republic of Korea

To overcome the serious technological issues affecting lithium-sulfur(Li-S) batteries,such as sluggish sulfur redox kinetics and the detrimental shuttle effect,heterostructure engineering has been investigated as a strategy to effectively capture soluble lithium polysulfide intermediates and promote their conversion reaction by integrating highly polar metal oxides with catalytically active metals ***,to fully exploit the outstanding properties of heterostructure-based composites,their detailed structure and interfacial contacts should be designed ***,optimally arranged TiO_(2)and MoS_(2)-based heterostructures(TiO_(2)@MoS_(2)) are fabricated on carbon cloth as a multifunctional interlayer to efficiently trap polysulfide intermediates and accelerate their redox *** to the synergistic effects between TiO_(2)and MoS_(2)and the uniform heterointerface distribution that induces the ideally oriented built-in electric field,Li-S batteries with TiO_(2)@MoS_(2)interlayers exhibit high rate capability(601 mA h g^(-1)at 5 C),good cycling stability(capacity-fade rate of 0.067% per cycle over 500 cycles at2 C),and satisfactory areal capacity(5.2 mA h cm^(-2)) under an increased sulfur loading of 5.2 mg cm^(-2).Moreover,by comparing with a MoS_(2)@TiO_(2)interlayer composed of reversely arranged heterostructures,the effect of the built-in electric field’s direction on the electrocatalytic reactions of polysulfide intermediates is thoroughly investigated for the first *** superior electrocatalytic activities of the rationally arranged TiO_(2)@MoS_(2)interlayer demonstrate the importance of optimizing the built-in electric field of heterostructures for producing high-performance Li-S batteries.

关键词： Lithium-sulfur batteries Shuttle effect TiO_(2)-MoS_(2)heterostructure engineering Built-in electric field Multifunctional interlayers

来源：评论

学校读者我要写书评

暂无评论

QoS-Based Beamforming and Compression Design for Cooperative Cellular Networks via Lagrangian Duality

引用

IEEE Transactions on Signal Processing 2025年

作者： Fan, Xilai Liu, Ya-Feng Liu, Liang Chang, Tsung-Hui Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China The Hong Kong Polytechnic University Department of Electronic and Information Engineering Hong Kong Hong Kong The Chinese University of HongKong School of Science and Engineering Shenzhen Shenzhen China Shenzhen Research Institute of Big Data China

This paper considers the quality-of-service (QoS)-based joint beamforming and compression design problem in the downlink cooperative cellular network, where multiple relay-like base stations (BSs), connected to the central processor via ratelimited fronthaul links, cooperatively transmit messages to the users. The problem of interest is formulated as the minimization of the total transmit power of the BSs, subject to all users' signal-to-interference-plus-noise ratio (SINR) constraints and all BSs' fronthaul rate constraints. In this paper, we first show that there is no duality gap between the considered joint optimization problem and its Lagrangian dual by showing the tightness of its semidefinite relaxation (SDR). Then, we propose an efficient algorithm based on the above duality result for solving the considered problem. The proposed algorithm judiciously exploits the special structure of an enhanced Karush-Kuhn-Tucker (KKT) conditions of the considered problem and approaches the solution that satisfies the enhanced KKT conditions via two fixed point iterations. Two key features of the proposed algorithm are: (1) it is able to detect whether the considered problem is feasible or not and find its globally optimal solution when it is feasible;(2) it is highly efficient because both of the fixed point iterations in the proposed algorithm are linearly convergent and function evaluations in the fixed point iterations are computationally cheap. Numerical results show the global optimality and efficiency of the proposed algorithm. © 1991-2012 IEEE.

关键词： Lagrange multipliers

来源：评论

学校读者我要写书评

暂无评论

Towards Autonomous Shooting Rover via Situation Aware Visual-Perception and Dynamic Action Execution

Towards Autonomous Shooting Rover via Situation Aware Visual...

引用

2024 IEEE/SICE International Symposium on System Integration, SII 2024

作者： Chikoti, Shreenaga Shubham Seelam, Yukkta Jain, Aditya Mehta, Nishi Watsa, Sidhartha Ranjan, Ayush Behera, L. Indian Institute of Technology Kanpur Department of Mathematics and Scientific Computing India Indian Institute of Technology Kanpur Department of Material Science and Engineering India Indian Institute of Technology Kanpur Department of Electrical Engineering India Indian Institute of Technology Kanpur Department of Computer Science and Engineering India Indian Institute of Technology Kanpur Department of Mechanical Engineering India

ISBN: (纸本)9798350312072

In this system paper, we present our approach to the DJI Robomaster AI Challenge, 2022 where our team ERA-IITK was ranked 3rd worldwide among 83 teams. We primarily focus on system hardware design and algorithmic components to achieve full autonomy. We first detail the hardware infrastructure, including intricate details on sensors and communication setup. Then we comprehensively describe our algorithmic pipeline and a state machine based on them to realize an autonomous system. Our major novelty is the high-speed and accurate visual perception module for target detection, and high-speed self-localization to maximize the likelihood of a target being shot. Our research endeavor in this paper can serve as a foundation for more complex systems and holds immense potential for various real-world applications. © 2024 IEEE.

关键词： Vision

来源：评论

学校读者我要写书评

暂无评论

INVESTIGATION OF LEADING-EDGE VORTICES ON A TRIPLE-DELTA-WING CONFIGURATION USING SCALE-ADAPTIVE SIMULATION 33

INVESTIGATION OF LEADING-EDGE VORTICES ON A TRIPLE-DELTA-WIN...

引用

33rd Congress of the International Council of the Aeronautical Sciences, ICAS 2022

作者： Di Fabbio, Tony Tangermann, Eike Klein, Markus University of the Bundeswehr Munich Department of Aerospace Engineering Institute of Applied Mathematics and Scientific Computing Neubiberg85577 Germany

ISBN: (纸本)9781713871163

A triple-delta wing configuration in transonic conditions has been investigated numerically with focus to the leading-edge vortices at sideslip flow. Two primary vortices occur in correspondence with the two wing sweep angles which interact with each other in the aft part of the wing. Besides, due to the transonic free-stream speed, several shock waves appear and also interact with the vortices. The side slip angle causes different flow conditions on the two wings, whose effects are connected. The present work focuses on the accuracy and efficiency of predicting aerodynamic coefficients and on analysis of the flow field to improve the understanding of the involved flow physical phenomena. Two different approaches of turbulence treatment have been applied and compared with the experimental data in order to determine the range of suitability of current turbulence models, namely scale-adaptive simulation (SAS) and kω-SST URANS. The SAS provides a promising approach to predict the flow physics over such configuration with a significantly better accuracy. © 2022 ICAS. All Rights Reserved.

关键词： Turbulence models

来源：评论

学校读者我要写书评

暂无评论

A New Function Space from Barron Class and Application to Neural Network Approximation

引用

Communications in computational Physics 2022年第10期32卷 1361-1400页

作者： Yan Meng Pingbing Ming School of Mathematics Renmin University of ChinaBeijing 100872China LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesNo.55East Road Zhong-Guan-CunBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China.

We introduce a new function space,dubbed as the Barron spectrum space,which arises from the target function space for the neural network *** give a Bernstein type sufficient condition for functions in this space,and clarify the embedding among the Barron spectrum space,the Bessel potential space,the Besov space and the Sobolev ***,the unexpected smoothness and the decaying behavior of the radial functions in the Barron spectrum space have been *** an application,we prove a dimension explicit L^(q) error bound for the two-layer neural network with the Barron spectrum space as the target function space,the rate is dimension independent.

关键词： Fourier transform Besov space Sobolev space radial function neural network

来源：评论

学校读者我要写书评

暂无评论

An Adaptive Proximal Inexact Gradient Framework and Its Application to Per-Antenna Constrained Joint Beamforming and Compression Design

arXiv

引用

arXiv 2025年

作者： Fan, Xilai Jiang, Bo Liu, Ya-Feng State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China

In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proximal gradient methods, the proposed framework introduces a new line search condition that jointly adapts to function and gradient errors, enabling adaptive stepsize selection while maintaining theoretical guarantees. Specifically, we prove that the proposed framework achieves an ϵ-stationary point within O(ϵ−2) iterations for nonconvex objectives and an ϵ-optimal solution within O(ϵ−1) iterations for convex cases, matching the best-known complexity in this context. We then custom-apply the APIG framework to an important signal processing problem: the joint beamforming and compression problem (JBCP) with per-antenna power constraints (PAPCs) in cooperative cellular networks. This customized application requires careful exploitation of the problem’s special structure such as the tightness of the semidefinite relaxation (SDR) and the differentiability of the dual. Numerical experiments demonstrate the superior performance of our custom-application over state-of-the-art benchmarks for the JBCP. © 2025, CC BY.

关键词： Beamforming

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：