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UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

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Journal of Computational Mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

Enhanced bifunctional oxygen electrochemical catalytic performance using La-doped CoFe_(2)O_(4)spinel supported by 3D-G for Zn-air batteries

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Journal of Energy Chemistry 2024年第7期94卷 778-788页

作者： Yinggang sun Tingwei Zhang Peng sun Jigang Wang Wenjie Duan Yanqiong Zhuang Likai Wang Zhongfang Li School of Chemistry and Chemical Engineering Shandong University of TechnologyZibo 255049ShandongChina

The preparation of bifunctional catalysts for oxygen reduction(ORR)and oxygen evolution(OER)is crucial for Zn-air ***,we report a La doped CoFe_(2)O_(4) spinel catalyst supported on threedimensional graphene(3D-G),where La can facilitate electron transfer from Co to Fe,leading to increased electron cloud density in Fe and improved catalytic *** redshift of the G peak in the Raman spectra indicates the interaction between theπbond of 3D-G and d orbitals in La_(0.2)CoFe_(1.8)O_(4).La_(0.2)CoFe_(1.8)/3D-G exhibits superior ORR performance(E_(1/2)=0.86 V ***)and OER performance(E_(j=10)=1.55 V ***)to CoFe_(2)O_(4)/3D-G(E_(1/2)=0.831 V ***,E_(j=10)=1.603 V ***).Furthermore,it demonstrates excellent bifunctional oxygen catalytic performance while maintaining high power density and stability in liquid zinc-air batteries(ZABs)and flexible ZABs(F-ZABs).This work presents a viable strategy for utilizing rare earth element doped spinels to enhance oxygen catalyst and ZABs performance.

关键词： Zn-air batteries Electrocatalysts La_(0.2)CoFe_(1.8)/3D-G Electron pump Bifunctional oxygen catalytic performance

A Note on Gradient Estimates for Elliptic Equations with Discontinuous Coefficients

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Chinese Annals of Mathematics,Series B 2024年第1期45卷 1-10页

作者： Yu PENG Xiandong sun Huichun ZHANG Department of Mathematics Sun Yat-Sen UniversityGuangzhou 510275China.

The authors will use a method in metric geometry to show an L^(P)-estimate for gradient of the weak solutions to elliptic equations with discontinuous coefficients,even the BMO semi-norms of the coefficients are not *... 详细信息

关键词： L^(p)-Estimate Elliptic equation Discontinuous coefficients

Optimal synthesis of heat-integrated distillation configurations using the two-column superstructure

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Chinese Journal of Chemical Engineering 2024年第2期66卷 238-249页

作者： Xiaodong Zhang Lu Jin Jinsheng sun School of Chemical Engineering and Technology Tianjin UniversityTianjin 300072China

In the realm of the synthesis of heat-integrated distillation configurations,the conventional approach for exploring more heat integration possibilities typically entails the splitting of a single column into a twocolumn ***,this approach frequently necessitates tedious enumeration procedures,resulting in a considerable computational *** surmount this formidable challenge,the present study introduces an innovative remedy:The proposition of a superstructure that encompasses both single-column and multiple two-column ***,a simultaneous optimization algorithm is applied to optimize both the process parameters and heat integration structures of the twocolumn *** effectiveness of this approach is demonstrated through a case study focusing on industrial organosilicon *** results underscore that the superstructure methodology not only substantially mitigates computational time compared to exhaustive enumeration but also furnishes solutions that exhibit comparable performance.

关键词： Superstructure Process synthesis Heat integration Simulation-based optimization Industrial organosilicon separation

Physical informed memory networks for solving PDEs:implementation and applications

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Communications in Theoretical Physics 2024年第2期76卷 51-61页

作者： Jiuyun sun Huanhe Dong Yong Fang College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

With the advent of physics informed neural networks(PINNs),deep learning has gained interest for solving nonlinear partial differential equations(PDEs)in recent *** this paper,physics informed memory networks(PIMNs)are proposed as a new approach to solving PDEs by using physical laws and dynamic behavior of *** the fully connected structure of the PINNs,the PIMNs construct the long-term dependence of the dynamics behavior with the help of the long short-term memory ***,the PDEs residuals are approximated using difference schemes in the form of convolution filter,which avoids information loss at the neighborhood of the sampling ***,the performance of the PIMNs is assessed by solving the Kd V equation and the nonlinear Schr?dinger equation,and the effects of difference schemes,boundary conditions,network structure and mesh size on the solutions are *** show that the PIMNs are insensitive to boundary conditions and have excellent solution accuracy even with only the initial conditions.

关键词： nonlinear partial differential equations physics informed memory networks physics informed neural networks numerical solution

Adversarial data splitting for domain generalization

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Science China(Information Sciences) 2024年第5期67卷 28-42页

作者： Xiang GU Jian sun Zongben XU School of Mathematics and Statistics Xi'an Jiaotong University

Domain generalization aims to learn a model that is generalizable to an unseen target domain,which is a fundamental and challenging task in machine learning for out-of-distribution generalization. This paper proposes a novel domain generalization approach that enforces the learned model to be able to generalize well over the train/val subset splitting of the training dataset. This idea is modeled herein as an adversarial data splitting framework, formulated as a min-max optimization problem inspired by the metalearning approach. The min-max optimization problem is solved by iteratively splitting the training dataset into the training and val subsets to maximize the domain shift measured by the objective function and updating the model parameters to enable the model to generalize well from the training subset to the val subset by minimizing the objective function. This adversarial training approach does not assume the known domain labels of the training data; instead, it automatically investigates the “hard” splitting of the train/val subsets to learn the generalizable model. Extensive experimental results using three benchmark datasets demonstrate the superiority of this approach. In addition, we derive a generalization error bound for the theoretical understanding of our proposed approach.

关键词： domain generalization adversarial learning data splitting meta-learning out of distribution

One-shot Face Reenactment with Dense Correspondence Estimation

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Machine Intelligence Research 2024年第5期21卷 941-953页

作者： Yunfan Liu Qi Li Zhenan sun School of Artificial Intelligence University of Chinese Academy of SciencesBeijing100049China Center for Research on Intelligent Perception and Computing Institute of AutomationChinese Academy of SciencesBeijing100190China

One-shot face reenactment is a challenging task due to the identity mismatch between source and driving *** existing methods fail to completely eliminate the interference of driving subjects’identity information,which may lead to face shape distortion and undermine the realism of reenactment *** solve this problem,in this paper,we propose using a 3D morphable model(3DMM)for explicit facial semantic decomposition and identity *** of using 3D coefficients alone for reenactment control,we take advantage of the generative ability of 3DMM to render textured face *** proxies contain abundant yet compact geometric and semantic information of human faces,which enables us to compute the face motion field between source and driving images by estimating the dense *** this way,we can approximate reenactment results by warping source images according to the motion field,and a generative adversarial network(GAN)is adopted to further improve the visual quality of warping *** experiments on various datasets demonstrate the advantages of the proposed method over existing state-of-the-art benchmarks in both identity preservation and reenactment fulfillment.

关键词： Generative adversarial networks face image manipulation face image synthesis face reenactment 3D morphable model

On the global smooth solutions of 3D incompressible Hall-MHD equations

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 319-327页

作者： YUE Gao-cheng sun Wen-da School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China

The present paper is devoted to the well-posedness issue for the 3D incompressible Hall-MHD system obtained from kinetic models. Our analysis strongly relies on the use of the Fourier analysis. We establish the global existence of smooth solutions for a class of large initial data, this result implies the initial velocity and magnetic field can be arbitrarily large.

关键词： 3D Hall-MHD well-posedness Fourier analysis

Application of system identification in a practical active noise control system

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Control Theory and Technology 2024年第2期22卷 282-291页

作者： Yu Yuan Zhaoyang sun Hongwei Zhang School of Mechanical Engineering Xihua UniversityChengdu610039SichuanChina School of Electrical Engineering Southwest Jiaotong UniversityChengdu611756SichuanChina School of Mechanical Engineering and Automation Harbin Institute of TechnologyShenzhen518055GuangdongChina

Noise pollution has become increasingly severe around the world due to fast urbanization. How to soundproof windows from outside noise is of significant interest for both academia and industry. This paper reports an experimental implementation of normalized minmax active noise control (ANC) algorithm on an open window system, where identifying the model of acoustic sound paths plays a central role. By doing this, traffic noise is attenuated by the ANC system, leading to a relatively quiet indoor environment, while the natural lighting and ventilation functions of a window are remained. Our experiments show that an average of 19 dB(A) noise reduction is achieved.

关键词： Active noise control Multi-input-multi-output system Normalized minimax algorithm System identification