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Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

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Applied Mathematics and Mechanics(English Edition) 2023年第7期44卷 1069-1084页

作者： Zhiping mao Xuhui MENG School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen 361005Fujian ProvinceChina Institute of Interdisciplinary Research for Mathematics and Applied Science School of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhan 430074China

We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this *** particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the *** first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual *** further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the *** procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large *** demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson *** has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual ***,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠ*** means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the ***,we also employ the similar adaptive sampling technique fo

关键词： physics-informed neural network(PINN) adaptive sampling high-dimension L-shape Poisson equation accuracy

Strongly Gorenstein graded modules

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Frontiers of Mathematics in China 2017年第1期12卷 157-176页

作者： Lixin mao Department of Mathematics and Physics Nanjing Institute of Technology Nanjing 211167China

Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded an... 详细信息

关键词： Strongly Gorenstein gr-projective module strongly Gorenstein gr-injective module strongly Gorenstein gr-flat module

COMPREHENSIVE STUDY OF COMBINING FLOW CONDITIONS AT PIPE JUNCTIONS

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Journal of Hydrodynamics 1996年第1期8卷 76-84页

作者： mao, Zeyu Tsinghau Univ Beijing China

Theoretical and experimental investigation for the behavior of pipe junction, either 45 or 90 degree, has been performed. The junction was formed by the meeting of three equal diameter pipe, which all had equal invert levels. The characteristics of each type of junctions were discussed. These equations were then incorporated into computer program and the numerical solution of St. Venant equations were obtained by using characteristic-difference method. The presented equations may also be used to determine the limiting capacity of a junction, if surcharge of the system was to be avoided. Excellent agreement was found to exist between the observed unsteady flow conditions at junction and those predicted using the derives relationships.

关键词： Channel flow Computer simulation Finite element method Flow interactions Fluid structure interaction Numerical analysis Unsteady flow

Generalizations of von Neumann regular rings, PP rings, and Baer rings

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Frontiers of Mathematics in China 2016年第2期11卷 377-400页

作者： Lixin mao Department of Mathematics and Physics Nanjing Institute of Technology Nanjing 211167China

We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer modules.

关键词： IDS Module IP module Baer* module von Neumann regularring PP ring Baer ring

Towards Connecting Discrete Mathematics and Software Engineering

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Tsinghua Science and Technology 2020年第3期25卷 325-335页

作者： Tun Li Wanwei Liu Juan Chen Xiaoguang mao Xinjun mao the School of Computer National University of Defense Technology and are also with Laboratory of Software Engineering for Complex Systems

To enhance training in software development,we argue that students of software engineering should be exposed to software development activities early in the *** entails meeting the challenge of engaging students in software development before they take the software engineering *** this paper,we propose a method to connect courses in the software engineering curriculum by setting comprehensive development projects to students in prerequisite courses for software *** the Discrete Mathematics(DM)course as an example,we describe the implementation of the proposed method and teaching practices using several practical and comprehensive projects derived from topics in discrete *** descriptions of the sample projects,their application,and training results are *** and lessons learned from applying these practices show that it is a promising way to connect courses in the software engineering curriculum.

关键词： Discrete Mathematics(DM) software engineering proof checker database management system symbolic execution engine

Preparation and characterization of nano-rare earth composite materials:application in selectivity catalytic oxidation of ammonia and its cytotoxicity study

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Journal of Rare Earths 2010年第S1期28卷 362-366页

作者： Chang-mao Hung Department of Vehicle Engineering Yung-Ta Institute of Technology and Commerce316 Chung-Shan RoadLinloPingtung 909Taiwan

The manufacture,physical characterization,environmental applications and cytotoxicity properties of nanocomposites consisting of CuO/CeO2 nano-rare earth composite materials prepared using the coprecipitation method at molar ratio of 6:4 with aqueous solutions of copper nitrate and cerium nitrate were *** performance of the selective catalytic oxidation of ammonia to N2(NH3-SCO) over a CuO/CeO2 nano-rare earth composite materials in a tubular fixed-bed reactor(TFBR) at temperatures from 423 to 673 K in the presence of oxygen was *** catalytic redox behavior was determined by cyclic voltammetry(CV).The nanocomposite particles were characterized by TEM,with a tiny particle size around 10 nm with high dispersion ***,cell cytotoxicity and the percentage cell survival were determined by using 3-(4,5-dimethylthiazol-2-yl)-5(3-carboxymethoxyphenol)-2-(4-sulfophenyl)-2H-tetra-zolium(MTS) assay on human lung MRC-5 cell *** results showed that no apparent cytotoxicity was observed when the MRC-5 was exposed to the CuO/CeO2 nanocomposite materials.

关键词： selective catalytic oxidation (SCO) tubular fixed-bed reactor (TFBR) ammonia CuO/CeO2 nanocomposite material cytotoxicity rare earths

Injective Cogenerators,Cotilting Modules and Cosilting Modules

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Acta Mathematica Sinica,English Series 2023年第9期39卷 1684-1700页

作者： Li Xin mao School of Mathematics and Physics Nanjing Institute of TechnologyNanjing211167P.R.China

It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting *** this paper,we further investigate the close connections among injective cogenerators,cotilting modules and cosilting modules from the viewpoint of morphism *** applications are also given.

关键词： Injective cogenerator cotilting module cosilting module morphism category

专利批量维权中恶意诉讼的认定标准与规制路径

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科技与法律（中英文） 2025年第1期 1-13页

作者：毛昊梁珂馨同济大学上海国际知识产权学院上海200082

目前,我国专利领域批量维权现象较为突出,“流水线”式的维权活动具有涉案专利权利基础相同、案情类似,对小规模终端销售主体批量公证取证后起诉等规律性特征。专利批量诉讼是权利人维护知识产权的合理手段,具备正当性,但批量维权行为... 详细信息

目前,我国专利领域批量维权现象较为突出,“流水线”式的维权活动具有涉案专利权利基础相同、案情类似,对小规模终端销售主体批量公证取证后起诉等规律性特征。专利批量诉讼是权利人维护知识产权的合理手段,具备正当性,但批量维权行为可能因以谋利为目的、使用权利基础不稳定的专利等因素而存在恶意诉讼的隐忧。国内部分法院在处理涉及专利批量维权的恶意诉讼案件时,普遍存在着认定标准不统一、规制手段单一等突出问题。结合美国和欧洲对NPE(非专利实施主体)和PAE(专利主张实体)恶意诉讼的认定及规制的域外经验,我国应从主观和客观两方面完善专利批量维权中恶意诉讼的认定标准,利用大数据、人工智能等技术甄别手段,完善批量维权审查修正机制与完善诉讼程序,综合运用法律、行政、经济、技术等多重规制措施实施综合治理,破解批量维权中的恶意诉讼难题。

关键词：专利批量维权恶意诉讼认定标准规制路径

Nucleation and Growth Processes During Molecular-Beam Epitaxy of Ternary Compounds

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Chinese Physics Letters 1996年第11期13卷 855-858页

作者： mao Hui-bing Department of Materials Science Fudan UniversityShanghai 200433

In this letter the effect of the different migration rates of two kinds of cations on the nucleation and growth processes during molecular-beam epitaxy of ternary systems was studied in detail by Monte Carlo *** AlGaAs ternary system,in which the migration rate of cation Ga is larger than that of Al,there are three types of nucleation:Ga-Ga,Al-Ga and Al-Al,which show different characteristics in the growth processes.

关键词： ternary simulation Ternary