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Deciphering and integrating invariants for neural operator learning with various physical mechanisms

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National Science Review 2024年第4期11卷 111-122页

作者： Rui Zhang Qi Meng zhi-ming Ma Academy of Mathematics and Systems Science Chinese Academy of Sciences(CAS) Microsoft Research

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation(PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose the physical invariant attention neural operator(PIANO) to decipher and integrate the physical invariants for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional layers.Compared to existing techniques, PIANO can reduce the relative error by 13.6%–82.2% on PDE forecasting tasks across varying coefficients, forces or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO.

关键词： neural operator PDE solver contrastive learning physical invariants

The symmetric space,strong isotropy irreducibility and equigeodesic properties

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Science China Mathematics 2024年第1期67卷 129-148页

作者： ming Xu Ju tan School of Mathematical Sciences Capital Normal UniversityBeijing 100048China School of Microelectronics and Data Science Anhui University of TechnologyMa'anshan 243032China

A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if for any x∈G/H and any nonzero y∈Tx(G/H),there exists a Riemannian equigeodesic c(t) with c(0)=x and ■(0)=y.These two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic spaces.We prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,respectively.Firstly,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible factors.Secondly,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU (3) or a symmetric space of compact type.These results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic properties.As an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are Berwald.It suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.

关键词： equigeodesic equigeodesic space flag manifold orbit type stratification symmetric space strongly isotropy irreducible space

Electrical characteristics of a fractional-order 3×n Fan network

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Communications in Theoretical Physics 2024年第4期76卷 176-187页

作者： zhi-Zhong tan Xin Wang Department of Physics Nantong UniversityNantong 226019China

In this article a new achievement of fractional-order 3×n Fan networks is presented.In the first step,the RT-I method is used to derive the general formulae of the equivalent impedance of fractional-order 3×n Fan networks.In the second part,the effects of five system parameters(L,C,n,α and β)on amplitude-frequency and phase-frequency characteristics are analyzed.At the same time,the amplitude-frequency and phase-frequency characteristics of the fractional order 3×n Fan network are revealed by Matlab drawing.This work has important theoretical and practical significance for resistor network models in the field of natural science and engineering technology.

关键词： fractional-order circuit amplitude-frequency characteristics phase-frequency characteristics RT-V theory

Changes in rheumatoid arthritis under ultrasound before and after sinomenine injection

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World Journal of Clinical Cases 2022年第1期10卷 35-42页

作者： Yi-Min Huang Yu Zhuang zhi-ming tan Department of Rheumatology and Immunology Huizhou Central People’s HospitalHuizhou 516001Guangdong ProvinceChina

BACKGROUND Rheumatoid arthritis(RA)is a prevalent clinical autoimmune disease that is commonly treated with diclofenac and methotrexate.In recent years,the application of traditional Chinese medicine in RA has received widespread attention;it promotes blood circulation,strengthens the immune system,and eliminates evil.The sinomenine preparation of zhingqeng Fengtongning is studied as a possible treatment for patients with RA.AIM To explore the value of sinomenine injection into the articular cavity for the treatment of RA.METHODS A total of 94 patients with RA treated from January 2019 to January 2021 were selected and divided into the study and control groups with 47 patients each using a simple random number table method.Both groups received conventional treatment with diclofenac sodium and methotrexate tablets.The control group received diproxone and lidocaine by intra-articular administration while the study group received an intra-articular administration of the sinomenine preparation of Zhengqing Fengning and lidocaine.χ^(2) test was used to evaluate the therapeutic effect and synovial thickness,degree of pain through the visual analog scale(VAS),blood flow grade,arthroinflammatory indexes[rheumatoid factor(RF),C-reactive protein(CRP),and erythrocyte sedimentation rate(ESR)]before and after treatment in the two groups.RESULTS The total effective rate of the study group(93.62%)was higher than that of the control group(78.72%)(P0.05).After treatment,the synovial thickness and VAS score were significantly lower(P<0.05)in the study group than in the control group(2.05±0.59 mm vs 2.87±0.64 mm and 2.11±0.62 vs 2.90±0.79 scores,respectively).The rate of blood flow at grade 0 in the study group(76.60%)was higher than that in the control group(57.45%),and the rate of blood flow at grade I(10.64%)was lower than that in the control group(31.91%)(P<0.05)

关键词： Rheumatoid arthritis Articular injection Sinomenine Ultrasonic changes Inflammatory factors Zhengqing Fengtongning

Strong invariance principle for a counterbalanced random walk

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 370-380页

作者： tan Hui-qun HU zhi-shui DONG Liang International Institute of Finance School of ManagementUniversity of Science and Technology of ChinaHefei 230026China Center for Basic Teaching and Experiment Nanjing University of Science and TechnologyJiangyin 214443China

We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).

关键词： random walk martingale invariance principle

Comparison of biliary protein spectrum in gallstone patients with obesity and those with normal body weight

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Hepatobiliary & Pancreatic Diseases International 2024年第4期23卷 385-392页

作者： Min-zhi Chen Ping Xie Xiao-Chang Wu Zhen-Hua tan Hai Qian zhi-Hong Ma Xing Yao Department of Hepatopancreatobiliary Surgery Huzhou Central HospitalAffiliated Huzhou HospitalZhejiang University School of MedicineHuzhou 313000China Huzhou Key Laboratory of Molecular Medicine Huzhou Central HospitalAffiliated Huzhou HospitalZhejiang University School of MedicineHuzhou 313000China

Background:Obesity is a common public health issue and is currently deemed a disease.Research has shown that the risk of gallstones in individuals with obesity is elevated.This study aimed to explore the bile proteomics differences between cholelithiasis patients with obesity and normal body weight.Methods:Bile samples from 20 patients(10 with obesity and 10 with normal body weight)who underwent laparoscopic cholecystectomy at our center were subjected to tandem mass tag labeling(TMT)and liquid chromatography-tandem mass spectrometry(LC-MS/MS),followed by further bioinformatic analysis.Results:Among the differentially expressed proteins,23 were upregulated and 67 were downregulated.Bioinformatic analysis indicated that these differentially expressed proteins were mainly involved in cell development,inflammatory responses,glycerolipid metabolic processes,and protein activation cascades.In addition,the activity of the peroxisome proliferator-activated receptor(PPAR,a subfamily of nuclear receptors)signaling pathway was decreased in the Kyoto Encyclopedia of Genes and Genomes(KEGG)enrichment analysis.Two downregulated proteins in the PPAR signaling pathway,APO A-I and APO A-II,were confirmed using enzyme-linked immunosorbent assay.Conclusions:The PPAR signaling pathway may play a crucial role in the development of cholelithiasis among patients with obesity.Furthermore,biliary proteomics profiling of gallstones patients with obesity is revealed,providing a reference for future research.

关键词： Proteome profiling Gallstones Obesity-associated gallstones tandem mass tag labeling PPAR signaling

Combustion mechanism of benzene in iron ore sintering process:experimental and simulation

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Journal of Iron and Steel Research(International) 2024年第1期31卷 195-203页

作者： zhi-gang Que Jin-ming Shi Xian-bin Ai Institute of Energy Research Jiangxi Academy of ScienceNanchang330096JiangxiChina Jiangxi Carbon Neutralization Research Center Nanchang330096JiangxiChina

Benzene is a typical component of volatile organic compounds(VOCs)in the iron ore sintering flue gas.The combustion behavior of benzene directly affects the emission of VOCs in iron ore sintering process.The effects of temperature,benzene,and oxygen concentrations on the conversion ratio of benzene were investigated by experiments and numerical simulation.The experiments were carried out in a tube reactor at temperatures of 773-1098 K,benzene concentrations of 0.01-0.03 vol.%,and oxygen concentrations of 10-21 vol.%.The numerical simulation was performed with the plug flow model in the CHEMKIN program based on a kinetic model that consists of 132 chemical species and 772 elementary step-like reactions.The experimental results reveal that increasing the temperature and benzene concentration could signifi-cantly promote benzene combustion.It is attributed to the increase in the reaction rates of all steps in the pathway for forming CO_(2)and H_(2)O.In addition,due to the large equivalent ratio of oxygen to benzene,the conversion ratio of benzene remained constant at different oxygen concentrations.The simulation results were in good agreement with the experimental results and indicated that six elementary reactions dominated the formations of CO_(2)and H_(2)O.The oxidations of C_(6)H_(5)O,CO,and C_(5)H_(4)O intermediates to CO_(2)were the limiting steps in the reaction pathways.

关键词： Benzene Volatile organic compound Iron ore sinter Combustion Simulation Temperature Oxygen

Classification of complete 3-dimensional self-shrinkers in the Euclidean space R^(4)

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Science China Mathematics 2024年第4期67卷 873-882页

作者： Qing-ming Cheng zhi Li Guoxin Wei Department of Applied Mathematics Faculty of ScienceFukuoka UniversityFukuoka 814-0180Japan College of Mathematics and Information Science Henan Normal UniversityXinxiang 453007China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

In this paper,we completely classify 3-dimensional complete self-shrinkers with the constant norm S of the second fundamental form and the constant f3in the Euclidean space R^(4),where hij’s are components of the sec... 详细信息

关键词： mean curvature ow self-shrinker the generalized maximum principle

Constructing highly safe and long-life calcium ion batteries based on hydratedvanadium oxide cathodes featuring a pillar structure

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Rare Metals 2024年第6期43卷 2597-2612页

作者： Chun-Fang Wang Shi-Wei Zhang Lan Huang Yuan-Min Zhu Feng Liu Jian-Chuan Wang Li-ming tan Chun-Yi zhi Cui-Ping Han Powder Metallurgy Research Institute Central South University Songshan Lake Materials Laboratory Research Institute of Interdisciplinary Science and School of Materials Science and Engineering Dongguan University of Technology Department of Materials Science and Engineering City University of Hong Kong Faculty of Materials Science and Energy Engineering/Institute of Technology for Carbon Neutrality Shenzhen Institute of Advanced TechnologyChinese Academy of Sciences

Calcium-ion batteries（CIBs） have generated intense interest due to the growing demand for safer,cheaper,and large-scale energy storage systems.However,their development is still in its infancy,owing to the lack of suitable cathodes for sustaining reversiblc Ca2+intercalation/deintercalation.Herein,layered H2V3O8（HVO） with Zn2+pre-insertion（ZHVO） is reported as a high-rate and highly durable cathode material for CIBs.The existence of Zn2+and H2O pillars could expand the interlayer spacing up to 1.8 nm,which is favorable for the diffusion of bulky Ca2+.The formation of Zn-O bonds facilitates electron transfer and enhances electrical conduction.Consequently,the ZHVO cathode achieves superior capacity performance(213.9 mAh·g-1at 0.2 A·g-1) and long lifespan(78.3% for 1,000 cycles at 5 A·g-1) compared to pristine HVO.Density functional theory（DFT） calculations revealed that Zn2+moved during Ca2+intercalation,thereby reducing the diffusion energy barrier and facilitating Ca2+diffusion.Finally,a safe aqueous calcium ion cell was successfully assembled.

关键词： Multivalent batteries Calcium-ion batteries Layered structure Vanadium oxide Cathode materials