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A Geometric Based Connection between Fractional Calculus and Fractal Functions

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Acta Mathematica Sinica,English Series 2024年第2期40卷 537-567页

作者： Yong Shun liang Wei yi SU School of Mathematics and Statistic Nanjing University of Science and TechnologyNanjing 210094P.R.China Department of Mathematics Nanjing UniversityNanjing 210023P.R.China

Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus theory.In the present paper,we investigate the relationship between fractional calculus and fractal functions,based only on fractal dimension considerations.Fractal dimension of the Riemann-Liouville fractional integral of continuous functions seems no more than fractal dimension of functions themselves.Meanwhile fractal dimension of the Riemann-Liouville fractional differential of continuous functions seems no less than fractal dimension of functions themselves when they exist.After further discussion,fractal dimension of the Riemann-Liouville fractional integral is at least linearly decreasing and fractal dimension of the Riemann-Liouville fractional differential is at most linearly increasing for the Holder continuous functions.Investigation about other fractional calculus,such as the Weyl-Marchaud fractional derivative and the Weyl fractional integral has also been given elementary.This work is helpful to reveal the mechanism of fractional calculus on continuous functions.At the same time,it provides some theoretical basis for the rationality of the definition of fractional calculus.This is also helpful to reveal and explain the internal relationship between fractional calculus and fractals from the perspective of geometry.

关键词： Fractional calculus fractal functions fractal dimension fractional calculus equation relationship

Mechanical Performance of Bio-inspired Bidirectional Corrugated Sandwich Pressure Shell Under External Hydrostatic Pressure

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China Ocean Engineering 2024年第2期38卷 297-312页

作者： ZHANG yi CHEN Yue YUN Lai liang Xu Ocean College Zhejiang UniversityZhoushan 316000China Hainan Institute Zhejiang UniversitySanya 572000China

This paper aims to enhance the compression capacity of underwater cylindrical shells by adopting the corrugated sandwich structure of cuttlebone.The cuttlebone suffers uniaxial external compression,while underwater cylindrical shells are in a biaxial compressive stress state.To suit the biaxial compressive stress state,a novel bidirectional corrugated sandwich structure is proposed to improve the bearing capacity of cylindrical shells.The static and buckling analysis for the sandwich shell and the unstiffened cylindrical shell with the same volume-weight ratio are studied by numerical simulation.It is indicated that the proposed sandwich shell can effectively reduce the ratio between circumferential and axial stress from 2 to 1.25 and improve the critical buckling load by about 1.63 times.Numerical simulation shows that optimizing and adjusting the structural parameters could significantly improve the advantage of the sandwich shell.Then,the hydrostatic pressure tests for shell models fabricated by 3D printing are carried out.According to the experimental results,the overall failure position of the sandwich shell is at the center part of the sandwich shell.It has been found the average critical load of the proposed sandwich shell models exceeds two times that of the unstiffened shell models.Hence,the proposed bio-inspired bidirectional corrugated sandwich structure can significantly enhance the pressure resistance capability of cylindrical shells.

关键词： bio-inspiration bidirectional corrugation sandwich shell external pressure buckling

Rainbow Pancyclicity in a Collection of Graphs Under the Dirac-type Condition

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 269-274页

作者： Lu-yi LI Ping LI Xue-liang LI Center for Combinatorics and LPMC Nankai UniversityTianjin 300071China School of Mathematics and Statistics Shaanxi Normal UniversityXi’an 710062China

Let G={Gi:i∈[n]} be a collection of not necessarily distinct n-vertex graphs with the same vertex set V,where G can be seen as an edge-colored(multi)graph and each Gi is the set of edges with color i.A graph F on V is called rainbow if any two edges of F come from different Gis’.We say that G is rainbow pancyclic if there is a rainbow cycle Cℓof lengthℓin G for each integerℓ2[3,n].In 2020,Joos and Kim proved a rainbow version of Dirac’s theorem:Ifδ(Gi)≥2/n for each i∈[n],then there is a rainbow Hamiltonian cycle in G.In this paper,under the same condition,we show that G is rainbow pancyclic except that n is even and G consists of n copies of Kn/2,n/2.This result supports the famous meta-conjecture posed by Bondy.

关键词： rainbow Hamiltonian cycle rainbow pancyclic meta-conjecture

A visual modeling method for spatiotemporal and multidimensional features in epidemiological analysis:Applied COVID-19 aggregated datasets

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Computational Visual Media 2024年第1期10卷 161-186页

作者： Yu Dong Christy Jie liang yi Chen Jie Hua School of Computer Science University of Technology SydneySydneyNSW2007Australia Beijing Key Laboratory of Big Data Technology for Food Safety Beijing Technology and Business UniversityBeijing100048China

The visual modeling method enables flexible interactions with rich graphical depictions of data and supports the exploration of the complexities of epidemiological analysis.However,most epidemiology visualizations do not support the combined analysis of objective factors that might influence the transmission situation,resulting in a lack of quantitative and qualitative evidence.To address this issue,we developed a portrait-based visual modeling method called+msRNAer.This method considers the spatiotemporal features of virus transmission patterns and multidimensional features of objective risk factors in communities,enabling portrait-based exploration and comparison in epidemiological analysis.We applied+msRNAer to aggregate COVID-19-related datasets in New South Wales,Australia,combining COVID-19 case number trends,geo-information,intervention events,and expert-supervised risk factors extracted from local government area-based censuses.We perfected the+msRNAer workflow with collaborative views and evaluated its feasibility,effectiveness,and usefulness through one user study and three subject-driven case studies.Positive feedback from experts indicates that+msRNAer provides a general understanding for analyzing comprehension that not only compares relationships between cases in time-varying and risk factors through portraits but also supports navigation in fundamental geographical,timeline,and other factor comparisons.By adopting interactions,experts discovered functional and practical implications for potential patterns of long-standing community factors regarding the vulnerability faced by the pandemic.Experts confirmed that+msRNAer is expected to deliver visual modeling benefits with spatiotemporal and multidimensional features in other epidemiological analysis scenarios.

关键词： visual modeling epidemiological analysis spatiotemporal multidimensional COVID-19

Rapid Unconscious Acquisition of Conditioned Fear with Low-Spatial-Frequency but Emotionally Neutral Stimuli

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Research 2024年第1期2023卷 753-762页

作者： Yujie Chen Si Chen Zhongju Sun Xilei Zhang Xiangyong Yuan liang Wang yi Jiang State Key Laboratory of Brain and Cognitive Sciences CAS Center for Excellence in Brain Science and Intelligence TechnologyInstitute of PsychologyChinese Academy of SciencesBeijing 100101China Department of Psychology University of Chinese Academy of SciencesBeijing 100049China Chinese Institute for Brain Research Beijing 102206China CAS Key Laboratory of Mental Health Institute of PsychologyChinese Academy of SciencesBeijing 100101China

It has long been proposed that emotionally“prepared”(i.e.,fear-related)stimuli are privileged in the unconscious acquisition of conditioned fear.However,as fear processing is suggested to highly depend on the coarse,low-spatial-frequency(LSF)components of the fear-related stimuli,it is plausible that LSF may play a unique role in the unconscious fear conditioning even with emotionally neutral stimuli.Here,we provided empirical evidence that,following classical fear conditioning,an invisible,emotionally neutral conditioned stimulus(CS+)with LSF,but not with high spatial frequency(HSF),can rapidly elicit stronger skin conductance responses(SCRs)and larger pupil diameters than its CS−counterpart.In comparison,consciously perceived emotionally neutral CS+with LSF and HSF elicited comparable SCRs.Taken together,these results support that the unconscious fear conditioning does not necessarily entail emotionally prepared stimuli but prioritizes LSF information processing and highlight the crucial distinctions between the unconscious and the conscious fear learning.These findings not only coincide with the postulation that a rapid,spatial-frequency-dependent subcortical route is engaged in unconscious fear processing but also suggest the existence of multiple routes for conscious fear processing.

关键词： neutral necessarily diameters

Deformation of Rigid Conjugate Self-dual Galois Representations

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1599-1644页

作者： yi Feng LIU yi Chao TIAN liang XIAO Wei ZHANG Xin Wen ZHU Institute for Advanced Study in Mathematics Zhejiang University Morningside Center of Mathematics AMSS Chinese Academy of Sciences New Cornerstone Lab Beijing International Center for Mathematical Research Peking University Department of Mathematics Massachusetts Institute of Technology Department of Mathematics Stanford University

In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation.

关键词： Galois deformation rigid conjugate self-dual Galois representations 11F80 11F03

Role of temperature in tribolayers in fretting wear ofγ-TiAl alloy

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Friction 2024年第5期12卷 939-953页

作者： Yulei YANG Hongfei SHANG Huiping PEI Jimin XU yi liang Minghui PAN School of Mechanical Engineering Nanjing University of Science and TechnologyNanjing210094China State Key Laboratory of Tribology in Advanced Equipment Tsinghua UniversityBeijing100084China Institute of Tribology Hefei University of TechnologyHefei230009China

The formation of tribolayers may play significant influences on fretting wear.At elevated temperature,the adhesion among wear debris and the increased diffusion rate facilitate the formation of tribolayers.However,the intensification of oxidation at elevated temperature and the low diffusion rate in oxides may play an adverse role.The present study aims to investigate the role of temperature in tribolayers in fretting wear using aγ-TiAl alloy.Scanning electron microscope,energy dispersive spectrometer,Raman spectrometer,transmission electron microscope and nanoindentation were utilized to investigate the wear debris,tribolayers,and wear scars.The fretting tests showed that,compared with that at room temperature(RT)and 350℃,significant reduction in wear rate and decrease in the fluctuation of friction coefficient occurred at 550 and 750℃.It was further revealed that when temperature raised from room temperature(RT)to 750℃,the oxidation of the wear debris increased slightly and the diffusion coefficients increased prominently,which facilities the formation of well tribo-sintered tribolayers.The well tribo-sintered tribolayers presented homogenous structure,nanocrystalline grains with excellent mechanical properties,and resulted in the improvement in the fretting wear resistance of theγ-TiAl alloy at 550 and 750℃.

关键词： tribolayer temperature fretting wear γ-TiAl alloy

Effects of NLRP3 Inflammasome Mediated Pyroptosis on Cardiovascular Diseases and Intervention Mechanism of Chinese Medicine

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Chinese Journal of Integrative Medicine 2024年第5期30卷 468-479页

作者： ZHONG yi LI Xin-yue liang Tian-jun DING Bao-zhu MA Ke-xin REN Wen-xuan liang Wen-jie College of Integrated Traditional Chinese and Western Medicine Hebei University of Chinese MedicineHebei Key Laboratory of Integrated Traditional Chinese and Western Medicine in Liver and Kidney DiseasesInstitute of Integrated Traditional Chinese and Western MedicineShijiazhuang 050200China Department of Cardiovascular Internal Medicine the Second Affiliated Hospital of Jiujiang UniversityJiujiangJiangxi Province 332000China Graduate School Hebei Medical UniversityShijiazhuang 050017China Rural Physician College Hebei Medical UniversityShijazhuang 050017China Medical Department the First Hospital of Hebei Medical UniversityShijiazhuang 050030China

Activation of the NOD-like receptor protein 3(NLRP3)inflammasome signaling pathway is an important mechanism underlying myocardial pyroptosis and plays an important role in inflammatory damage to myocardial tissue in patients with cardiovascular diseases(CVDs),such as diabetic cardiomyopathy,ischemia/reperfusion injury,myocardial infarction,heart failure and hypertension.Noncoding RNAs(nc RNAs)are important regulatory factors.Many Chinese medicine(CM)compounds,including their effective components,can regulate pyroptosis and exert myocardium-protecting effects.The mechanisms underlying this protection include inhibition of inflammasome protein expression,Toll-like receptor 4–NF-κB signal pathway activation,oxidative stress,endoplasmic reticulum stress(ERS),and mixed lineage kinase 3 expression and the regulation of silent information regulator 1.The NLRP3 protein is an important regulatory target for CVD prevention and treatment with CM.Exploring the effects of the interventions mediated by CM and the related mechanisms provides new ideas and perspectives for CVD prevention and treatment.

关键词： pyroptosis cardiovascular diseases Chinese medicine NOD-like receptor protein 3 mechanisms

Principal Model Analysis Based on Bagging PLS and PCA and Its Application in Financial Statement Fraud

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Journal of Systems Science and Information 2024年第2期12卷 212-228页

作者： Xiao liang Qiwei XIE Chunyan LUO liang TANG yi SUN School of Economics and Management Beijing University of TechnologyBeijing 100124China Shanghai Tongtu Semiconductor Technology Co. LtdShanghai 210203China School of Finance Anhui University of Finance&EconomicsBengbu 233000China

Motivated by the Bagging Partial Least Squares(Bagging PLS)and Principal Component Analysis(PCA)algorithms,a novel approach known as Principal Model Analysis(PMA)method is introduced in this paper.In the proposed PMA algorithm,the PCA and the Bagging PLS are combined.In this method,multiple PLS models are trained on sub-training sets,derived from the training set using the random sampling with replacement approach.The regression coefficients of all the sub-PLS models are fused in a joint regression coefficient matrix.The final projection direction is then estimated by performing the PCA on the joint regression coefficient matrix.Subsequently,the proposed PMA method is compared with other traditional dimension reduction methods,such as PLS,Bagging PLS,Linear discriminant analysis(LDA)and PLS-LDA.Experimental results on six public datasets demonstrate that our proposed method consistently outperforms other approaches in terms of classification performance and exhibits greater stability.Additionally,it is employed in the application of financial statement fraud identification.PMA and other five algorithms are utilized to financial statement fraud which concerned by the academic community,and the results indicate that the classification of PMA surpassed that of the other methods.

关键词： principal model analysis partial least squares principal component analysis dimension reduction ensemble learning financial statement fraud detection