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Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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Science China Mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes school of Mathematics Southwestern University of Finance and EconomicsChengdu611130China school of Mathematics Shandong UniversityJinan250100China Applied and Computational Mathematics Division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme

Machine learning model based on non-convex penalized huberized-SVM

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Journal of Electronic Science and Technology 2024年第1期22卷 81-94页

作者： Peng Wang Ji Guo Lin-Feng Li school of finance and Economics Xizang Minzu UniversityXianyang712082China Research Center for Quality Development of Xizang Special Industries Xianyang712082China school of Computer Science and Technology Xinjiang UniversityUrumqi830017China

The support vector machine(SVM)is a classical machine learning *** the hinge loss and least absolute shrinkage and selection operator(LASSO)penalty are usually used in traditional ***,the hinge loss is not differentiable,and the LASSO penalty does not have the Oracle *** this paper,the huberized loss is combined with non-convex penalties to obtain a model that has the advantages of both the computational simplicity and the Oracle property,contributing to higher accuracy than traditional *** is experimentally demonstrated that the two non-convex huberized-SVM methods,smoothly clipped absolute deviation huberized-SVM(SCAD-HSVM)and minimax concave penalty huberized-SVM(MCP-HSVM),outperform the traditional SVM method in terms of the prediction accuracy and classifier *** are also superior in terms of variable selection,especially when there is a high linear correlation between the *** they are applied to the prediction of listed companies,the variables that can affect and predict financial distress are accurately filtered *** all the indicators,the indicators per share have the greatest influence while those of solvency have the weakest *** companies can assess the financial situation with the indicators screened by our algorithm and make an early warning of their possible financial distress in advance with higher precision.

关键词： Huberized loss Machine learning Non-convex penalties Support vector machine(SVM)

Translating solitons in Rof linear Weingarten type

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Acta Mathematica Sinica,English Series 2024年

作者： Yu Fu Rafael López Yanru Luo Dan Yang school of Data Science and Artificial Intelligence.Dongbei University of finance and Economics Departamento de Geometría y Topología.Universidad de Granada school of Economics Dongbei University of Finance and Economics school of Mathematics.Liaoning University

In this paper,we consider λ-translating solitons in *** surfaces are critical points of the weighted area when the density is a coordinate *** λ=0,these surfaces evolve by translations along the mean curvature *** give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their *** surfaces are planes,circular cylinders,grim reapers and certain types of cylindrical *** also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.

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Enhanced Temporal Correlation for Universal Lesion Detection

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Computer Modeling in Engineering & Sciences 2024年第3期138卷 3051-3063页

作者： Muwei Jian Yue Jin Hui Yu school of Computer Science and Technology Shandong University of Finance and EconomicsJinanChina school of Information Science and Technology Linyi UniversityLinyiChina school of Creative Technologies University of PortsmouthPortsmouthUK

Universal lesion detection(ULD)methods for computed tomography(CT)images play a vital role in the modern clinical medicine and intelligent *** is well known that single 2D CT slices lack spatial-temporal characteristics and contextual information compared to 3D CT ***,3D CT blocks necessitate significantly higher hardware resources during the learning ***,efficiently exploiting temporal correlation and spatial-temporal features of 2D CT slices is crucial for ULD *** this paper,we propose a ULD network with the enhanced temporal correlation for this purpose,named *** designed TCE module is applied to enrich the discriminate feature representation of multiple sequential CT ***,we employ multi-scale feature maps to facilitate the localization and detection of lesions in various *** experiments are conducted on the DeepLesion benchmark demonstrate that thismethod achieves 66.84%and 78.18%for FS@0.5 and FS@1.0,respectively,outperforming compared state-of-the-art methods.

关键词： Universal lesion detection computational biology medical computing deep learning enhanced temporal correlation

Recent advances in g-C_(3)N_(4)-based direct Z-scheme photocatalysts for environmental and energy applications

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Chinese Journal of Structural Chemistry 2024年第2期43卷 66-84页

作者： Xiaoming Fu Haibo Huang Guogang Tang Jingmin Zhang Junyue Sheng Hua Tang school of Intelligent Engineering and Technology Jiangsu Vocational College of Finance&EconomicsHuai'anJiangsu223003PR China school of Modem Equipment Manufacturing Changzhou institute of Light Industry Technology ChangzhouJiangsu213164PR China school of Environmental Science and Engineering Qingdao UniversityQingdao266071PR China school of Materials Science and Engineering Hainan UniversityHaikou570228PR China

In the midst of the rapid advancement of photocatalysis,direct Z-scheme heterojunction photocatalysts have emerged as a powerful solution to address environmental challenges and the looming energy *** precise engineering of direct Z-scheme heterojunction photocatalysts proves highly beneficial in optimizing their elec-tronic structure,ultimately enhancing their photocatalytic ***,graphitic carbon nitride(g-C_(3)N_(4))has recently gained recognition as a leading candidate for the creation of direct Z-scheme heterojunctions,owing to its favorable attributes such as a moderate band-gap(2.7 eV),high reduction potential and abundant active *** this review,we offer a concise overview of the fundamental principles and recent advancements in g-C_(3)N_(4)-based direct Z-scheme photocatalytic ***,we delve into the various practical applica-tions of g-C_(3)N_(4)-based direct Z-scheme photocatalysts,specifically in the realms of energy conversion and envi-ronmental *** applications include the removal of contaminant pollutants through photocatalytic degradation,water splitting(comprising H_(2)-generation,O_(2)-evolution,and overall water splitting),and CO_(2)***,we present comprehensive characterization methods and strategies aimed at further enhancing the photocatalytic activity of g-C_(3)N_(4)-based direct Z-scheme photocatalytic *** conclude,this review offers summarizing insights and a brief discussion on future challenges and prospects pertaining to g-C_(3)N_(4)-based direct Z-scheme *** believe that this review will inspire continued exploration and foster a deeper understanding of the groundbreaking possibilities within photocatalytic *** also provides valuable guidance for the design and construction of innovative direct Z-scheme photocatalysts.

关键词： Carbon nitride Photocatalyst Z-scheme systems Environmental remediation Energy conversion

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

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Defence Technology（防务技术） 2024年第2期32卷 412-429页

作者： Wenxue Chen Yudong Hu Changsheng Gao Ruoming An school of Astronautics Harbin Institute of TechnologyHarbin 150001China

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost ***,the velocity control in such trajectory tracking guidance systems of missiles is *** our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking *** global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional ***,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid ***,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify *** obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

关键词： BP network neural Integral sliding mode control(ISMC) Missile defense Prescribed performance function(PPF) State observer Tracking guidance system

Three-Rigid-Body-Particle Modeling and Optimization of Trajectory and Posture for Alpine Skiing

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Journal of Systems Science & Complexity 2024年第2期37卷 581-608页

作者： ZHANG Yijia FEI Qing YAO Xiaolan SUN Jian ZHANG Yanjun CHEN Zhen school of Automation Beijing Institute of TechnologyBeijing 100081China

This paper presents a new study on modeling and optimization of trajectory and posture for the super-giant(SG)slalom of alpine *** is the first time that a Three-Rigid-Body-Particle model based on rigorous derivations and stability analysis is established to represent skiers trajectory and posture characteristics,as it is more accurate than the single-rigid-body model which is commonly used in existing *** addition,the Radau pseudospectral method is applied to solve the trajectory and posture optimization problem in order to obtain better skiing trajectory,skiing posture,and some key kinematic parameters of ***,this paper analyzes the effects of different body types,minimum turning radii,and flexor and extensor strength of knees and hip joint on skiing ***,based on the findings of the study,some advice about how to improve the performance of the SG slalom in view of science and technology is given to skiers and coaches for reference.

关键词： Alpine skiing modeling posture optimization Three-Rigid-Body-Particle model trajectory optimization

Isolation performances and optimization of triple quasi-zero stiffness isolators

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Science China(Physics,Mechanics & Astronomy) 2024年第7期67卷 124-141页

作者： Yuntian Zhang Guangnan Zhu Qingjie Cao school of Astronautics Harbin Institute of TechnologyHarbin 150001China

In this paper,triple quasi-zero stiffness(QZS)passive vibration isolators whose restoring force curve has a three-stage softening effect are ***-coupled SD oscillators with three independent geometrical parameters are used as negative stiffness mechanisms to achieve QZS characteristics at the origin and symmetrical positions on both sides of the *** performances of different triple QZS isolators are analyzed to show influences of the selection of QZS regions away from the origin on the range of isolation *** optimizations of system parameters are carried out to get a larger range of small restoring force regions and small stiffness *** performances of two triple QZS isolators are discussed to show the influence of different Pareto optimization solutions through the comparisons with single and double QZS *** showed that triple QZS isolators have both the advantages of single and double QZS isolators which results in better isolation performances under both small and large excitation *** improvement in isolation performances for triple QZS isolators is found with the decrease in average stiffness due to the appearance of two symmetrical QZS regions away from the *** displacements of QZS regions away from the origin result in better isolation performances when excitation amplitude is large,and triple QZS characteristics are similar to double QZS isolators at this *** restoring forces of QZS regions away from the origin lead to better isolation performances when excitation amplitude is small,and triple QZS characteristics are similar to single QZS isolators at this *** with the decrease in average stiffness,the improvement of isolation performances shows a hysteresis phenomenon due to the difference between static and dynamic characteristics.

关键词： triple quasi-zero stiffness vibration isolation Pareto optimization force transmissibility geometrical nonlinear

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Spatial Differentiation and Convergence Trend of High-quality Development Level of China’s Tourism Economy

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Chinese Geographical Science 2024年第2期34卷 230-249页

作者： CAO Shanshan HE Zhaoli NIU Jinlan WANG Songmao ZHAO Lei school of Geography and Ocean Science Nanjing UniversityNanjing 210046China school of Business Administration Nanjing University of Finance and EconomicsNanjing 210046China school of Economics and Management Shandong Agricultural Uni-versityTai’an 271018China school of Hotel Management Shanghai Business SchoolShanghai 201400China school of Man-agement Zhejiang University of TechnologyHangzhou 310014China

This paper aims to interpret the connotation of high-quality development of tourism economy(HQTE)from the perspective of the new development concepts of innovation,coordination,green,openness and sharing,and then to evaluate the spatial differenti-ation of China’s HQTE based on provincial panel data from 2009 to ***,we employ the spatial convergence model to ex-plore the absolute and conditionalβconvergence trends of HQTE in the whole country and the eastern,central and western regions of *** empirical results reveal that:1)within the decade,from 2009 to 2018,regions of China with the highest HQTE index is its eastern region followed by the central region and then the western region,but the fastest growing one is the western region of China fol-lowed by the central region and then the eastern region.2)Whether or not the spatial effect is included,there are absolute and condition-alβconvergence in HQTE in the whole country and aforementioned three regions.3)The degree of government attention as well as the level of economic development and location accessibility are the positive driving factors for the convergence of HQTE in the whole country and the three *** degree of marketization and human capital have not passed the significance test either in the whole country or in the three *** above conclusions could deepen the understanding of the regional imbalance and spatial conver-gence characteristics of HQTE,clarify the primary development objects,and accomplish the goal of China’s HQTE.

关键词： new development concepts high-quality development of tourism economy(HQTE) spatial convergence China