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SEMI-IMPLICIT SPECTRAL DEFERRED CORRECTION METHODS BASED ON SECOND-ORDER TIME INTEGRATION SCHEMES FOR NONLINEAR PDES

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Journal of Computational Mathematics 2024年第1期42卷 111-133页

作者： Ruihan Guo Yan xu School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026China

In[20],a semi-implicit spectral deferred correction(SDC)method was proposed,which is efficient for highly nonlinear partial differential equations(PDEs).The semi-implicit SDC method in[20]is based on first-order time integration methods,which are corrected iteratively,with the order of accuracy increased by one for each additional iteration.In this paper,we will develop a class of semi-implicit SDC methods,which are based on second-order time integration methods and the order of accuracy are increased by two for each additional iteration.For spatial discretization,we employ the local discontinuous Galerkin(LDG)method to arrive at fully-discrete schemes,which are high-order accurate in both space and time.Numerical experiments are presented to demonstrate the accuracy,efficiency and robustness of the proposed semi-implicit SDC methods for solving complex nonlinear PDEs.

关键词： Spectral deferred correction method Nonlinear PDEs Local discontinuous Galerkin method Second-order scheme

MODIFIED STOCHASTIC EXTRAGRADIENT METHODS FOR STOCHASTIC VARIATIONAL INEQUALITY

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Journal of Computational Mathematics 2024年第2期42卷 390-414页

作者： Ling Zhang Lingling xu School of Management and Economic Beijing Institute of TechnologyBeijing 100081China School of Mathematical Sciences Nanjing Normal UniversityNanjing 210023China School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS Nanjing Normal UniversityNanjing 210023China

In this paper,we consider two kinds of extragradient methods to solve the pseudo-monotone stochastic variational inequality problem.First,we present the modified stochastic extragradient method with constant step-size(MSEGMC)and prove the convergence of it.With the strong pseudo-monotone operator and the exponentially growing sample sequences,we establish the R-linear convergence rate in terms of the mean natural residual and the oracle complexity O(1/ǫ).Second,we propose a modified stochastic extragradient method with adaptive step-size(MSEGMA).In addition,the step-size of MSEGMA does not depend on the Lipschitz constant and without any line-search procedure.Finally,we use some numerical experiments to verify the effectiveness of the two algorithms.

关键词： Stochastic variational inequality Pseudo-monotone Modified stochastic ex-tragradient methods Adaptive step-size

Periodic Variation Studies of the Two Short Period W UMa-type Eclipsing Binaries: LX Lyn and V0853 Aur

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Research in Astronomy and Astrophysics 2024年第1期24卷 273-284页

作者： xu Zhang Bin Zhang School of Physics and Electronic Science Guizhou Normal UniversityGuiyang 550001China Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing Guizhou Normal UniversityGuiyang 550025China

In this paper,new light curves(LCs) of contact eclipsing binary(CEB) systems LX Lyn and V0853 Aur are presented and analyzed by using the 2015 version of the Wilson-Devinney(W-D) code.In order to explain their asymmetric LCs,cool starspots on the components were employed.It is suggested that their fill-out degrees are f=12.0%(LX Lyn) and f=26.3%(V0853 Aur).At the same time,we found that LX Lyn is a W-type eclipsing binary(EB) with an orbital inclination of i=84°.88 and a mass ratio of q=2.31.V0853 Aur is also a W-type CEB with a mass ratio of q=2.77 and an orbital inclination of i= 79°.26.Based on all available times of light minimum,their orbital period changes are studied by using the O-C method.The O-C diagram of LX Lyn reveals a cyclic oscillation with a period of about 14.84 yr and an amplitude of 0.0019 days,which can be explained by the light-travel time effect(LTTE) due to the presence of a third body with a minimum mass of0.06M_⊙.For V0853 Aur,it is discovered that the O-C diagram of the system also shows a cyclic oscillation with a period of 9.64 yr and an amplitude of 0.03365 days.The cyclic oscillation of V0853 Aur can be attributed to the LTTE by means of a third body with a mass no less than 3.77M_⊙.The third body may play an important role in the formation and evolution of these systems.

关键词： stars:activity (stars:)binaries(including multiple):close (stars:)binaries:eclipsing (stars:)brown dwarfs stars:evolution stars:formation

Bio-inspired inorganic-protein coating on Mg-based biomaterials for bioengineering applications

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Science China Materials 2024年第5期67卷 1678-1680页

作者： xuwen Peng Haolan xu Department of Chemistry Engineering Tsinghua UniversityBeijing100084China Department of Chemical and Materials Engineering University of AlbertaEdmontonAlbertaT6G 1H9Canada Future Industries Institute UniSA STEMUniversity of South AustraliaMawson Lakes CampusAdelaideSouth Australia5095Australia

Developing smart and advanced functional materials inspired by the unparalleled complexity and efficiency of biological tissues has received much attention across various fields.Magnesium alloys,particularly pure magnesium,have emerged as notable candidates in orthopedics and dentistry due to their exceptional biocompatibility,degradability,and ability to promote bone regeneration[1].However,the highly reactive chemical nature of magnesium and its rapid degradation upon exposure to water.

关键词： coating alloys magnesium

Experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering boundary effect

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Journal of Rock Mechanics and Geotechnical Engineering 2024年第3期16卷 1072-1084页

作者： xuwei Wang Yeshuang xu State Key Laboratory of Ocean Engineering School of Naval ArchitectureOceanand Civil EngineeringShanghai Jiao Tong UniversityShanghai200240China Shanghai Key Laboratory for Digital Maintenance of Buildings and Infrastructure Department of Civil EngineeringShanghai Jiao Tong UniversityShanghai200240China

The boundary condition is a crucial factor affecting the permeability variation due to suffusion.An experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering the boundary effect is conducted,where the hydraulic head difference(DH)varies,and the boundary includes non-loss and soil-loss conditions.Soil samples are filled into seven soil storerooms connected in turn.After evaluation,the variation in content of fine sand(ΔR_(f))and the hydraulic conductivity of soils in each storeroom(C_(i))are analyzed.In the non-loss test,the soil sample filling area is divided into runoff,transited,and accumulated areas according to the negative or positive ΔR_(f) values.ΔR_(f) increases from negative to positive along the seepage path,and Ci decreases from runoff area to transited area and then rebounds in accumulated area.In the soil-loss test,all soil sample filling areas belong to the runoff area,where the gentle-loss,strengthened-loss,and alleviated-loss parts are further divided.ΔR_(f) decreases from the gentle-loss part to the strengthened-loss part and then rebounds in the alleviated-loss part,and C_(i) increases and then decreases along the seepage path.The relationship between ΔR_(f) and Ci is different with the boundary condition.Ci exponentially decreases with ΔR_(f) in the non-loss test and increases with ΔR_(f) generally in the soil-loss test.

关键词： Suffusion Permeability Experimental investigation Boundary effect Horizontal seepage

STRONG CONVERGENCE OF JUMP-ADAPTED IMPLICIT MILSTEIN METHOD FOR A CLASS OF NONLINEAR JUMP-DIFFUSION PROBLEMS

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Journal of Computational Mathematics 2024年第1期42卷 248-270页

作者： xu Yang Weidong Zhao School of Mathematics China University of Mining and TechnologyXuzhou 221116China School of Mathematics Shandong UniversityJinan 250100China

In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario simulation.However,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz setting.We provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully recovered.Numerical experiments are carried out to verify the theoretical findings.

关键词： Jump-diffusion Jump-adapted implicit Milstein method Poisson jumps Strong convergence rate Non-Lipschitz coefficients

Tumor-associated telocytes

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Chinese Medical Journal 2024年第4期137卷 490-492页

作者： Jinqing Zhang Ying xu Department of General Surgery Shandong Provincial Third HospitalShandong UniversityJinanShandong 250117China

To the Editor:It has been eighteen years since telocytes(TCs)were first categorized by Popescu et al^([1])in 2005.TCs were classified into interstitial cells of the Cajal(ICC)type based on their ultrastructure and immunohistochemical features,which are similar to mesenchymal cells.^([2])In the following ten years,TCs were found to have their own distinctive characteristics in terms of three-dimensional structure,immunological biomarkers,genomics,and multiple functions.Interestingly,TCs are definitely distinct from fibroblasts,mesenchymal stem cells,and endothelial cells in multiple organs of human beings and animals.^([3])

关键词： cytes organs definitely

Tracked robot with underactuated tension-driven RRP transformable mechanism:ideas and design

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Frontiers of Mechanical Engineering 2024年第1期19卷 85-104页

作者： Ran xu Chao LIU School of Mechanical Electronic and Control EngineeringBeijing Jiaotong UniversityBeijing 100044China Key Laboratory of Vehicle Advanced Manufacturing Measuring and Control Technology(Ministry of Education)Beijing Jiaotong UniversityBeijing 100044China

Robots with transformable tracked mechanisms are widely used in complex terrains because of their high adaptability,and many studies on novel locomotion mechanisms have been conducted to make them able to climb higher obstacles.Developing underactuated transformable mechanisms for tracked robots could decrease the number of actuators used while maintaining the flexibility and obstacle-crossing capability of these robots,and increasing their cost performance.Therefore,the underactuated tracked robots have appreciable research potential.In this paper,a novel tracked robot with a newly proposed underactuated revolute‒revolute‒prismatic(RRP)transformable mechanism,which is inspired by the sit-up actions of humans,was developed.The newly proposed tracked robot has only two actuators installed on the track pulleys for moving and does not need extra actuators for transformations.Instead,it could concentrate the track belt’s tension toward one side,and the unbalanced tension would drive the linkage mechanisms to change its configuration.Through this method,the proposed underactuated design could change its external shape to create support points with the terrain and move its center of mass actively at the same time while climbing obstacles or crossing other kinds of terrains,thus greatly improving the climbing capability of the robot.The geometry and kinematic relationships of the robot and the crossing strategies for three kinds of typical obstacles are discussed.On the basis of such crossing motions,the parameters of links in the robot are designed to make sure the robot has sufficient stability while climbing obstacles.Terrain-crossing dynamic simulations were run and analyzed to prove the feasibility of the robot.A prototype was built and tested.Experiments show that the proposed robot could climb platforms with heights up to 33.3%of the robot’s length or cross gaps with widths up to 43.5%of the robot’s length.

关键词： mechanical design tracked robot underactuated mechanisms RRP mechanism obstacle crossing strategy

Vasculopathy in dermatomyositis

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Chinese Medical Journal 2024年第2期137卷 247-249页

作者： Hui xu Jie Qian Department of Rheumatology Affiliated Hospital of Nantong UniversityNantongJiangsu 226001China

To the Editor:Dermatomyositis(DM)is a rare autoimmune disease characterized by specific cutaneous manifestations and proximal muscle weakness,in which abnormalities of nailfold capillary(NFC)and serum levels of vascular biomarkers are common.Dynamic changes in vascular lesions play an important role in the occurrence and development of DM and reflect the disease activity and treatment efficacy.Due to the diversity of clinical manifestations in DM patients,vascular involvement is often under-evaluated,causing the treatment of refractory vascular damage challenging.This review aims to explore the mechanisms,clinical manifestations,and treatment options of vasculopathy in DM to achieve early recognition and improve prognosis.

关键词： involvement clinical myositis