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UNCONDITIONAL ERROR ANALYSIS OF VEMS FOR A GENERALIZED NONLINEAR SCHRODINGER EQUATION

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Journal of Computational Mathematics 2024年第2期42卷 500-543页

作者： meng Li Jikun Zhao Shaochun Chen School of Mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China

In this work,we focus on the conforming and nonconforming leap-frog virtual element methods for the generalized nonlinear Schrodinger equation,and establish their unconditional stability and optimal error *** constructing a time-discrete system,the error between the solutions of the continuous model and the numerical scheme is separated into the temporal error and the spatial error,which makes the spatial error τ-*** inverse inequalities in the existing conforming and new constructed nonconforming virtual element spaces are utilized to derive the L^(∞)-norm uniform boundedness of numerical solutions without any restrictions on time-space step ratio,and then unconditionally optimal error estimates of the numerical schemes are obtained *** needs to be emphasized is that if we use the pre-existing nonconforming virtual elements,there is no way to derive the L^(∞)-norm uniform boundedness of the functions in the nonconforming virtual element spaces so as to be hard to get the corresponding inverse ***,several numerical examples are reported to confirm our theoretical results.

关键词： Conforming and nonconforming Virtual element methods Leap-frog scheme Generalized nonlinear Schrodinger system Unconditionally optimal error estimates

WEAK APPROXIMATIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL NOISE

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Journal of Computational Mathematics 2024年第3期42卷 735-754页

作者： meng Cai Siqing Gan Xiaojie Wang School of Mathematics and Statistics HNP-LAMACentral South UniversityChangshaChina

This paper aims to analyze the weak approximation error of a fully discrete scheme for a class of semi-linear parabolic stochastic partial differential equations(SPDEs)driven by additive fractional Brownian motions with the Hurst parameter H∈(1/2,1).The spatial approximation is performed by a spectral Galerkin method and the temporal discretization by an exponential Euler *** far as we know,the weak error analysis for approximations of fractional noise driven SPDEs is absent in the literature.A key difficulty in the analysis is caused by the lack of the associated Kolmogorov *** the present work,a novel and efficient approach is presented to carry out the weak error analysis for the approximations,which does not rely on the associated Kolmogorov equations but relies on the Malliavin *** the best of our knowledge,the rates of weak convergence,shown to be higher than the strong convergence rates,are revealed in the fractional noise driven SPDE setting for the first *** examples corroborate the claimed weak orders of convergence.

关键词： Parabolic SPDEs Fractional Brownian motion Weak convergence rates Spec-tral Galerkin method Exponential Euler method Malliavin calculus

Attractor for the Extensible Beam Equation with Nonlocal Weak Damping on Time–Dependent Space

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1115-1126页

作者： Chun Xiang ZHAO Feng Juan meng Institute of Applied System Analysis Jiangsu UniversityZhenjiang 212013P.R.China School of Mathematics and Physics Jiangsu University of TechnologyChangzhou 213001P.R.China

In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at *** the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed *** results obtained essentially improve and complete some previous works.

关键词： Time-dependent attractor extensible beams equation nonlocal weak damping

A Tri-mode of Mock-Walker Cells

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Advances in Atmospheric Sciences 2024年第4期41卷 671-679页

作者： Han QIN Ji NIE Zhiyong meng Laboratory for Climate and Ocean-Atmosphere Studies Department of Atmospheric and Oceanic SciencesSchool of PhysicsPeking UniversityBeijing 100871China China Meteorological Administration Tornado Key Laboratory Foshan 528061China

This work uses cloud-resolving simulations to study mock-Walker cells driven by a specified sea surface temperature(SST).The associated precipitation in the mock-Walker cells exhibits three different modes,including a single peak of precipitation over the SST maximum(mode 1),symmetric double peaks of precipitation straddling the SST maximum(mode 2),and a single peak of precipitation on one side of the SST maximum(mode 3..The three modes are caused by three distinct convective activity center migration *** indicate that the virtual effect of water vapor plays an important role in differentiating the three *** the SST gradient is large,the virtual effect may be strong enough to overcome the temperature effect,generating a low-level low-pressure anomaly below the ascending branch of the Walker cell off the *** results here highlight the importance of the virtual effect of water vapor and its interaction with convection and large-scale circulation in the Walker circulation.

关键词： Walker circulation cloud-resolving simulation virtual effect

In memoriam:Shizhu Wen(193.-2023.

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Friction 2024年第7期12卷 1341-1346页

作者： Jianbin LUO Yonggang meng Yu TIAN State Key Laboratory of Tribology in Advanced Equipment Tsinghua UniversityBeijing 100084China

Professor Shizhu Wen,the winner of the 2015 Tribology Gold Medal,passed away due to illness on November 3.2023.at the age of *** was a professor of Tsinghua University,an academician of the Chinese Academy of Sciences,and the Honorary President of the Chinese Tribology Institute(CTI)from 1997 to *** Wen was born in 193. in Jiangxi Province of China and graduated from Tsinghua University in 1955,where he was awarded the Outstanding Graduate Gold Medal and then remained as an assistant professor at the *** Wen was promoted to full professor in *** had undertaken tribology research at the Imperial College London in 1979 and *** 1985,he presided over the establishment of the State Key Laboratory of Tribology(SKLT)of Tsinghua University and served as the first director of the SKLT.

关键词： sided professor zhu

Cobalt-catalyzed reductive alkynylation to construct C(sp)-C(sp^(3.)and C(sp)-C(sp^(2))bonds

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Chinese Chemical Letters 2024年第7期35卷 253-258页

作者： Lei Wan Yizhou tong Xi Lu Yao Fu Hefei National Research Center for Physical Sciences at the Microscale iChEMCAS Key Laboratory of Urban Pollutant ConversionAnhui Province Key Laboratory of Biomass Clean EnergyUniversity of Science and Technology of ChinaHefei 230026China Key Laboratory of Precision and Intelligent Chemistry School of Chemistry and Materials ScienceUniversity of Science and Technology of ChinaHefei 230026China

Transition-metal-catalyzed cross-electrophile coupling has emerged as a reliable method for constructing carbon–carbon ***,we report a general method,cobalt-catalyzed reductive alkynylation,to construct C(sp)-C(sp^(3.)and C(sp)-C(sp^(2))*** presented reaction has a broad substrate scope,enabling the efficient cross-electrophile coupling between alkynyl bromides with alkyl halides and aryl or alkenyl(pseudo)*** presented reaction is conducted under mild conditions,tolerating many functional groups,thus suitable for the modification and synthesis of biologically active molecules.

关键词： Cobalt-catalysis Cross-electrophile coupling Carbon-carbon bond formation Reductive alkynylation Alkyne synthesis

Research on Risk Identification and Industrial Governance of Digital Education Products Based on Data Annotation Technology

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China Communications 2024年第3期21卷 273-282页

作者： tong Lili Zeng Jia Di Ying Wang Nan Faculty of Education Beijing Normal University Beijing 100875China China Unicom Beijing 102211China

The social transformation brought aboutby digital technology is deeply impacting various *** education products, with core technologiessuch as 5G, AI, IoT (Internet of Things),etc., are continuously penetrating areas such as teaching,management, and evaluation. Apps, miniprograms,and emerging large-scale models are providingexcellent knowledge performance and flexiblecross-media output. However, they also exposerisks such as content discrimination and algorithmcommercialization. This paper conducts anevidence-based analysis of digital education productrisks from four dimensions: “digital resourcesinformationdissemination-algorithm design-cognitiveassessment”. It breaks through corresponding identificationtechnologies and, relying on the diverse characteristicsof governance systems, explores governancestrategies for digital education products from the threedomains of “regulators-developers-users”.

关键词： digital education products industry governance risk identification

Corrugated Graphene Paper Reinforced Silicone Resin Composite for Efficient Interface Thermal Management

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Chinese Journal of Polymer Science 2024年第7期42卷 1002-1014,I0010页

作者： Bo-Wen Wang Heng Zhang Qing-Xia He Hui-Tao Yu meng-meng Qin Wei Feng Tianjin Key Laboratory of Composite and Functional Materials School of Materials Science and EngineeringTianjin UniversityTianjin300350China International Engineering Institute Tianjin UniversityTianjin300350China

With the rapid development of high-power-density electronic devices,interface thermal resistance has become a critical barrier for effective heat management in high-performance electronic ***,there is an urgent demand for advanced thermal interface materials(TIMs)with high cross-plane thermal conductivity and excellent compressibility to withstand increasingly complex operating *** achieve this aim,a promising strategy involves vertically arranging highly thermoconductive graphene on ***,with the currently available methods,achieving a balance between low interfacial thermal resistance,bidirectional high thermal conductivity,and large-scale production is ***,we prepared a graphene framework with continuous filler structures in in-plane and cross-plane directions by bonding corrugated graphene to planar graphene *** interface interaction between the graphene paper framework and polymer matrix was enhanced via surface functionalization to reduce the interface thermal *** resulting three-dimensional thermal framework endows the polymer composite material with a cross-plane thermal conductivity of 14.4 W·m^(-1)·K^(-1)and in-plane thermal conductivity of 13.W·m^(-1)·K^(-1)when the thermal filler loading is 10.1 wt%,with a thermal conductivity enhancement per 1 wt%filler loading of 83.%,outperforming various graphene structures as *** its high thermal conductivity,low contact thermal resistance,and low compressive modulus,the developed highly thermoconductive composite material demonstrates superior performance in TIM testing compared with TFLEX-700,an advanced commercial TIM,effectively solving the interfacial heat transfer issues in electronic *** novel filler structure framework also provides a solution for achieving a balance between efficient thermal management and ease of processing.

关键词： Graphene paper Vertically aligned structure Cross-plane thermal conductivity Low compressive modulus Thermal interface material

LEGENDRE-GAUSS-RADAU SPECTRAL COLLOCATION METHOD FOR NONLINEAR SECOND-ORDER INITIAL VALUE PROBLEMS WITH APPLICATIONS TO WAVE EQUATIONS

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Journal of Computational Mathematics 2024年第1期42卷 217-247页

作者： Lina Wang Qian tong Lijun Yi Mingzhu Zhang Department of Mathematics Shanghai Normal UniversityShanghai 200234China School of Science Henan University of EngineeringZhengzhou 451191China

We propose and analyze a single-interval Legendre-Gauss-Radau(LGR)spectral collocation method for nonlinear second-order initial value problems of ordinary differential *** design an efficient iterative algorithm and prove spectral convergence for the single-interval LGR collocation *** more effective implementation,we propose a multi-interval LGR spectral collocation scheme,which provides us great flexibility with respect to the local time steps and local approximation ***,we combine the multi-interval LGR collocation method in time with the Legendre-Gauss-Lobatto collocation method in space to obtain a space-time spectral collocation approximation for nonlinear second-order evolution *** results show that the proposed methods have high accuracy and excellent long-time *** comparison between our methods and several commonly used methods are also provided.

关键词： Legendre-Gauss-Radau collocation method Second-order initial value problem Spectral convergence Wave equation