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Normalized Solution for p-Kirchhoff Equation with a L2.supercritical Growth

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 414-429页

作者： Zhi-min REN Yong-yi LAN School of Sciences Jimei UniversityXiamen 361005China

In this paper,we investigate the following p-Kirchhoff equation{∫R^(N)|u|^(2.dx=ρ,(a+b)∫RN(|Δu}^(p)+|u|^(p))dx)(-Δpu+|u|^(p-2.)=|u|^(s-2.u+μu,x∈R^(N),where a>0,b≥0,p>0 are constants,constants,p*=N-P/Np is the critical Sobolev exponent,μis a Lagrange multiplier,-Δpu=-div(|Δu|_(p-2.u),2.p2.,μ∈R,and s∈(2./N+2.-2.p*).We demonstratethat he p-Kirchhoff equation has a normalized solution using the mountain pass lemma and some analysis techniques.

关键词： p-Kirchhoff equation normalized solution mountain-pass lemma

On the Difference Between the Skew-rank of an Oriented Graph and the Rank of Its Underlying Graph

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 129-136页

作者： Jia-min Zhu Bo-jun Yuan yi Wang School of Mathematical Sciences Anhui UniversityHefei230601China School of Science Zhejiang University of Science and TechnologyHangzhou310023China

Let G be a simple graph and G~σ be the oriented graph with G as its underlying graph and orientation σ.The rank of the adjacency matrix of G is called the rank of G and is denoted by r(G).The rank of the skew-adjacency matrix of G~σ is called the skew-rank of G~σ and is denoted by sr(G~σ).Let V(G)be the vertex set and E(G) be the edge set of *** cyclomatic number of G,denoted by c(G),is equal to |E(G)|-|V(G)|+ω(G),where ω(G) is the number of the components of *** is proved for any oriented graph G~σ that-2.(G)≤sr(G~σ)-r(G)≤2.(G).In this paper,we prove that there is no oriented graph G~σwith sr(G~σ)-r(G)=2.(G)-1,and in addition,there are infinitely many oriented graphs G~σ with connected underlying graphs such that c(G)=k and sr(G~σ)-r(G)=2.(G)-l for every integers k,l satisfying 0 ≤l≤4k and l≠1.

关键词： cyclomatic number rank skew-rank

Strain Gradient Finite Element Formulation of Flexoelectricity in Ferroelectric Material Based on Phase-Field Method

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Acta Mechanica Solida Sinica 2024年第4期37卷 570-579页

作者： Shuai Wang Hengchang Su min yi Li-Hua Shao National Key Laboratory of Strength and Structural Integrity Institute of Solid MechanicsSchool of Aeronautic Science and EngineeringBeihang UniversityBeijing100191People’s Republic of China State Key Laboratory of Mechanics and Control for Aerospace Structures and Institute for Frontier Science and Key Laboratory for Intelligent Nano Materials and Devices of ministry of Education and College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing210016People’s Republic of China

Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group ***,the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric *** this study,we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect.A four-node quadrilateral element with 2. degrees of freedom is constructed without introducing high-order shape *** microstructure evolution of domains is described by an independent order parameter,namely the spontaneous polarization governed by the time-dependent Ginzburg–Landau *** model is developed based on a thermodynamic framework,in which a set of microforces is introduced to construct the constitutive relation and evolution *** the flexoelectric part of electric enthalpy,the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric *** model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric *** model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids.A comparison is made between the polarization distribution in dielectrics and *** model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube,and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.

关键词： Flexoelectricity Phase-field method Ferroelectrics Domain configuration

Digital twin driven and intelligence enabled content delivery in end-edge-cloud collaborative 5G networks

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Digital Communications and Networks 2024年第2期10卷 328-336页

作者： Bo yi Jianhui Lv Xingwei Wang Lianbo Ma min Huang College of Computer Science and Engineering Northeastern UniversityShenyang110169China Pengcheng Lab. Shenzhen518055China College of Software Northeastern UniversityShenyang110819China College of Information Science and Engineering Northeastern UniversityShenyang110819China

The rapid development of 5G/6G and AI enables an environment of Internet of Everything(IoE)which can support millions of connected mobile devices and applications to operate smoothly at high speed and low ***,these massive devices will lead to explosive traffic growth,which in turn cause great burden for the data transmission and content *** challenge can be eased by sinking some critical content from cloud to *** this case,how to determine the critical content,where to sink and how to access the content correctly and efficiently become new *** work focuses on establishing a highly efficient content delivery framework in the IoE *** particular,the IoE environment is re-constructed as an end-edge-cloud collaborative system,in which the concept of digital twin is applied to promote the *** on the digital asset obtained by digital twin from end users,a content popularity prediction scheme is firstly proposed to decide the critical content by using the Temporal Pattern Attention(TPA)enabled Long Short-Term Memory(LSTM)***,the prediction results are input for the proposed caching scheme to decide where to sink the critical content by using the Reinforce Learning(RL)***,a collaborative routing scheme is proposed to determine the way to access the content with the objective of minimizing *** experimental results indicate that the proposed schemes outperform the state-of-the-art benchmarks in terms of the caching hit rate,the average throughput,the successful content delivery rate and the average routing overhead.

关键词： Digital twin IoE Content delivery Caching Routing

Photoinduced bismuth vanadate-catalyzed C(sp^(2.)-H functionalization

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Chinese Chemical Letters 2024年第3期35卷 1-2页

作者： Rong-Nan yi Wei-min He Key Laboratory of Food&Environment&Drug Monitoring and Testing of Universities in Hunan Province Hunan Police AcademyChangsha 410138China School of Chemistry and Chemical Engineering University of South ChinaHengyang 421001China

Visible light-induced organic reactions have gained much attention in recent years due to their mild conditions and high efficiency[1,2..In this context,many efficient photocatalysts including transition metal complex... 详细信息

关键词： bismuth catalyzed gained

Theoretical study on magnetocaloric effect and its electric-field regulation in CrI_(3)/metal heterostructure

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Science China(Physics,Mechanics & Astronomy) 2024年第2期67卷 134-141页

作者： Weiwei He Ziming Tang Qihua Gong min {2. Wanlin Guo State Key Laboratory of Mechanics and Control for Aerospace Structures Key Laboratory for Intelligent Nano Materials and Devices of Ministry of EducationInstitute for Frontier ScienceNanjing University of Aeronautics and AstronauticsNanjing 210016China MIIT Key Laboratory of Aerospace Information Materials and Physics College of PhysicsNanjing University of Aeronautics and AstronauticsNanjing 211106China

The extraordinary properties of a heterostructure by stacking atom-thick van der Waals(vdW)magnets have been extensively ***,the magnetocaloric effect(MCE)of heterostructures that are based on monolayer magnets remains to be ***,we deliberate MCE of vd W heterostructure composed of a monolayer CrI_(3)and metal atomic layers(Ag,Hf,Au,and Pb).It is revealed that heterostructure engineering by introducing metal substrate can improve MCE of CrI_(3),particularly boosting relative cooling power to 471.72.J m^(-2.and adiabatic temperature change to 2.1 K at 5 T for CrI_(3)/*** improved MCE is ascribed to the enhancement of magnetic moment and intralayer exchange coupling in CrI_(3)due to the CrI_(3)/metal heterointerface induced charge *** field is further found to tune MCE of CrI_(3)in heterostructures and could shift the peak temperature by around 10 K in CrI_(3)/Hf,thus manipulating the working temperature window of *** theoretical results could enrich the research on low-dimensional magnetocaloric materials.

关键词： magnetocaloric effect heterostructure metal substrate

Photocatalytic minisci-type multicomponent reaction for the synthesis of 1-(halo)alkyl-3-heteroaryl bicyclo[1.1.1] pentanes

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Chinese Chemical Letters 2024年第10期35卷 6-8页

作者： Rong-Nan yi Wei-min He Key Laboratory of Food&Environment&Drug Monitoring and Testing of Universities in Hunan Province Hunan Police Academy.Changsha 410138China School of Chemistry and Chemical Engineering University of South ChinaHengyang 421001China

Bioisosteres play an important role in pharmaceutical and agricultural compound design that has been developed to enhance the properties of *** a sp3-rich small ring cage hydrocarbons,bicyclo[1.1.1]pentanes(BCPs)were commonly considered as a bioisostere of the para-substituted arenes,internal alkynes,and tert-butyl groups,and its introduction can significantly improve pharmacokinetic properties,including passive permeability,aqueous solubility,metabolic stability[1].Over the past decades,numerous pharmaceutically relevant molecules with biaryl frameworks were improved by the approach of bioisosteric *** strategies for the synthesis of such BCP-aryls derivatives mostly depend on the stepwise C-C formation via the direct addition to bridgehead C-C bond of[1.1.1]propellane to provide active BCP-intermediates and followed by a second transitionmetal cross-coupling ***,these pioneer works were limited by the low step economy,the use of unstable reagents,and harsh conditions in industrial productions.

关键词： synthesis substituted alkyl

Unraveling the mysteries of volatile cycling and habitability on Earth and beyond

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National Science Review 2024年第06期11卷 8-9页

作者： yi-Gang Xu Ri-Xiang Zhu min-Han Dai State Key Laboratory of Isotope Geochemistry Guangzhou Institute of Geochemistry Chinese Academy of Sciences State Key Laboratory of Lithosphere Evolution Institute of Geology and Geophysics Chinese Academy of Sciences State Key Laboratory of Marine Environmental Science Xiamen University

The origin and cycling of volatiles, including water, carbon dioxide, and nitrogen, are fundamental to the very existence of habitable planets. These volatile compounds, often taken for granted,are the lifeblood of planetary systems, influencing almost everything from atmospheric composition and climate regulation to deep Earth processes and the emergence of life.

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The importance of data assimilation components for initial conditions and subsequent error growth

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Science China Earth Sciences 2024年第1期67卷 105-116页

作者： Zhongrui WANG Haohao SUN Lili LEI Zhe-min TAN yi ZHANG Key Laboratory of Mesoscale Severe Weather Ministry of Educationand School of Atmospheric SciencesNanjing UniversityNanjing 210023China Frontiers Science Center for Critical Earth Material Cycling Nanjing UniversityNanjing 210023China

Despite a specific data assimilation method,data assimilation(DA)in general can be decomposed into components of the prior information,observation forward operator that is given by the observation type,observation error covariances,and background error *** a classic Lorenz model,the influences of the DA components on the initial conditions(ICs)and subsequent forecasts are systematically investigated,which could provide a theoretical basis for the design of DA for different scales of *** forecast errors undergo three typical stages:a slow growth stage from 0 h to 5 d,a fast growth stage from 5 d to around 15 d with significantly different error growth rates for ensemble and deterministic forecasts,and a saturation stage after 15 *** strategies that provide more accurate ICs can improve the *** assimilation is superior to offline assimilation,and a flow-dependent background error covariance matrix(Pf)provides better analyses than a static background error covariance matrix(B)for instantaneous observations and frequent time-averaged observations;but the opposite is true for infrequent time-averaged observations,since cycling simulation cannot construct informative priors when the model lacks predictive skills and the flow-dependent Pf cannot effectively extract information from low-informative observations as the static *** observations contain more information than time-averaged observations,thus the former is preferred,especially for infrequent observing ***,ensemble forecasts have advantages over deterministic forecasts,and the advantages are enlarged with less informative observations and lower predictive-skill model priors.

关键词： Data assimilation Atmospheric predictability Background error covariances Ensemble forecasts