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GLOBAL BOUND ON THE GRADIENT OF SOLUTIONS TO p-LAPLACE TYPE EQUATIONS WITH MIXED DATA

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Acta Mathematica Scientia 2024年第4期44卷 1394-1414页

作者： Minh-Phuong TRAN The-Quang TRAN Thanh-Nhan NGUYEN Applied analysis Research group Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam Nguyen Huu Huan High School Thu Duc CityVietnam group of analysis and Applied Mathematics Department of MathematicsHo Chi Minh City University of EducationVietnam

In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is *** particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many *** on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal *** to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.

关键词： gradient estimates p-Laplace quasilinear elliptic equation fractional maximal operators Lorentz-Morrey spaces

Incense smoke(IS)inhalation exposure system:Physicochemical characterization,IS particle deposition and clearance in human airway using MPPD model

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Particuology 2024年第4期87卷 271-285页

作者： Vyas Kumar Hafsa Hashmi Anshita Nasreen Ghazi Ansari Jyotsna Singh Inhalation Toxicology Facility Regulatory Toxicology GroupCSR-Indian Institute of Toxicology ResearchLucknow22001UPIndi Academy of scientific and Innovative Research(AcsSIR) Ghaziabad201002UPIndia Analytical Chemistry Regulatory Toxicology GroupCSIR-Indian Institute of Toxicology ResearchLucknow226001UPIndia

Incense smoke(IS)is source of indoor air pollution and key risk for diverse human *** in-formation is available regarding controlled IS rodent inhalation exposure system and IS particulate matter(PM)deposition in human *** aimed to demonstrate stable ISPM physicochemical parameters of 10 incense products inside the customized whole body inhalation exposure chamber(without animal)connected to smoke generation unit via aerosol mixing *** analyzed for size segregated PM emission,ISPM in vitro aerodynamics(MMAD and GSD determination),fine and ultrafine particle's SEM,SEM-EDX and PAH *** real life exposure scenario by utilizing MMAD,GSD and PM concentration after Tier 1 exposure assessment as key input parameters,ISPM dosimetry in infant(3 months)and adult(21 years male and female)human airways was calculated using multiple-path particle dosimetry(MPPD 3.04)*** median aerodynamic diameter(MMAD)and geo-metric standard deviation(GSD)ranged between 0.55 and 2.10μm and 1.22 to 1.77(polydisperse)***1.0 and PM0.1 showed multiple morphology and presence of heavy and trace *** like acenaphthylene,anthracene,fluorene,naphthalene and phenanthrene were detected(0.84-143.17μg/g).MPPD results showed higher ISPM deposition in pulmonary region and lowest in trachea bronchial *** deposition in tissue was higher in lower,peripheral lung as compared to upper and central lung *** body inhalation exposure system showed stable IS atmosphere(physi-cochemical parameters)indicating the device suitability in future inhalation *** ISPM deposition fraction and clearance data showed deep lung penetrating and retention behavior with higher risk in infant followed by female and then *** modeled particle deposition and clearance data may be useful in risk assessment analysis of IS.

关键词： Inhalation Incense smoke Multiple-path particle dosimetry(MPPD) Particle deposition Particulate matter(PM) Mass median aerodynamic diameter (MMAD) Human airway

The spectrum and stability of travelling pulses in a coupled FitzHugh-Nagumo equation

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Science China Mathematics 2024年第5期67卷 975-1010页

作者： Qi Qiao Xiang Zhang School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of scientific and Engineering Computing(Ministry of Education) and Shanghai Frontier Science Center of Modern Analysis(CMA-Shanghai)Shanghai Jiao Tong UniversityShanghai 200240China

For a coupled slow-fast FitzHugh-Nagumo(FHN)equation derived from a reaction-diffusionmechanics(RDM)model,Holzer et al.(2013)studied the existence and stability of the travelling pulse,which consists of two fast orbit arcs and two slow ones,where one fast segment passes the unique fold point with algebraic decreasing and two slow ones follow normally hyperbolic critical curve *** and Zhang(2021)obtained the existence of the travelling pulse,whose two fast orbit arcs both exponentially decrease,and one of the slow orbit arcs could be normally hyperbolic or not at the ***,we characterize both the nonlinear and spectral stability of this travelling pulse.

关键词： coupled FitzHugh-Nagumo equation singular perturbation travelling pulse spectrum nonlinear stability spectral stability

Radial solution of the Logarithmic Laplacian system

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 114-124页

作者： ZHANG Li-hong NIE Xiao-feng WANG Guo-tao Bashir Ahmad School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041004China Nonlinear analysis and Applied Mathematics(NAAM)Research group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia.

The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of th... 详细信息

关键词： the Logarithmic Laplacian system radial symmetry the direct method of moving planes

What diameter?What height?Influence of measures of average tree size on area-based allometric volume relationships

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Forest Ecosystems 2024年第1期11卷 100-109页

作者： Yilin Wang John A.Kershaw Mark J.Ducey Yuan Sun James B.McCarter Integrated Forest Mensuration and Systems analysis Laboratory Faculty of Forestry and Environmental ManagementUniversity of New BrunswickFrederictonNBCanada Department of Natural Resources and the Environment University of New HampshireDurhamNHUSA College of Forestry Nanjing Forestry UniversityNanjing210037China scientific Programmer RayonierYuleeFLUSA

Volume is an important attribute used in many forest management *** from 83 fixed-area plots located in central New Brunswick,Canada,are used to examine how different measures of stand-level diameter and height influence volume prediction using a stand-level variant of Honer's(1967)volume *** density was included in the models(Volume=f(Diameter,Height,Density))choice of diameter measure was more important than choice of height *** density was not included(Volume=f(Diameter,Height)),the opposite was *** models with density included,moment-based estimators of stand diameter and height performed better than all other *** models without density,largest tree estimators of stand diameter and height performed better than other *** overall best equation used quadratic mean diameter,Lorey's height,and density(root mean square error=5.26 m^3·ha^(-1);1.9%relative error).The best equation without density used mean diameter of the largest trees needed to calculate a stand density index of 400 and the mean height of the tallest 400 trees per ha(root mean square error=32.08 m^(3)·ha^(-1);11.8%relative error).The results of this study have some important implications for height subsampling and LiDAR-derived forest inventory analyses.

关键词： Allometric relationships Stand structure Volume estimation Stand-level attributes

Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

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Computer Modeling in Engineering & Sciences 2024年第5期139卷 2001-2026页

作者： Weida Wu Yiqiang Wang Zhonghao Gao Pai Liu State Key Laboratory of Structural analysis for Industrial Equipment Dalian University of TechnologyDalian116024China

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy ***,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR *** address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free *** unit cell microstructural topologies are described with the material-field series-expansion(MFSE)*** MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design *** conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model ***,we use homogenization to find a preliminary NPR design under a small deformation *** the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large *** this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% ***,typical microstructure designs are fabricated and tested through *** experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

关键词： Topology optimization microstructural design negative Poisson’s ratio large deformation

Assessing gully erosion and rehabilitation using multi temporal LiDAR DEMs:Case study from the Great Barrier Reef catchments,Australia

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International Soil and Water Conservation Research 2024年第1期12卷 184-199页

作者： Sana Khan Rebecca Bartley Anne Kinsey-Henderson Aaron Hawdon The Commonwealth scientific and Industrial Research Organisation(CSIRO) Environment1 James Cook DrDouglas4814Australia The Commonwealth scientific and Industrial Research Organisation(CSIRO) EnvironmentGPO Box 2583BrisbaneQLD4001Australia

Millions of dollars are being spent on gully rehabilitation to help reduce excess fine sediment delivery to the Great Barrier Reef(GBR).There is an urgent need for(i)prioritisation of active gullies for rehabilitation and(ii)the development of methodologies to inform the effectiveness of *** this study we analyse DEMs of Difference derived from 0.5 m resolution 2-3 year interval multi-temporal LiDAR data collected pre and post rehabilitation at three variable gully morphologies in the Burdekin *** analysis indicates that the highest annual average fine sediment erosion rates for the untreated control gullies occur at the linear gully(53.38 t ha^(-1)y^(-1))followed by linear-alluvial gully(34.24 t ha^(-1)y^(-1))and least at the alluvial gully(14.41 t ha^(-1)y^(-1)).The proportional loss or export of fine sediment from the gullies in their un-treated condition ranges from∼68 to 90%of what is eroded,and when the gullies are treated the proportion of fine sediment that is retained in the gully proportional to what is eroded increases to∼60%at all *** pre-treatment baseline erosion rates,and additional post treatment LiDAR captures,it is difficult to quantify the treatment *** results offer insights in the erosion mechanisms within different geomorphic gully morphologies and rehabilitation effects in these erosional *** study provides crucial knowledge of gully dynamics that can be coupled with other lines of evidence for better prioritisation of rehabilitation in the GBR catchments.

关键词： Digital elevation models (dis)connectivity Restoration Geomorphic change detection Geomorphic effectiveness GIS

Application of CFD and FEA Coupling to Predict Structural Dynamic Responses of A Trimaran in Uni-and Bi-Directional Waves

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China Ocean Engineering 2024年第1期38卷 81-92页

作者： LIAO Xi-yu XIA Jin-song CHEN Zhan-yang TANG Qin ZHAO Nan ZHAO Wei-dong GUI Hong-bin Marine Design&Research Institute of China Shanghai 200011China Ship Structure Division China Ship Scientific Research CenterWuxi 214082China College of Ocean Engineering Harbin Institute of TechnologyWeihaiWeihai 264209China State Key Laboratory of Structural analysis Optimization and CAE Software for Industrial EquipmentDalian University of TechnologyDalian 116024China School of Foreign Studies Jiangnan UniversityWuxi 214122China

To predict the wave loads of a flexible trimaran in different wave fields,a one-way interaction numerical simulation method is proposed by integrating the fluid solver(Star-CCM+)and structural solver(Abaqus).Differing from the existing coupled CFD-FEA method for monohull ships in head waves,the presented method equates the mass and stiffness of the whole ship to the hull shell so that any transverse and longitudinal section stress of the hull in oblique waves can be ***,verification study and sensitivity analysis are carried out by comparing the trimaran motions using different mesh sizes and time step *** on the wave elevation of uni-and bi-directional waves is also carried *** a comprehensive analysis on the structural responses of the trimaran in different uni-directional regular wave and bi-directional cross sea conditions is carried out,***,the differences in structural response characteristics of trimaran in different wave fields are *** results show that the present method can reduce the computational burden of the two-way fluid-structure interaction simulations.

关键词： CFD-FEA fluid-structure coupling structural responses trimaran bi-directional cross sea

Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System

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Communications in Mathematical Research 2024年第1期40卷 43-63页

作者： Yue Li Li Chen Zhipeng Zhang Department of Mathematics Nanjing UniversityNanjing 210093P.R.China Institute for analysis and scientific Computing Vienna University of TechnologyWiedner Hauptstrafβe 8-10Vienna 1040Austria School of Business Informatics and Mathematics University of MannheimMannheim 68131Germany

In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole *** convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential,where the mollification is of algebraic *** main idea of the proof is to study the time evolution of a stopped process and obtain a Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.

关键词： Stochastic particle systems cross-diffusion system mean-field limit population dynamics