In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in ...Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
Tuojiang River Basin is a first-class tributary of the upper reaches of the Yangtze River—which is the longest river in China.As phytoplankton are sensitive indicators of trophic changes inwater bodies,characterizing...Tuojiang River Basin is a first-class tributary of the upper reaches of the Yangtze River—which is the longest river in China.As phytoplankton are sensitive indicators of trophic changes inwater bodies,characterizing phytoplankton communities and their growth influencing factors in polluted urban rivers can provide new ideas for pollution control.Here,we used direct microscopic count and environmental DNA(eDNA)metabarcoding methods to investigate phytoplankton community structure in Tuojiang River Basin(Chengdu,Sichuan Province,China).The association between phytoplankton community structure and water environmental factors was evaluated by Mantel analysis.Additional environmental monitoring data were used to pinpoint major factors that influenced phytoplankton growth based on structural equation modeling.At the phylum level,the dominant phytoplankton taxa identified by the conventional microscopic method mainly belonged to Bacillariophyta,Chlorophyta,and Cyanophyta,in contrast with Chlorophyta,Dinophyceae,and Bacillariophyta identified by eDNA metabarcoding.Inα-diversity analysis,eDNA metabarcoding detected greater species diversity and achieved higher precision than the microscopic method.Phytoplankton growth was largely limited by phosphorus based on the nitrogen-to-phosphorus ratios>16:1 in all water samples.Redundancy analysis and structural equation modeling also confirmed that the nitrogen-to-phosphorus ratio was the principal factor influencing phytoplankton growth.The results could be useful for implementing comprehensive management of the river basin environment.It is recommended to control the discharge of point-and surface-source pollutants and the concentration of dissolved oxygen in areas with excessive nutrients(e.g.,Jianyang-Ziyang).Algae monitoring techniques and removal strategies should be improved in 201 Hospital,Hongrihe Bridge and Colmar Town areas.展开更多
The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The n...The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
Objectives:Teachers are facing unprecedented new challenges leading them to face an increasing number of tasks that are not part of their job,as well as having to cope with the additional skills acquisition that comes...Objectives:Teachers are facing unprecedented new challenges leading them to face an increasing number of tasks that are not part of their job,as well as having to cope with the additional skills acquisition that comes with non-traditional forms of teaching and learning,and increased work pressure leading to an increase in the rate of teachers leaving the profession.Therefore,this study aims to explore the mechanism of the career calling on job burnout through career adaptability and work engagement.Methods:This study conducted a cross-sectional survey of 465 primary and secondary school teachers(PSST)in China's Mainland from the perspective of work adjustment and used structural equation modeling(SEM)to examine the mediating roles of career adaptability and work engagement in the relationship between teachers’career calling and job burnout.Results:The results show that PSSTs are above average in career calling,career adaptability,and work engagement,while job burnout is below average.A significant positive or negative correlation exists between career calling,career adaptability,work engagement,and job burnout.The result of path analysis indicates that career adaptability and work engagement exert an indirect influence on the job burnout of PSST through three paths:namely,the independent intermediary role of career adaptability(EV=−0.144),the independent intermediary role of work engagement(EV=0.172)and the chain intermediary role of the two(EV=0.176).Conclusion:This study emphasizes the importance of career adaptability and work engagement in teacher development in regulating career calling and job burnout.Therefore,on the one hand,we think that if managers want to reduce teachers’job burnout,they need to pay more attention to teachers’career adaptability and work engagement,rather than relying solely on teachers’career calling.On the other hand,it is to remind teachers not to rely on their adjustment to adapt to the work,but also to need outside help as much as possible.展开更多
The large-scale exploitation of vanadium(Ⅴ) bearing minerals has led to a massive accumulation of Ⅴ tailings, of which Ⅴ pollution poses severe ecological risks. Although the mechanisms of Ⅴ stress to the microbia...The large-scale exploitation of vanadium(Ⅴ) bearing minerals has led to a massive accumulation of Ⅴ tailings, of which Ⅴ pollution poses severe ecological risks. Although the mechanisms of Ⅴ stress to the microbial community have been reported, the influential pathways in a multi-medium-containing system, for example, the soil-tailings-groundwater system,are unknown. The dynamic redox conditions and substance exchange within the system exhibited complex Ⅴ stress on the local microbial communities. In this study, the influence pathways of Ⅴ stress to the microbial community in the soil-tailings-groundwater system were first investigated. High Ⅴ contents were observed in groundwater(139.2 ± 0.15 μg/L) and soil(98.0–323.8 ± 0.02 mg/kg), respectively. Distinct microbial composition was observed for soil and groundwater, where soil showed the highest level of diversity and richness. Firmicutes, Proteobacteria, Actinobacteria, and Acidobacteria were dominant in soil and groundwater with a sum relative abundance of around 80 %. Based on redundancy analysis and structural equation models, Ⅴ was one of the vital driving factors affecting microbial communities. Groundwater microbial communities were influenced by Ⅴ via Cr, dissolved oxygen, and total nitrogen, while Fe, Mn, and total phosphorus were the key mediators for Ⅴ to affect soil microbial communities. Ⅴ affected the microbial community via metabolic pathways related to carbonaceous matter, which was involved in the establishment of survival strategies for metal stress. This study provides novel insights into the influence pathways of Ⅴ on the microorganisms in tailings reservoir for pollution bioremediation.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
The hot deformation behavior of the premium GH4738 alloy was investigated in the temperature range of 1313 to 1353 K at strain rates of 0.01 to 1 s^(−1)using the hot compression test.To accurately predict flow stress,...The hot deformation behavior of the premium GH4738 alloy was investigated in the temperature range of 1313 to 1353 K at strain rates of 0.01 to 1 s^(−1)using the hot compression test.To accurately predict flow stress,three novel strain compensation constitutive equations were developed and rigorously assessed.The results indicate that the power function model(correlation coefficients r=0.98544)demonstrates greater prediction accuracy compared to other functions,with a calculated average activation energy of 507.968 kJ mol−1.Additionally,electron backscattered diffraction technology and transmission electron microscopy were used to analyze the evolution of the alloy microstructure during dynamic recrystallization under different deformation conditions.The results show that under high-temperature and large deformation conditions,the dislocation density and the degree of grain rotation increase,which promotes the formation and growth of new recrystallized grains,so that recrystallization is completed when the deformation amount reaches 30%.Besides,the increase in the temperature not only enhances the thermal activation mechanism,but also improves the grain size uniformity and texture consistency.Meanwhile,the carbide inhibits grain overgrowth by pinning grain boundaries,maintaining a fine and uniform grain structure of the alloy,and thereby improving the plasticity of the material.展开更多
In this work,fow behavior and dynamic recrystallization(DRX)mechanism of a low carbon martensitic stainless bearing steel,CSS-42L,were investigated using a thermomechanical simulator under the temperature and strain r...In this work,fow behavior and dynamic recrystallization(DRX)mechanism of a low carbon martensitic stainless bearing steel,CSS-42L,were investigated using a thermomechanical simulator under the temperature and strain rate ranges of 900 to 1100℃ and 0.1 to 20 s^(−1),respectively.The Arrhenius-type constitutive equation was established based on the fow stress curves.Moreover,the peak stress decreased with the increase in deformation temperature and the decrease in strain rate.There were two DRX mechanisms during hot deformation of the current studied steel,the main one being discontinuous dynamic recrystallization mechanism,acting through grain boundary bulging and migration,and the auxiliary one being continuous dynamic recrystallization mechanism,working through the rotation of sub-grains.On the basis of microstructural characterizations,power dissipation maps and fow instability maps,the optimized hot deformation parameters for CSS-42L bearing steel were determined as 1050℃/0.1 s^(−1) and 1100℃/1 s^(−1).展开更多
This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case ...This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).展开更多
The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytica...The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.展开更多
The evacuation of people under threat is an effective disaster prevention and mitigation measure in response to flash floods and geological hazards,and it is also an essential element of pre-disaster planning.However,...The evacuation of people under threat is an effective disaster prevention and mitigation measure in response to flash floods and geological hazards,and it is also an essential element of pre-disaster planning.However,the effect of the interactions between perception factors on residents'willingness to evacuate is an urgent problem to be solved.Therefore,this paper introduces risk,stakeholder,and protective action perceptions from the protective action decision model as the main explanatory variables.These three core perceptions are subdivided into affective risk perception,cognitive risk perception,government perception,other-stakeholder perception,resourcerelated attributes,and hazard-related attributes.A questionnaire survey was conducted from June to July 2023 among residents of mountainous communities in nine villages in three towns in Sichuan Province,China.359 cross-sectional data were analyzed using structural equation modeling to explore the effects of six perception factors on evacuation intentions.The results of the study showed that:(1)affective risk perception,government perception,other-stakeholder perception,and hazard-related attributes all directly and positively influence residents'intentions to evacuate;(2)cognitive risk perception is mediated by stakeholder and protective action perceptions,which indirectly and positively affect residents'intentions to evacuate.Based on the hypothesized paths,strategies to improve residents'willingness to evacuate are discussed from the perspective of three core perceptions:strengthening disaster risk education,improving residents'cohesion,and building government credibility.The results of this study can provide theoretical support and practical suggestions for emergency management departments to formulate emergency evacuation strategies,which can aid decision-makers in better understanding residents'intentions to evacuate,optimizing evacuation information dissemination pathways,and strengthening disaster risk management capabilities.展开更多
For the first time,the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work.The plate comprises a lattic...For the first time,the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work.The plate comprises a lattice core located in the middle and several homogeneous orthotropic layers that are symmetrical relative to it.For this purpose,the partial differential equations of motion have been derived based on the first-order shear deformation theory,employing Hamilton’s principle and Von Kármán’s nonlinear displacement-strain relations.Then,the nonlinear partial differential equations of the plate are converted into a time-dependent nonlinear ordinary differential equation(Duffing equation)by applying the Galerkin method.From the solution of this equation,the natural frequencies are extracted.Then,to calculate the non-linear frequencies of the plate,the non-linear equation of the plate has been solved analytically using the method of multiple scales.Finally,the effect of some critical parameters of the system,such as the thickness,height,and different angles of the stiffeners on the linear and nonlinear frequencies,has been analyzed in detail.To confirmthe solution method,the results of this research have been compared with the reported results in the literature and finite elements in ABAQUS,and a perfect match is observed.The results reveal that the geometry and configuration of core ribs strongly affect the natural frequencies of the plate.展开更多
Thermospheric neutral winds(TNWs)refer to the neutral gases in the thermosphere circulating as tides,which play a crucial role in the dynamics of the thermosphere-ionosphere system(TIS).Global geospace neutral winds,p...Thermospheric neutral winds(TNWs)refer to the neutral gases in the thermosphere circulating as tides,which play a crucial role in the dynamics of the thermosphere-ionosphere system(TIS).Global geospace neutral winds,particularly over the magnetic equator,have been a subject of study for several decades.However,despite the known importance of neutral winds,a comprehensive understanding and characterization of the winds is still lacking.Various ground-based and satellite missions have provided valuable information on the contribution of neutral winds to the global atmospheric dynamics.However,efforts in the global monitoring of neutral winds are still lacking,and the drivers behind the behavior of TNWs as well as their influence on the TIS remain incomplete.To address these knowledge gaps in the global circulation of TNWs,it is crucial to develop a deep understanding of the neutral wind characteristics over different regions.The low-latitude equatorial region in particular has been observed to exert complex influences on TNWs because of the unique effects of the Earth’s magnetic field at the dip equator.Studying neutral winds over this region will provide valuable insights into the unique dynamics and processes that occur in this region,thereby enhancing our understanding of their role in the overall dynamics of the TIS.Additionally,through empirical observations,an improved ability to accurately model and predict the behavior of this region can be achieved.This review article addresses challenges in understanding equatorial winds by reviewing historical measurements,current missions,and the interactions of ionospheric and thermospheric phenomena,emphasizing the need for comprehensive measurements to improve global atmospheric dynamics and weather forecasting.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported by the Development and Application Project of Ship CAE Software.
文摘Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
基金supported by the National Natural Science Foundation of China (No.72091511)the Science Fund for Distinguished Young Scholars of Hebei Province (No.E2022402064).
文摘Tuojiang River Basin is a first-class tributary of the upper reaches of the Yangtze River—which is the longest river in China.As phytoplankton are sensitive indicators of trophic changes inwater bodies,characterizing phytoplankton communities and their growth influencing factors in polluted urban rivers can provide new ideas for pollution control.Here,we used direct microscopic count and environmental DNA(eDNA)metabarcoding methods to investigate phytoplankton community structure in Tuojiang River Basin(Chengdu,Sichuan Province,China).The association between phytoplankton community structure and water environmental factors was evaluated by Mantel analysis.Additional environmental monitoring data were used to pinpoint major factors that influenced phytoplankton growth based on structural equation modeling.At the phylum level,the dominant phytoplankton taxa identified by the conventional microscopic method mainly belonged to Bacillariophyta,Chlorophyta,and Cyanophyta,in contrast with Chlorophyta,Dinophyceae,and Bacillariophyta identified by eDNA metabarcoding.Inα-diversity analysis,eDNA metabarcoding detected greater species diversity and achieved higher precision than the microscopic method.Phytoplankton growth was largely limited by phosphorus based on the nitrogen-to-phosphorus ratios>16:1 in all water samples.Redundancy analysis and structural equation modeling also confirmed that the nitrogen-to-phosphorus ratio was the principal factor influencing phytoplankton growth.The results could be useful for implementing comprehensive management of the river basin environment.It is recommended to control the discharge of point-and surface-source pollutants and the concentration of dissolved oxygen in areas with excessive nutrients(e.g.,Jianyang-Ziyang).Algae monitoring techniques and removal strategies should be improved in 201 Hospital,Hongrihe Bridge and Colmar Town areas.
基金Projects(52205069,52075083,52304049)supported by the National Natural Science Foundation of ChinaProject(2021-BS-164)supported by the Liaoning Province Doctoral Research Startup Fund,China+2 种基金Project(LJKZ0264)supported by the Science and Technology Research Projects of Education Department of Liaoning Province,ChinaProject(G2022003010L)supported by the High-end Foreign Experts Recruitment Plan of ChinaProject(E2021203095)supported by the Natural Science Foundation for Young Scholars of Hebei Province,China。
文摘The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金funded by Humanities and Social Sciences Foundation and Natural Science Foundation of Nanjing University of Posts and Telecommunications(NYY222055,NY224176)General Subject of Educational Science Planning in Jiangsu Province(C/2024/01/76)National Natural Science Foundation of China(62307025).
文摘Objectives:Teachers are facing unprecedented new challenges leading them to face an increasing number of tasks that are not part of their job,as well as having to cope with the additional skills acquisition that comes with non-traditional forms of teaching and learning,and increased work pressure leading to an increase in the rate of teachers leaving the profession.Therefore,this study aims to explore the mechanism of the career calling on job burnout through career adaptability and work engagement.Methods:This study conducted a cross-sectional survey of 465 primary and secondary school teachers(PSST)in China's Mainland from the perspective of work adjustment and used structural equation modeling(SEM)to examine the mediating roles of career adaptability and work engagement in the relationship between teachers’career calling and job burnout.Results:The results show that PSSTs are above average in career calling,career adaptability,and work engagement,while job burnout is below average.A significant positive or negative correlation exists between career calling,career adaptability,work engagement,and job burnout.The result of path analysis indicates that career adaptability and work engagement exert an indirect influence on the job burnout of PSST through three paths:namely,the independent intermediary role of career adaptability(EV=−0.144),the independent intermediary role of work engagement(EV=0.172)and the chain intermediary role of the two(EV=0.176).Conclusion:This study emphasizes the importance of career adaptability and work engagement in teacher development in regulating career calling and job burnout.Therefore,on the one hand,we think that if managers want to reduce teachers’job burnout,they need to pay more attention to teachers’career adaptability and work engagement,rather than relying solely on teachers’career calling.On the other hand,it is to remind teachers not to rely on their adjustment to adapt to the work,but also to need outside help as much as possible.
基金supported by the National Natural Science Foundation of China(No.42377415)the Natural Science Foundation of Sichuan Province(No.2023NSFSC0811),Sichuan Science and Technology Program(Nos.2021JDTD0013 and 2021YFQ0066)+1 种基金the Science and Technology Major Project of Xizhang Autonomous Region of China(No.XZ202201ZD0004G06)the Everest Scientific Research Program(No.80000-2023ZF11405).
文摘The large-scale exploitation of vanadium(Ⅴ) bearing minerals has led to a massive accumulation of Ⅴ tailings, of which Ⅴ pollution poses severe ecological risks. Although the mechanisms of Ⅴ stress to the microbial community have been reported, the influential pathways in a multi-medium-containing system, for example, the soil-tailings-groundwater system,are unknown. The dynamic redox conditions and substance exchange within the system exhibited complex Ⅴ stress on the local microbial communities. In this study, the influence pathways of Ⅴ stress to the microbial community in the soil-tailings-groundwater system were first investigated. High Ⅴ contents were observed in groundwater(139.2 ± 0.15 μg/L) and soil(98.0–323.8 ± 0.02 mg/kg), respectively. Distinct microbial composition was observed for soil and groundwater, where soil showed the highest level of diversity and richness. Firmicutes, Proteobacteria, Actinobacteria, and Acidobacteria were dominant in soil and groundwater with a sum relative abundance of around 80 %. Based on redundancy analysis and structural equation models, Ⅴ was one of the vital driving factors affecting microbial communities. Groundwater microbial communities were influenced by Ⅴ via Cr, dissolved oxygen, and total nitrogen, while Fe, Mn, and total phosphorus were the key mediators for Ⅴ to affect soil microbial communities. Ⅴ affected the microbial community via metabolic pathways related to carbonaceous matter, which was involved in the establishment of survival strategies for metal stress. This study provides novel insights into the influence pathways of Ⅴ on the microorganisms in tailings reservoir for pollution bioremediation.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
基金supported by the National Key R&D Program of China(No.2021YFB3700403).
文摘The hot deformation behavior of the premium GH4738 alloy was investigated in the temperature range of 1313 to 1353 K at strain rates of 0.01 to 1 s^(−1)using the hot compression test.To accurately predict flow stress,three novel strain compensation constitutive equations were developed and rigorously assessed.The results indicate that the power function model(correlation coefficients r=0.98544)demonstrates greater prediction accuracy compared to other functions,with a calculated average activation energy of 507.968 kJ mol−1.Additionally,electron backscattered diffraction technology and transmission electron microscopy were used to analyze the evolution of the alloy microstructure during dynamic recrystallization under different deformation conditions.The results show that under high-temperature and large deformation conditions,the dislocation density and the degree of grain rotation increase,which promotes the formation and growth of new recrystallized grains,so that recrystallization is completed when the deformation amount reaches 30%.Besides,the increase in the temperature not only enhances the thermal activation mechanism,but also improves the grain size uniformity and texture consistency.Meanwhile,the carbide inhibits grain overgrowth by pinning grain boundaries,maintaining a fine and uniform grain structure of the alloy,and thereby improving the plasticity of the material.
基金fnancially supported by the Scientifc Research Project of the Department of Education in Hunan Prov ince,China(Grant No.23B0533).
文摘In this work,fow behavior and dynamic recrystallization(DRX)mechanism of a low carbon martensitic stainless bearing steel,CSS-42L,were investigated using a thermomechanical simulator under the temperature and strain rate ranges of 900 to 1100℃ and 0.1 to 20 s^(−1),respectively.The Arrhenius-type constitutive equation was established based on the fow stress curves.Moreover,the peak stress decreased with the increase in deformation temperature and the decrease in strain rate.There were two DRX mechanisms during hot deformation of the current studied steel,the main one being discontinuous dynamic recrystallization mechanism,acting through grain boundary bulging and migration,and the auxiliary one being continuous dynamic recrystallization mechanism,working through the rotation of sub-grains.On the basis of microstructural characterizations,power dissipation maps and fow instability maps,the optimized hot deformation parameters for CSS-42L bearing steel were determined as 1050℃/0.1 s^(−1) and 1100℃/1 s^(−1).
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802)。
文摘This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).
基金supported by the National Natural Science Foundation of China(12172023).
文摘The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.
基金supported by the National Natural Science Foundation of China(U20A20111)the National key R&D Program(2022YFC3080100)。
文摘The evacuation of people under threat is an effective disaster prevention and mitigation measure in response to flash floods and geological hazards,and it is also an essential element of pre-disaster planning.However,the effect of the interactions between perception factors on residents'willingness to evacuate is an urgent problem to be solved.Therefore,this paper introduces risk,stakeholder,and protective action perceptions from the protective action decision model as the main explanatory variables.These three core perceptions are subdivided into affective risk perception,cognitive risk perception,government perception,other-stakeholder perception,resourcerelated attributes,and hazard-related attributes.A questionnaire survey was conducted from June to July 2023 among residents of mountainous communities in nine villages in three towns in Sichuan Province,China.359 cross-sectional data were analyzed using structural equation modeling to explore the effects of six perception factors on evacuation intentions.The results of the study showed that:(1)affective risk perception,government perception,other-stakeholder perception,and hazard-related attributes all directly and positively influence residents'intentions to evacuate;(2)cognitive risk perception is mediated by stakeholder and protective action perceptions,which indirectly and positively affect residents'intentions to evacuate.Based on the hypothesized paths,strategies to improve residents'willingness to evacuate are discussed from the perspective of three core perceptions:strengthening disaster risk education,improving residents'cohesion,and building government credibility.The results of this study can provide theoretical support and practical suggestions for emergency management departments to formulate emergency evacuation strategies,which can aid decision-makers in better understanding residents'intentions to evacuate,optimizing evacuation information dissemination pathways,and strengthening disaster risk management capabilities.
文摘For the first time,the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work.The plate comprises a lattice core located in the middle and several homogeneous orthotropic layers that are symmetrical relative to it.For this purpose,the partial differential equations of motion have been derived based on the first-order shear deformation theory,employing Hamilton’s principle and Von Kármán’s nonlinear displacement-strain relations.Then,the nonlinear partial differential equations of the plate are converted into a time-dependent nonlinear ordinary differential equation(Duffing equation)by applying the Galerkin method.From the solution of this equation,the natural frequencies are extracted.Then,to calculate the non-linear frequencies of the plate,the non-linear equation of the plate has been solved analytically using the method of multiple scales.Finally,the effect of some critical parameters of the system,such as the thickness,height,and different angles of the stiffeners on the linear and nonlinear frequencies,has been analyzed in detail.To confirmthe solution method,the results of this research have been compared with the reported results in the literature and finite elements in ABAQUS,and a perfect match is observed.The results reveal that the geometry and configuration of core ribs strongly affect the natural frequencies of the plate.
基金the Ministry of Higher Education(KPT)Malaysia for the MyBrainSc program.Idahwati Sarudin was supported by Universiti Sains Malaysia through a Short-Term Grant(Project No.304/PFIZIK/6315730)Nurul Shazana Abdul Hamid received funding from Universiti Kebangsaan Malaysia for funding this work through a University Research Grant(Grant No.GUP-2023-048)。
文摘Thermospheric neutral winds(TNWs)refer to the neutral gases in the thermosphere circulating as tides,which play a crucial role in the dynamics of the thermosphere-ionosphere system(TIS).Global geospace neutral winds,particularly over the magnetic equator,have been a subject of study for several decades.However,despite the known importance of neutral winds,a comprehensive understanding and characterization of the winds is still lacking.Various ground-based and satellite missions have provided valuable information on the contribution of neutral winds to the global atmospheric dynamics.However,efforts in the global monitoring of neutral winds are still lacking,and the drivers behind the behavior of TNWs as well as their influence on the TIS remain incomplete.To address these knowledge gaps in the global circulation of TNWs,it is crucial to develop a deep understanding of the neutral wind characteristics over different regions.The low-latitude equatorial region in particular has been observed to exert complex influences on TNWs because of the unique effects of the Earth’s magnetic field at the dip equator.Studying neutral winds over this region will provide valuable insights into the unique dynamics and processes that occur in this region,thereby enhancing our understanding of their role in the overall dynamics of the TIS.Additionally,through empirical observations,an improved ability to accurately model and predict the behavior of this region can be achieved.This review article addresses challenges in understanding equatorial winds by reviewing historical measurements,current missions,and the interactions of ionospheric and thermospheric phenomena,emphasizing the need for comprehensive measurements to improve global atmospheric dynamics and weather forecasting.
