A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients...This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator-prey system.展开更多
The prey-predator system of three species with cross-diffusion pressure is known to possess a local solution with the maximal existence time T ≤ ∞.By obtaining the bounds of W21-norms of the local solution independe...The prey-predator system of three species with cross-diffusion pressure is known to possess a local solution with the maximal existence time T ≤ ∞.By obtaining the bounds of W21-norms of the local solution independent of T,it is established the global existence of the solution.展开更多
A chemostat model with maintenance energy and crossdiffusion is considered,and the formation of patterns is caused by the cross-diffusion. First, through linear stability analysis, the necessary conditions for the for...A chemostat model with maintenance energy and crossdiffusion is considered,and the formation of patterns is caused by the cross-diffusion. First, through linear stability analysis, the necessary conditions for the formation of the spatial patterns are given. Then numerical simulations by changing the values of crossdiffusions in the unstable domain are performed. The results showthat the cross-diffusion coefficient plays an important role in the formation of the pattern, and the different values of the crossdiffusion coefficients may lead to different types of pattern formation.展开更多
We investigate the Turing instability and pattern formation mechanism of a plant-wrack model with both self-diffusion and cross-diffusion terms.We first study the effect of self-diffusion on the stability of equilibri...We investigate the Turing instability and pattern formation mechanism of a plant-wrack model with both self-diffusion and cross-diffusion terms.We first study the effect of self-diffusion on the stability of equilibrium.We then derive the conditions for the occurrence of the Turing patterns induced by cross-diffusion based on self-diffusion stability.Next,we analyze the pattern selection by using the amplitude equation and obtain the exact parameter ranges of different types of patterns,including stripe patterns,hexagonal patterns and mixed states.Finally,numerical simulations confirm the theoretical results.展开更多
The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential condition...The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential conditions for Turing instability are obtained.It indicates that the emergence of cross-diffusion terms leads to the destabilizing mechanism.Then the amplitude equations and the asymptotic solutions of the model closed to the onset of instability are derived by using the weakly nonlinear analysis.展开更多
Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also sh...Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.展开更多
In this paper,we consider the positive steady state solutions of a predator-prey model with Holling type Ⅱfunctional response and cross-diffusion,where two cross-diffusion rates represent the tendency of prey to keep...In this paper,we consider the positive steady state solutions of a predator-prey model with Holling type Ⅱfunctional response and cross-diffusion,where two cross-diffusion rates represent the tendency of prey to keep away from its predator and the tendency of the predator to chase its prey,respectively.Applying the fixed point index theory,some sufficient conditions for the existence of positive steady state solutions are established.Furthermore,the non-existence of positive steady state solutions is studied.展开更多
Convolutional neural network(CNN)with the encoder-decoder structure is popular in medical image segmentation due to its excellent local feature extraction ability but it faces limitations in capturing the global featu...Convolutional neural network(CNN)with the encoder-decoder structure is popular in medical image segmentation due to its excellent local feature extraction ability but it faces limitations in capturing the global feature.The transformer can extract the global information well but adapting it to small medical datasets is challenging and its computational complexity can be heavy.In this work,a serial and parallel network is proposed for the accurate 3D medical image segmentation by combining CNN and transformer and promoting feature interactions across various semantic levels.The core components of the proposed method include the cross window self-attention based transformer(CWST)and multi-scale local enhanced(MLE)modules.The CWST module enhances the global context understanding by partitioning 3D images into non-overlapping windows and calculating sparse global attention between windows.The MLE module selectively fuses features by computing the voxel attention between different branch features,and uses convolution to strengthen the dense local information.The experiments on the prostate,atrium,and pancreas MR/CT image datasets consistently demonstrate the advantage of the proposed method over six popular segmentation models in both qualitative evaluation and quantitative indexes such as dice similarity coefficient,Intersection over Union,95%Hausdorff distance and average symmetric surface distance.展开更多
Second language(L2)motivation has been a topic which receives intensive attention.However,the peer effect on L2 motivation is insufficiently researched,although it is considered a crucial factor which may significantl...Second language(L2)motivation has been a topic which receives intensive attention.However,the peer effect on L2 motivation is insufficiently researched,although it is considered a crucial factor which may significantly mediate learners’L2 motivation.Hence,the current study adopted Dörnyei’s L2 Motivational Self System(L2MSS)as a theoretical framework and investigated in which specific aspects peers might affect the learners’L2 motivation and whether such effect was long-lasting.The research was designed as a small-scale qualitative study which was located in a language-focused experimental class project in China.Ten participants were recruited and individual interviews were conducted.The results demonstrated that,first,peers could remarkably influence the L2 motivation possessed by the students in the experimental class since they tended to create a clearer ideal L2 self and a more powerful ought-to L2 self.Second,although they had both positive and negative views towards the curriculum,a motivated peer climate could alleviate the pressure caused by the curriculum and reinforce positive attitudes.Third,such peer effect was not long-lasting.Based on the research results,pedagogical implications were proposed in terms of establishing a positive peer group and adjusting the emphasis of the curriculum.展开更多
In order to understand the transmission mechanism of West Nile virus(WNv)in birds(especially crows)and mosquitoes populations,this paper extends the traditional ordinary differential model of WNv to a reaction-diffusi...In order to understand the transmission mechanism of West Nile virus(WNv)in birds(especially crows)and mosquitoes populations,this paper extends the traditional ordinary differential model of WNv to a reaction-diffusion system with more complex cross-diffusion.We explore the relationship between the basic reproduction number and cross-diffusion coefficients involving various parameters,and investigate the effect of vertical transmission of the virus on the transmission mechanism.We use the method of upper and lower solutions to investigate the existence of the coexistence solutions.The theoretical analysis and numerical simulation show that the WNv carried by birds and mosquitoes will coexist when the low-risk threshold R0*≥1,which is a disadvantage to the prevention and control of this virus,and disappear when the high-risk threshold R*0≤1,which is an advantage to that.展开更多
Everyone is busy.But it's easy to be too busy.Then you may feel anxious or stressed.You need to take care of yourself.How can you do that?First,make time to text or call your family and friends.They care about you...Everyone is busy.But it's easy to be too busy.Then you may feel anxious or stressed.You need to take care of yourself.How can you do that?First,make time to text or call your family and friends.They care about you and can support you.Get regular exercise.展开更多
The meaning of growth is increasing experiences and self-improvement. No one’s life is always good, and many people have the power to change it but don’t take action. It’s better to change ourselves than to try to ...The meaning of growth is increasing experiences and self-improvement. No one’s life is always good, and many people have the power to change it but don’t take action. It’s better to change ourselves than to try to change the people and things around us.Self-improvement is very important. First, it helps us to become more confident. When we make progress, we will feel more confident. And this confidence will make us do more and do better.展开更多
Are you tred of regular selfies?Try a self-photo studio!The lights and camera are ready for you.At the studio,you can fix your hair.There are clothes and props.You can use those and take fun photos.Bring your friends ...Are you tred of regular selfies?Try a self-photo studio!The lights and camera are ready for you.At the studio,you can fix your hair.There are clothes and props.You can use those and take fun photos.Bring your friends with you.Then you can take photos together.Pose in silly ways and have fun!You can take the photos home and remember your good time.展开更多
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
基金Project supported by the National Natural Science Foundation of China (Grant No 60771026)Program for New Century Excellent Talents in University of China (Grant No NCET050271)the Special Scientific Research Foundation for the Subjects of Doctors in University of China (Grant No 20060110005)
文摘This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator-prey system.
基金Supported by the Fundamental Research Funds for the Central Universities SCUT(2009ZM0014)
文摘The prey-predator system of three species with cross-diffusion pressure is known to possess a local solution with the maximal existence time T ≤ ∞.By obtaining the bounds of W21-norms of the local solution independent of T,it is established the global existence of the solution.
基金National Natural Science Foundation of China(No.11571227)
文摘A chemostat model with maintenance energy and crossdiffusion is considered,and the formation of patterns is caused by the cross-diffusion. First, through linear stability analysis, the necessary conditions for the formation of the spatial patterns are given. Then numerical simulations by changing the values of crossdiffusions in the unstable domain are performed. The results showthat the cross-diffusion coefficient plays an important role in the formation of the pattern, and the different values of the crossdiffusion coefficients may lead to different types of pattern formation.
基金the National Natural Science Foundation of China(Grant Nos.10971009,11771033,and12201046)Fundamental Research Funds for the Central Universities(Grant No.BLX201925)China Postdoctoral Science Foundation(Grant No.2020M670175)。
文摘We investigate the Turing instability and pattern formation mechanism of a plant-wrack model with both self-diffusion and cross-diffusion terms.We first study the effect of self-diffusion on the stability of equilibrium.We then derive the conditions for the occurrence of the Turing patterns induced by cross-diffusion based on self-diffusion stability.Next,we analyze the pattern selection by using the amplitude equation and obtain the exact parameter ranges of different types of patterns,including stripe patterns,hexagonal patterns and mixed states.Finally,numerical simulations confirm the theoretical results.
基金National Natural Science Foundation of China(No.11371087)
文摘The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential conditions for Turing instability are obtained.It indicates that the emergence of cross-diffusion terms leads to the destabilizing mechanism.Then the amplitude equations and the asymptotic solutions of the model closed to the onset of instability are derived by using the weakly nonlinear analysis.
基金supported by the National Natural Science Foundation of China (Nos. 10701024, 10601011)
文摘Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.
基金Supported by the National Natural Science Foundation of China(Grant No.11761063).
文摘In this paper,we consider the positive steady state solutions of a predator-prey model with Holling type Ⅱfunctional response and cross-diffusion,where two cross-diffusion rates represent the tendency of prey to keep away from its predator and the tendency of the predator to chase its prey,respectively.Applying the fixed point index theory,some sufficient conditions for the existence of positive steady state solutions are established.Furthermore,the non-existence of positive steady state solutions is studied.
基金National Key Research and Development Program of China,Grant/Award Number:2018YFE0206900China Postdoctoral Science Foundation,Grant/Award Number:2023M731204+2 种基金The Open Project of Key Laboratory for Quality Evaluation of Ultrasound Surgical Equipment of National Medical Products Administration,Grant/Award Number:SMDTKL-2023-1-01The Hubei Province Key Research and Development Project,Grant/Award Number:2023BCB007CAAI-Huawei MindSpore Open Fund。
文摘Convolutional neural network(CNN)with the encoder-decoder structure is popular in medical image segmentation due to its excellent local feature extraction ability but it faces limitations in capturing the global feature.The transformer can extract the global information well but adapting it to small medical datasets is challenging and its computational complexity can be heavy.In this work,a serial and parallel network is proposed for the accurate 3D medical image segmentation by combining CNN and transformer and promoting feature interactions across various semantic levels.The core components of the proposed method include the cross window self-attention based transformer(CWST)and multi-scale local enhanced(MLE)modules.The CWST module enhances the global context understanding by partitioning 3D images into non-overlapping windows and calculating sparse global attention between windows.The MLE module selectively fuses features by computing the voxel attention between different branch features,and uses convolution to strengthen the dense local information.The experiments on the prostate,atrium,and pancreas MR/CT image datasets consistently demonstrate the advantage of the proposed method over six popular segmentation models in both qualitative evaluation and quantitative indexes such as dice similarity coefficient,Intersection over Union,95%Hausdorff distance and average symmetric surface distance.
文摘Second language(L2)motivation has been a topic which receives intensive attention.However,the peer effect on L2 motivation is insufficiently researched,although it is considered a crucial factor which may significantly mediate learners’L2 motivation.Hence,the current study adopted Dörnyei’s L2 Motivational Self System(L2MSS)as a theoretical framework and investigated in which specific aspects peers might affect the learners’L2 motivation and whether such effect was long-lasting.The research was designed as a small-scale qualitative study which was located in a language-focused experimental class project in China.Ten participants were recruited and individual interviews were conducted.The results demonstrated that,first,peers could remarkably influence the L2 motivation possessed by the students in the experimental class since they tended to create a clearer ideal L2 self and a more powerful ought-to L2 self.Second,although they had both positive and negative views towards the curriculum,a motivated peer climate could alleviate the pressure caused by the curriculum and reinforce positive attitudes.Third,such peer effect was not long-lasting.Based on the research results,pedagogical implications were proposed in terms of establishing a positive peer group and adjusting the emphasis of the curriculum.
基金Supported by the Anhui Province Graduate Education Quality Engineering Project(2022jyjxggyj168)Anhui Province Higher Education Provincial-Level Quality Engineering Major Project(2022jcbs020)Anhui Province Higher Education Provincial-Level Quality Engineering General Project(2022jyxm527).
文摘In order to understand the transmission mechanism of West Nile virus(WNv)in birds(especially crows)and mosquitoes populations,this paper extends the traditional ordinary differential model of WNv to a reaction-diffusion system with more complex cross-diffusion.We explore the relationship between the basic reproduction number and cross-diffusion coefficients involving various parameters,and investigate the effect of vertical transmission of the virus on the transmission mechanism.We use the method of upper and lower solutions to investigate the existence of the coexistence solutions.The theoretical analysis and numerical simulation show that the WNv carried by birds and mosquitoes will coexist when the low-risk threshold R0*≥1,which is a disadvantage to the prevention and control of this virus,and disappear when the high-risk threshold R*0≤1,which is an advantage to that.
文摘Everyone is busy.But it's easy to be too busy.Then you may feel anxious or stressed.You need to take care of yourself.How can you do that?First,make time to text or call your family and friends.They care about you and can support you.Get regular exercise.
文摘The meaning of growth is increasing experiences and self-improvement. No one’s life is always good, and many people have the power to change it but don’t take action. It’s better to change ourselves than to try to change the people and things around us.Self-improvement is very important. First, it helps us to become more confident. When we make progress, we will feel more confident. And this confidence will make us do more and do better.
文摘Are you tred of regular selfies?Try a self-photo studio!The lights and camera are ready for you.At the studio,you can fix your hair.There are clothes and props.You can use those and take fun photos.Bring your friends with you.Then you can take photos together.Pose in silly ways and have fun!You can take the photos home and remember your good time.
