In permafrost regions with warm frozen soil,subgrade thaw-collapse phenomenon commonly occurs,facing thaw collapse problems of the existed frozen soil subgrade,thus it is difficult to use traditional methods such as a...In permafrost regions with warm frozen soil,subgrade thaw-collapse phenomenon commonly occurs,facing thaw collapse problems of the existed frozen soil subgrade,thus it is difficult to use traditional methods such as active cooling and passive protection technology to stabilize the existed warm frozen soil subgrade.This study derives a novel stabilizer method,a long-short(L-S)cement-mixed batter pile composite foundation to stabilize the existed warm frozen soil subgrade.To solve the thawcollapse problems in warm frozen soil subgrade,high water content and large compressibility characteristics were compared between soft soil and warm frozen soils.Theoretical analysis of heat conduction and numerical simulation of finite element model were used to study the freeze–thaw process and evaluate the stabilized effects of the L-S cement-mixed batter piles on the warm frozen soil foundation of the Qinghai-Xizang Highway.Furthermore,the thaw process and mechanical properties of foundation and piles were analyzed by introducing the hydration heat factor in the thermodynamic control equation.The results indicate that the thawing displacement of the existed warm frozen soil subgrade was reduced owing to the“support”and“grasp”effects of the L-S cement-mixed batter piles on the surrounding soil.The composite ground formed by strengthening the warm frozen ground with batter piles could considerably improve the bearing capacity of the existed warm frozen ground,effectively restrain the deformation of the upper embankment,and improve the strength of the ground.The analysis can provide method for the construction design of cement mixing batter pile foundation in cold regions.展开更多
Over the next 20 years,China's urban rail transit(hereinafter referred to as'urban rail')will face large-scalerenovation of existing line facilities and equipment,with more than 1000 km of renovated lines ...Over the next 20 years,China's urban rail transit(hereinafter referred to as'urban rail')will face large-scalerenovation of existing line facilities and equipment,with more than 1000 km of renovated lines to be added eachyear.In 2024,the China Association of Metros issued the Guiding Opinions on the Renovation of Existing UrbanRail Transit Lines in China,providing guiding opinions on norms,standards,and implementation approaches forthe renovation of existing lines in the coming period.In the practical work of renovating existing urban rail lines,it is necessary to continuously explore and refine relevant theoretical methods in line with industry developmenttrends and urban development requirements.The following are the author's recent reflections on theoreticalinnovation in this field.展开更多
The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield...The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield tunneling remains inadequate.The analytical solution for calculating the deformation of the ground and existing tunnel induced by overlapped curved shield tunneling is derived by the Mirror theory,Mindlin solution and Euler-Bernoulli-Pasternak model,subsequently validated through both finite element simulation and field monitoring.It is determined that the overcutting plays a crucial role in the ground settlement resulting from curved shield tunneling compared to straight shield tunneling.The longitudinal settlement distribution can be categorized into five areas,with the area near the tunnel surface experiencing the most dramatic settlement changes.The deformation of the existing tunnel varies most significantly with turning radius compared to tunnel clearance and grouting pressure,especially when the turning radius is less than 30 times the tunnel diameter.The tunnel crown exhibits larger displacement than the tunnel bottom,resulting in a distinctive‘vertical egg'shape.Furthermore,an optimized overcutting mode is proposed,involving precise control of the extension speed and angular velocity of the overcutting cutter,which effectively mitigates ground deformation,ensuring the protection of the existing tunnel during the construction.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
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contr...In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contribution,we establish non-negativity,boundedness of some solution components,existence globally in time,and uniqueness on a time interval[0,T]for an arbitrary T>0 for the time-continuous problem which extends known results of Kirschner’s model in the literature.As our second analytical result,we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question.Our third contribution is the formulation of a non-standard finite-difference method which preserves non-negativity,boundedness of some time-discrete solution components,equilibria,and their stabilities.As our final theoretical result,we prove linear convergence of our non-standard finite-difference-formulation towards the time-continuous solution.Conclusively,we present numerical examples to illustrate our theoretical findings.展开更多
Objective:To explore symptom experiences and self-coping patterns during the early and late stages of chemotherapy in these patients to provide a basis for developing targeted symptom management strategies.Methods:A t...Objective:To explore symptom experiences and self-coping patterns during the early and late stages of chemotherapy in these patients to provide a basis for developing targeted symptom management strategies.Methods:A total of 27 patients with pancreatic cancer undergoing chemotherapy at two medical institutions were recruited between November 2023 and August 2024.Semi-structured interviews were conducted in person or over the phone.Data were analyzed using traditional content and thematic analyses.Results:Three themes were identified:symptom experience,self-coping patterns,and existing obstacles.During the early stages of chemotherapy,patients reported a higher frequency of unpleasant symptoms and recognized these symptoms earlier in the treatment course.Patients in the early stages primarily relied on external support to cope with symptoms,while those in the later stages adopted self-care strategies.Several challenges related to unpleasant symptoms were observed,which appeared to correlate with the self-coping patterns employed.Conclusion:Patients with pancreatic cancer undergoing chemotherapy experience a complex and diverse range of symptoms,with varying coping patterns at different stages of treatment.Symptom management during chemotherapy presents significant challenges.Healthcare providers should improve the ongoing monitoring of symptoms post-chemotherapy.By linking patients’symptom experiences and self-coping patterns at different stages of chemotherapy to their specific challenges,personalized symptom management strategies can be developed to enhance care quality.展开更多
This paper proposes a mixed game with finitely many leaders and follower populations.In such a game,two types of equilibria are defined.First,a Nash equilibrium is introduced for the scenario in which leaders and foll...This paper proposes a mixed game with finitely many leaders and follower populations.In such a game,two types of equilibria are defined.First,a Nash equilibrium is introduced for the scenario in which leaders and follower populations are in perfect competition,each maximizing its own payoff.Second,a cooperative equilibrium is proposed for the case where leaders and follower populations,respectively,form coalitions and cooperate.Moreover,the existence of both Nash and cooperative equilibria is proved under the condition that the payoff functions are continuous and quasi-concave.Finally,we demonstrate the generic stability of cooperative equilibria in mixed games.More concretely,in the sense of Baire category,the cooperative equilibria in most mixed games are stable under perturbations of the payoff functions.In short,this paper presents two main contributions.On the one hand,we provide a novel mixed-game framework,which differs from both classical leader-follower games and leader-follower population games.On the other hand,the Nash and cooperative equilibria in our mixed games are distinct from those in existing leader-follower population games.The results are further illustrated with examples.展开更多
In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function i...In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.展开更多
The construction of the new tunnel under the existing railway will break the original stress balance in the engineering area, resulting in the secondary redistribution of surrounding rock stress. The large amount of e...The construction of the new tunnel under the existing railway will break the original stress balance in the engineering area, resulting in the secondary redistribution of surrounding rock stress. The large amount of excavation unloading of the soil below is also easy to induce the uneven settlement deformation of the existing structure above, affecting the safety of driving. Based on the shield tunnel project between Caoqiao Station and Lize Business District Station of Beijing Metro, this paper restores the construction site by constructing the finite element numerical model of the project area, calculates and analyzes the deformation and stress of the existing railway structure before and after the construction of the tunnel, and determines the safety impact of the new structure on the existing railway. The results show that the shield tunnel undercrossing construction will cause the “concave” settlement of the railway subgrade above. Under the condition of grouting reinforcement, the “concave” settlement curve is slower and the distribution range is wider. With the advancement of the construction step, the settlement deformation of the subgrade gradually increases. When the tunnel approaches and passes directly below the subgrade, the settlement deformation curve of the subgrade changes from slow to steep. After the tunnel passes away, the curve changes from steep to slow, and the deformation of the subgrade reaches the maximum after the tunnel is connected. Under the grouting condition, the maximum settlement deformation of the subgrade is 2.08 mm, which is about 45% of the settlement deformation of the subgrade under the non-grouting condition. The ground grouting reinforcement can effectively control the subgrade settlement, and the field monitoring verifies the rationality of the calculation results. After the tunnel passes underneath, the most unfavorable section of the existing railway frame bridge is located at the top plate of the structure, and the maximum crack width is 0.178 mm. After grouting reinforcement, the stress environment of the structure is improved, the crack width generated by the structure is smaller, the reinforcement area required for calculation is less, and the structural safety meets the requirements.展开更多
As an integral part of China’s higher education system,higher vocational colleges play a significant role in talent cultivation,social services,and cultural inheritance.With the development of the times and the advan...As an integral part of China’s higher education system,higher vocational colleges play a significant role in talent cultivation,social services,and cultural inheritance.With the development of the times and the advancement of educational reform,the role of scientific research in higher vocational colleges has become increasingly prominent.This paper started from the necessity of conducting scientific research in higher vocational colleges,providing an in-depth analysis of its importance in improving teaching quality,promoting teachers’professional development,driving social services,and enhancing the college’s core competitiveness.At the same time,addressing the existing problems in current scientific research work at higher vocational colleges,this paper proposed innovative pathways focusing on the scientific research management system,scientific research team construction,scientific research funding investment,and scientific research outcome transformation.The aim is to provide valuable references for the scientific research development of higher vocational colleges.展开更多
In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperat...In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.展开更多
In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a b...In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.展开更多
We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navi...We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navier-Stokes equations for(ρ,u)through a drag force term n(w−u).We prove the global existence of strong solutions to the coupled system when the initial data are small perturbations of the constant equilibrium state.However,due to the pressureless structure,one can only deal with the density n of the pressureless flow through the transport equation and it is crucial to obtain the exact time-decay rates for the corresponding velocity w of the pressureless flow.To this end,we make use of the spectral analysis,low-high frequency decomposition and time-weighted energy method to deduce the large time behavior of(w,ρ,u)and consequently establish the Lyapunov stability of the density n in Sobolev space.展开更多
In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as ...In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as well as the global existence of small data weak solution u when the nonlinearity power p is larger than some critical power p_(crit)(μ).Our proof is based on a class of new weighted Strichartz estimates with the weight t^(θ)|(1-μ)^(2)t^(2/|1-μ|)-x^(2)|^(γ)(θ>0andγ>0 are appropriate constants)for the solution of linear generalized Tricomi equation∂_(t)^(2)φ-t^(m)∂_(x)^(2)φ=0 with m being any fixed positive number.展开更多
In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying ...In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying an appropriate fixed point theorem and Lyapunov functional method.Finally,a numerical example with simulation is given to illuminate our theoretical results.展开更多
In recent years,to better address soil erosion,the Loess Plateau area has seen a surge in the construction of warping dam projects.Warping dams have strong functions in soil and water conservation as well as warping f...In recent years,to better address soil erosion,the Loess Plateau area has seen a surge in the construction of warping dam projects.Warping dams have strong functions in soil and water conservation as well as warping for farmland creation,serving as a key support for ecological restoration and economic development in the Loess Plateau area in the new era.However,in light of practical conditions,there are many problems in their construction process,which have affected their actual operation quality.In this regard,while expounding on the value and significance of warping dam project construction in the Loess Plateau area,this paper discusses the existing problems and effective countermeasures,aiming to provide some references for relevant personnel.展开更多
In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)deriva...In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.展开更多
The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No.3 is“Good Health and Well-being”,which mainly emphasizes the strategies to be a...The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No.3 is“Good Health and Well-being”,which mainly emphasizes the strategies to be adopted for maintaining a healthy life.The Monkeypox Virus disease was first reported in 1970.Since then,various health initiatives have been taken,including by the WHO.In the present work,we attempt a fractional model of Monkeypox virus disease,which we feel is crucial for a better understanding of this disease.We use the recently introduced ABC fractional derivative to closely examine the Monkeypox virus disease model.The evaluation of this model determines the existence of two equilibrium states.These two stable points exist within the model and include a disease-free equilibrium and endemic equilibrium.The disease-free equilibrium has undergone proof to demonstrate its stability properties.The system remains stable locally and globally whenever the effective reproduction number remains below one.The effective reproduction number becoming greater than unity makes the endemic equilibrium more stable both globally and locally than unity.To comprehensively study the model’s solutions,we employ the Picard-Lindelof approach to investigate their existence and uniqueness.We investigate the Ulam-Hyers and UlamHyers Rassias stability of the fractional order nonlinear framework for the Monkeypox virus disease model.Furthermore,the approximate solutions of the ABC fractional order Monkeypox virus disease model are obtained with the help of a numerical technique combining the Lagrange polynomial interpolation and fundamental theorem of fractional calculus with the ABC fractional derivative.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.41971086)Natural Science Foundation of Shanxi Province(Grant No.2023-JC-QN-0626,2022JQ-467).
文摘In permafrost regions with warm frozen soil,subgrade thaw-collapse phenomenon commonly occurs,facing thaw collapse problems of the existed frozen soil subgrade,thus it is difficult to use traditional methods such as active cooling and passive protection technology to stabilize the existed warm frozen soil subgrade.This study derives a novel stabilizer method,a long-short(L-S)cement-mixed batter pile composite foundation to stabilize the existed warm frozen soil subgrade.To solve the thawcollapse problems in warm frozen soil subgrade,high water content and large compressibility characteristics were compared between soft soil and warm frozen soils.Theoretical analysis of heat conduction and numerical simulation of finite element model were used to study the freeze–thaw process and evaluate the stabilized effects of the L-S cement-mixed batter piles on the warm frozen soil foundation of the Qinghai-Xizang Highway.Furthermore,the thaw process and mechanical properties of foundation and piles were analyzed by introducing the hydration heat factor in the thermodynamic control equation.The results indicate that the thawing displacement of the existed warm frozen soil subgrade was reduced owing to the“support”and“grasp”effects of the L-S cement-mixed batter piles on the surrounding soil.The composite ground formed by strengthening the warm frozen ground with batter piles could considerably improve the bearing capacity of the existed warm frozen ground,effectively restrain the deformation of the upper embankment,and improve the strength of the ground.The analysis can provide method for the construction design of cement mixing batter pile foundation in cold regions.
文摘Over the next 20 years,China's urban rail transit(hereinafter referred to as'urban rail')will face large-scalerenovation of existing line facilities and equipment,with more than 1000 km of renovated lines to be added eachyear.In 2024,the China Association of Metros issued the Guiding Opinions on the Renovation of Existing UrbanRail Transit Lines in China,providing guiding opinions on norms,standards,and implementation approaches forthe renovation of existing lines in the coming period.In the practical work of renovating existing urban rail lines,it is necessary to continuously explore and refine relevant theoretical methods in line with industry developmenttrends and urban development requirements.The following are the author's recent reflections on theoreticalinnovation in this field.
基金financially supported by the National Natural Science Foundation of China(Grant No.52078334)the National Key Research and Development Program of China(Grant No.2017YFC0805402)the Tianjin Research Innovation Project for Postgraduate Students(Grant No.2021YJSB141).
文摘The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield tunneling remains inadequate.The analytical solution for calculating the deformation of the ground and existing tunnel induced by overlapped curved shield tunneling is derived by the Mirror theory,Mindlin solution and Euler-Bernoulli-Pasternak model,subsequently validated through both finite element simulation and field monitoring.It is determined that the overcutting plays a crucial role in the ground settlement resulting from curved shield tunneling compared to straight shield tunneling.The longitudinal settlement distribution can be categorized into five areas,with the area near the tunnel surface experiencing the most dramatic settlement changes.The deformation of the existing tunnel varies most significantly with turning radius compared to tunnel clearance and grouting pressure,especially when the turning radius is less than 30 times the tunnel diameter.The tunnel crown exhibits larger displacement than the tunnel bottom,resulting in a distinctive‘vertical egg'shape.Furthermore,an optimized overcutting mode is proposed,involving precise control of the extension speed and angular velocity of the overcutting cutter,which effectively mitigates ground deformation,ensuring the protection of the existing tunnel during the construction.
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.
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
文摘In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contribution,we establish non-negativity,boundedness of some solution components,existence globally in time,and uniqueness on a time interval[0,T]for an arbitrary T>0 for the time-continuous problem which extends known results of Kirschner’s model in the literature.As our second analytical result,we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question.Our third contribution is the formulation of a non-standard finite-difference method which preserves non-negativity,boundedness of some time-discrete solution components,equilibria,and their stabilities.As our final theoretical result,we prove linear convergence of our non-standard finite-difference-formulation towards the time-continuous solution.Conclusively,we present numerical examples to illustrate our theoretical findings.
基金supported by the State Key Laboratory of Ultrasonic Medical Engineering/the Chongqing Science and Technology Bureau(Project No.2022KFKT7011)the Postdoctoral Fellowship Program of CPSF(GZC20233357)+1 种基金the Health Commission of Sichuan Province Medical Science and Technology Program(24QNMP007)the Medical Research Program of Health Commission of Chengdu(2023535).
文摘Objective:To explore symptom experiences and self-coping patterns during the early and late stages of chemotherapy in these patients to provide a basis for developing targeted symptom management strategies.Methods:A total of 27 patients with pancreatic cancer undergoing chemotherapy at two medical institutions were recruited between November 2023 and August 2024.Semi-structured interviews were conducted in person or over the phone.Data were analyzed using traditional content and thematic analyses.Results:Three themes were identified:symptom experience,self-coping patterns,and existing obstacles.During the early stages of chemotherapy,patients reported a higher frequency of unpleasant symptoms and recognized these symptoms earlier in the treatment course.Patients in the early stages primarily relied on external support to cope with symptoms,while those in the later stages adopted self-care strategies.Several challenges related to unpleasant symptoms were observed,which appeared to correlate with the self-coping patterns employed.Conclusion:Patients with pancreatic cancer undergoing chemotherapy experience a complex and diverse range of symptoms,with varying coping patterns at different stages of treatment.Symptom management during chemotherapy presents significant challenges.Healthcare providers should improve the ongoing monitoring of symptoms post-chemotherapy.By linking patients’symptom experiences and self-coping patterns at different stages of chemotherapy to their specific challenges,personalized symptom management strategies can be developed to enhance care quality.
基金supported by the National Natural Science Foundation of China(Grant No.11271098)the Guizhou Provincial Basic Research Program(Grant No.MS[2025]676)。
文摘This paper proposes a mixed game with finitely many leaders and follower populations.In such a game,two types of equilibria are defined.First,a Nash equilibrium is introduced for the scenario in which leaders and follower populations are in perfect competition,each maximizing its own payoff.Second,a cooperative equilibrium is proposed for the case where leaders and follower populations,respectively,form coalitions and cooperate.Moreover,the existence of both Nash and cooperative equilibria is proved under the condition that the payoff functions are continuous and quasi-concave.Finally,we demonstrate the generic stability of cooperative equilibria in mixed games.More concretely,in the sense of Baire category,the cooperative equilibria in most mixed games are stable under perturbations of the payoff functions.In short,this paper presents two main contributions.On the one hand,we provide a novel mixed-game framework,which differs from both classical leader-follower games and leader-follower population games.On the other hand,the Nash and cooperative equilibria in our mixed games are distinct from those in existing leader-follower population games.The results are further illustrated with examples.
文摘In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.
文摘The construction of the new tunnel under the existing railway will break the original stress balance in the engineering area, resulting in the secondary redistribution of surrounding rock stress. The large amount of excavation unloading of the soil below is also easy to induce the uneven settlement deformation of the existing structure above, affecting the safety of driving. Based on the shield tunnel project between Caoqiao Station and Lize Business District Station of Beijing Metro, this paper restores the construction site by constructing the finite element numerical model of the project area, calculates and analyzes the deformation and stress of the existing railway structure before and after the construction of the tunnel, and determines the safety impact of the new structure on the existing railway. The results show that the shield tunnel undercrossing construction will cause the “concave” settlement of the railway subgrade above. Under the condition of grouting reinforcement, the “concave” settlement curve is slower and the distribution range is wider. With the advancement of the construction step, the settlement deformation of the subgrade gradually increases. When the tunnel approaches and passes directly below the subgrade, the settlement deformation curve of the subgrade changes from slow to steep. After the tunnel passes away, the curve changes from steep to slow, and the deformation of the subgrade reaches the maximum after the tunnel is connected. Under the grouting condition, the maximum settlement deformation of the subgrade is 2.08 mm, which is about 45% of the settlement deformation of the subgrade under the non-grouting condition. The ground grouting reinforcement can effectively control the subgrade settlement, and the field monitoring verifies the rationality of the calculation results. After the tunnel passes underneath, the most unfavorable section of the existing railway frame bridge is located at the top plate of the structure, and the maximum crack width is 0.178 mm. After grouting reinforcement, the stress environment of the structure is improved, the crack width generated by the structure is smaller, the reinforcement area required for calculation is less, and the structural safety meets the requirements.
文摘As an integral part of China’s higher education system,higher vocational colleges play a significant role in talent cultivation,social services,and cultural inheritance.With the development of the times and the advancement of educational reform,the role of scientific research in higher vocational colleges has become increasingly prominent.This paper started from the necessity of conducting scientific research in higher vocational colleges,providing an in-depth analysis of its importance in improving teaching quality,promoting teachers’professional development,driving social services,and enhancing the college’s core competitiveness.At the same time,addressing the existing problems in current scientific research work at higher vocational colleges,this paper proposed innovative pathways focusing on the scientific research management system,scientific research team construction,scientific research funding investment,and scientific research outcome transformation.The aim is to provide valuable references for the scientific research development of higher vocational colleges.
基金supported by the National Natural Science Foundation of China(No.11931013)the Natural Science Foundation of Guangxi Province(No.2022GXNSFDA035078)the Foundamental Research Funds for the Central Universities,CHD(No.300102122115).
文摘In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.
基金supported by the Key Project of the NSFC(12131010)the NSFC(12271032)+2 种基金supported by the NSFC(12371205)the NSF of Guangdong Province(2025A1515012026)supported by the NSF of Guangdong Province(2024A1515013238)。
文摘In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.
基金supported by the National Natural Science Foundation of China(11931010,12226326,12226327)the Key Research Project of Academy for Multidisciplinary Studies,Capital Normal Universitysupported by the Anhui Provincial Natural Science Foundation(2408085QA031).
文摘We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navier-Stokes equations for(ρ,u)through a drag force term n(w−u).We prove the global existence of strong solutions to the coupled system when the initial data are small perturbations of the constant equilibrium state.However,due to the pressureless structure,one can only deal with the density n of the pressureless flow through the transport equation and it is crucial to obtain the exact time-decay rates for the corresponding velocity w of the pressureless flow.To this end,we make use of the spectral analysis,low-high frequency decomposition and time-weighted energy method to deduce the large time behavior of(w,ρ,u)and consequently establish the Lyapunov stability of the density n in Sobolev space.
基金supported by the NSFC(12331007)the National Key Research and Development Program of China(2020YFA0713803)。
文摘In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as well as the global existence of small data weak solution u when the nonlinearity power p is larger than some critical power p_(crit)(μ).Our proof is based on a class of new weighted Strichartz estimates with the weight t^(θ)|(1-μ)^(2)t^(2/|1-μ|)-x^(2)|^(γ)(θ>0andγ>0 are appropriate constants)for the solution of linear generalized Tricomi equation∂_(t)^(2)φ-t^(m)∂_(x)^(2)φ=0 with m being any fixed positive number.
文摘In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying an appropriate fixed point theorem and Lyapunov functional method.Finally,a numerical example with simulation is given to illuminate our theoretical results.
文摘In recent years,to better address soil erosion,the Loess Plateau area has seen a surge in the construction of warping dam projects.Warping dams have strong functions in soil and water conservation as well as warping for farmland creation,serving as a key support for ecological restoration and economic development in the Loess Plateau area in the new era.However,in light of practical conditions,there are many problems in their construction process,which have affected their actual operation quality.In this regard,while expounding on the value and significance of warping dam project construction in the Loess Plateau area,this paper discusses the existing problems and effective countermeasures,aiming to provide some references for relevant personnel.
基金extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/174/46.
文摘In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.
基金sponsored by Prince Sattam Bin Abulaziz University(PSAU)as part of funding for its SDG Roadmap Research Funding Programme Project Number PSAU-2023-SDG-107.
文摘The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No.3 is“Good Health and Well-being”,which mainly emphasizes the strategies to be adopted for maintaining a healthy life.The Monkeypox Virus disease was first reported in 1970.Since then,various health initiatives have been taken,including by the WHO.In the present work,we attempt a fractional model of Monkeypox virus disease,which we feel is crucial for a better understanding of this disease.We use the recently introduced ABC fractional derivative to closely examine the Monkeypox virus disease model.The evaluation of this model determines the existence of two equilibrium states.These two stable points exist within the model and include a disease-free equilibrium and endemic equilibrium.The disease-free equilibrium has undergone proof to demonstrate its stability properties.The system remains stable locally and globally whenever the effective reproduction number remains below one.The effective reproduction number becoming greater than unity makes the endemic equilibrium more stable both globally and locally than unity.To comprehensively study the model’s solutions,we employ the Picard-Lindelof approach to investigate their existence and uniqueness.We investigate the Ulam-Hyers and UlamHyers Rassias stability of the fractional order nonlinear framework for the Monkeypox virus disease model.Furthermore,the approximate solutions of the ABC fractional order Monkeypox virus disease model are obtained with the help of a numerical technique combining the Lagrange polynomial interpolation and fundamental theorem of fractional calculus with the ABC fractional derivative.
