This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invarianee of some sets under the ...The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invarianee of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of solutions are given. Finally, the problem with critical initial conditions are discussed.展开更多
This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate ...This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.展开更多
In this article,we deal with the blow-up phenomenon of a pseudo-parabolic equation with memory and convection terms.By constructing some appropriate auxiliary functions and using the modified concavity method,the blow...In this article,we deal with the blow-up phenomenon of a pseudo-parabolic equation with memory and convection terms.By constructing some appropriate auxiliary functions and using the modified concavity method,the blow-up criterion of the weak solution is given.展开更多
A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary ...A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.展开更多
Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission i...Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission is investigated.We aim to study the existence,nonexistence and minimum wave speed of traveling wave solutions to the model.The results show that the existence and nonexistence of traveling wave solutions are fully determined by the threshold values,which are,the basic reproduction number R0 and critical wave speed c^(*)>0.Specifically,when R0>1 and the wave speed c≥c^(*),the existence of the traveling wave solution is obtained by using Schauder's fixed point theorem and Lyapunov functional.It is proven that the model has no nontrivial traveling wave solutions for R0≤1 or R0>1 and 0<c<c^(*)by employing comparison principle and limit theory.As a consequence,we conclude that the critical wave speed c^(*)is the minimum wave speed of the model.Finally,numerical simulations are carried out to illustrate the effects of several important parameters on the minimum wave speed.展开更多
In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Bot...In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous.We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise.The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method.展开更多
This article aims to analyze the repercussions of food trade between China and various regions of the world to understand the dynamics of food flows and offer a novel perspective on the contemporary globalization proc...This article aims to analyze the repercussions of food trade between China and various regions of the world to understand the dynamics of food flows and offer a novel perspective on the contemporary globalization process.Understanding these flows involves analyzing the global production and commercialization of food and the effects of these movements on exporting and importing countries in economic terms and food security.The concept of unequal caloric exchange is applied to the case of China,which allows for an understanding of how its economic growth and participation in international trade have transformed its global and internal commercial dynamics by establishing links with self-sufficiency and the composition of its population’s diet.The results show that China is increasingly dependent on international markets for its food supply.From 1961 to 2021,food consumption in China has tripled in calories and experienced qualitative changes,with a reduction in high-quality carbohydrates and vegetable proteins and an increase in cereals,vegetable oils,alcohol,and vegetables.This dietary transformation is related to economic growth and greater dependence on international trade.From 1987 to 2022,China has shown a growing deficit in the food trade balance,with imports exceeding exports in volume,value,and calories,although it maintains favorable terms of trade.Food self-sufficiency has decreased from 95%in 1961 to 76%in 2022,and the diet has diversified,replacing traditional foods with products demanded in international trade.展开更多
In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof ar...In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .展开更多
This study investigates translation strategies for Chinese cultural terms in academic texts through a case study of Chapter 7 from“Jade Myth Belief and Chinese Spirit”.Using a qualitative research approach based on ...This study investigates translation strategies for Chinese cultural terms in academic texts through a case study of Chapter 7 from“Jade Myth Belief and Chinese Spirit”.Using a qualitative research approach based on cultural context framework and cognitive model,the study analyzes translation challenges and solutions in rendering cultural terms related to jade mythology and archaeological concepts.The research identifies three primary translation strategies:transliteration with annotation,domestication with explanation,and cognitive-based translation.The findings reveal that effective translation requires a balanced approach between maintaining academic precision and preserving cultural authenticity.The study demonstrates that successful translation of cultural terms in academic contexts demands a sophisticated understanding of both source and target cultural contexts,along with careful consideration of the academic audience’s needs.This research contributes to the field by providing practical insights for translators working with Chinese cultural texts in academic settings and proposing an approach to handling complex cultural terminology.展开更多
It is well known that the A-square term must be considered in both cavity and circuit quantum electrodynamics systems,because it arises in the derivation from the minimal coupling Hamiltonian at any finite coupling st...It is well known that the A-square term must be considered in both cavity and circuit quantum electrodynamics systems,because it arises in the derivation from the minimal coupling Hamiltonian at any finite coupling strength.In this paper,we study the quantum Rabi model with A-square terms using the Bogoliubov operator approach.After a unitary transformation,the A-square terms can be eliminated,resulting in a modified quantum Rabi model with renormalized parameters.A transcendental function responsible for the exact solution is then derived.The presence of the A-square terms is found to significantly alter the energy spectrum.The dynamics are also studied using the obtained exact wave function,which is sensitive to the strength of the A-square terms at strong coupling.We believe that these results could be observed in future light–matter interaction systems in the ultra-strong and deep strong coupling regimes.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 different languages and cultures, color terms usually indicate their specific cultural concepts and metaphorical implicature. This paper makes a typological study on the universality and relativity of the Conceptua...In different languages and cultures, color terms usually indicate their specific cultural concepts and metaphorical implicature. This paper makes a typological study on the universality and relativity of the Conceptual Metaphors （CM） of color terms in different languages. It attempts to explore the cognitive differences and similarities in the process of categorization and metaphorization of color terms of oriental and western peoples. It proposes that the CM system of color terms is determined by the interactivity of three factors as neurophysiologic mechanisms, general cognitive psychological mechanisms and socio-cultural selective mechanisms. The CM of color terms in different languages carry their specific cognitive characteristics and cultural values, and reflect self-similarity of the language and culture.展开更多
An excellent translation of proprietary business brand terms is more important in international trade.Diverse cultural backgrounds and purposiveness of products are the most influential factors.The research tries to a...An excellent translation of proprietary business brand terms is more important in international trade.Diverse cultural backgrounds and purposiveness of products are the most influential factors.The research tries to analyze the elements of cultural background and aims of products that affect E-C translation of proprietary business brand terms by descriptive study method and experience summary method,and then to provide methods to overcome these difficulties.展开更多
Within the scope of human beings, some addressing terms are similar. However, different addressing terms still exist,which are influenced by the background of high context communication or low context communication. A...Within the scope of human beings, some addressing terms are similar. However, different addressing terms still exist,which are influenced by the background of high context communication or low context communication. A good example is that Chinese traditional culture, a typical instance of high context communication, puts much emphasis on etiquette, which is represented in addressing terms as more complex and definite; In western, with the background of low context communication, every individual is more equal and they address each other more generally and much simpler. This paper tries to explore the addressing terms both in Chinese and in English from the perspective of frame theory.展开更多
The Holy Bible,as one of major sources of Western Culture,has a great influence on the Christian culture and Christian thoughts.Because language is a carrier of culture,the English study will be water without a source...The Holy Bible,as one of major sources of Western Culture,has a great influence on the Christian culture and Christian thoughts.Because language is a carrier of culture,the English study will be water without a source and a tree without roots if we ignore The Holy Bible which is the core of Christianity.To study English demands not only grammar and vocabulary,but also the culture behind the language.A brief analysis of connotative meanings of color terms,which are influenced by The Holy Bible and applied in literatures,will be given,in order to offer some help to English learners to know the connotations of color terms better,to understand literatures more profoundly and to have a general feeling about the impact which The Holy Bible has on language.展开更多
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
基金the National Natural Science Foundation of China(No.10271034)the Basic Research Foundation of Harbin Engineering University(No.HEUF04012)
文摘The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invarianee of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of solutions are given. Finally, the problem with critical initial conditions are discussed.
基金supported by the National Natural Science Foundation of China(No.12271399)the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.
基金Supported by Scientific Research Fund of Hunan Provincial Education Department(23A0361)。
文摘In this article,we deal with the blow-up phenomenon of a pseudo-parabolic equation with memory and convection terms.By constructing some appropriate auxiliary functions and using the modified concavity method,the blow-up criterion of the weak solution is given.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12275065,12275064,12475203)the Natural Science Foundation of Hebei Province(Grant Nos.A2021201010 and A2024201020)+3 种基金Interdisciplinary Research Program of Natural Science of Hebei University(Grant No.DXK202108)Hebei Provincial Central Government Guiding Local Science and Technology Development Funds(Grant No.236Z1501G)Scientific Research and Innovation Team Foundation of Hebei University(Grant No.IT2023B03)the Excellent Youth Research Innovation Team of Hebei University(Grant No.QNTD202402)。
文摘A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.
基金supported by the National Natural Science Foundation of China(12271317,11871316)。
文摘Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission is investigated.We aim to study the existence,nonexistence and minimum wave speed of traveling wave solutions to the model.The results show that the existence and nonexistence of traveling wave solutions are fully determined by the threshold values,which are,the basic reproduction number R0 and critical wave speed c^(*)>0.Specifically,when R0>1 and the wave speed c≥c^(*),the existence of the traveling wave solution is obtained by using Schauder's fixed point theorem and Lyapunov functional.It is proven that the model has no nontrivial traveling wave solutions for R0≤1 or R0>1 and 0<c<c^(*)by employing comparison principle and limit theory.As a consequence,we conclude that the critical wave speed c^(*)is the minimum wave speed of the model.Finally,numerical simulations are carried out to illustrate the effects of several important parameters on the minimum wave speed.
文摘In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous.We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise.The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method.
基金supported by the Government of Catalonia,and the ETOS project(TED2021-132032A-I00)supported by the Spanish Ministry of Science and Innovation.
文摘This article aims to analyze the repercussions of food trade between China and various regions of the world to understand the dynamics of food flows and offer a novel perspective on the contemporary globalization process.Understanding these flows involves analyzing the global production and commercialization of food and the effects of these movements on exporting and importing countries in economic terms and food security.The concept of unequal caloric exchange is applied to the case of China,which allows for an understanding of how its economic growth and participation in international trade have transformed its global and internal commercial dynamics by establishing links with self-sufficiency and the composition of its population’s diet.The results show that China is increasingly dependent on international markets for its food supply.From 1961 to 2021,food consumption in China has tripled in calories and experienced qualitative changes,with a reduction in high-quality carbohydrates and vegetable proteins and an increase in cereals,vegetable oils,alcohol,and vegetables.This dietary transformation is related to economic growth and greater dependence on international trade.From 1987 to 2022,China has shown a growing deficit in the food trade balance,with imports exceeding exports in volume,value,and calories,although it maintains favorable terms of trade.Food self-sufficiency has decreased from 95%in 1961 to 76%in 2022,and the diet has diversified,replacing traditional foods with products demanded in international trade.
基金supported by the NSFC(12271141)supported by the Fundamental Research Funds for the Central Universities(B240205026)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX24_0821).
文摘In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .
基金sponsored by the Humanities and Social Sciences Project of the Ministry of Education under Grant No.24YJCZH443Shanghai Philosophy and Social Science Planning Project under Grant No.2024EYY015Shanghai Municipal Philosophy and Social Sciences Planning Project under Grant No.2024EYY011.
文摘This study investigates translation strategies for Chinese cultural terms in academic texts through a case study of Chapter 7 from“Jade Myth Belief and Chinese Spirit”.Using a qualitative research approach based on cultural context framework and cognitive model,the study analyzes translation challenges and solutions in rendering cultural terms related to jade mythology and archaeological concepts.The research identifies three primary translation strategies:transliteration with annotation,domestication with explanation,and cognitive-based translation.The findings reveal that effective translation requires a balanced approach between maintaining academic precision and preserving cultural authenticity.The study demonstrates that successful translation of cultural terms in academic contexts demands a sophisticated understanding of both source and target cultural contexts,along with careful consideration of the academic audience’s needs.This research contributes to the field by providing practical insights for translators working with Chinese cultural texts in academic settings and proposing an approach to handling complex cultural terminology.
基金supported by the National Science Foundation of China under Grant Nos.12305009(XYC)and 11834005(QHC)the China Postdoctoral Science Foundation under Grant No.2022M720387(XYC).
文摘It is well known that the A-square term must be considered in both cavity and circuit quantum electrodynamics systems,because it arises in the derivation from the minimal coupling Hamiltonian at any finite coupling strength.In this paper,we study the quantum Rabi model with A-square terms using the Bogoliubov operator approach.After a unitary transformation,the A-square terms can be eliminated,resulting in a modified quantum Rabi model with renormalized parameters.A transcendental function responsible for the exact solution is then derived.The presence of the A-square terms is found to significantly alter the energy spectrum.The dynamics are also studied using the obtained exact wave function,which is sensitive to the strength of the A-square terms at strong coupling.We believe that these results could be observed in future light–matter interaction systems in the ultra-strong and deep strong coupling regimes.
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.
文摘In different languages and cultures, color terms usually indicate their specific cultural concepts and metaphorical implicature. This paper makes a typological study on the universality and relativity of the Conceptual Metaphors （CM） of color terms in different languages. It attempts to explore the cognitive differences and similarities in the process of categorization and metaphorization of color terms of oriental and western peoples. It proposes that the CM system of color terms is determined by the interactivity of three factors as neurophysiologic mechanisms, general cognitive psychological mechanisms and socio-cultural selective mechanisms. The CM of color terms in different languages carry their specific cognitive characteristics and cultural values, and reflect self-similarity of the language and culture.
文摘An excellent translation of proprietary business brand terms is more important in international trade.Diverse cultural backgrounds and purposiveness of products are the most influential factors.The research tries to analyze the elements of cultural background and aims of products that affect E-C translation of proprietary business brand terms by descriptive study method and experience summary method,and then to provide methods to overcome these difficulties.
文摘Within the scope of human beings, some addressing terms are similar. However, different addressing terms still exist,which are influenced by the background of high context communication or low context communication. A good example is that Chinese traditional culture, a typical instance of high context communication, puts much emphasis on etiquette, which is represented in addressing terms as more complex and definite; In western, with the background of low context communication, every individual is more equal and they address each other more generally and much simpler. This paper tries to explore the addressing terms both in Chinese and in English from the perspective of frame theory.
文摘The Holy Bible,as one of major sources of Western Culture,has a great influence on the Christian culture and Christian thoughts.Because language is a carrier of culture,the English study will be water without a source and a tree without roots if we ignore The Holy Bible which is the core of Christianity.To study English demands not only grammar and vocabulary,but also the culture behind the language.A brief analysis of connotative meanings of color terms,which are influenced by The Holy Bible and applied in literatures,will be given,in order to offer some help to English learners to know the connotations of color terms better,to understand literatures more profoundly and to have a general feeling about the impact which The Holy Bible has on language.
