The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding sto...The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.展开更多
A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positi...A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positive solution.Second,by selecting an appropriate Lyapunov function,we provide the sufficient condition for the existence of a positive T-periodic solution.Finally,numerical simulations illustrate our theoretical results,which show that the impulse or the white noises can result in the extinction of the predator in a certain condition.展开更多
In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is als...In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.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
The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian proc...The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian process. The investigation begins with the derivation of stochastic solitary wave solutions using the modified exp(-Ψ(ξ)) expansion method. To illustrate the noise effects, 3D and 2D visualizations are displayed for different non-negative values of noise parameter under suitable parameter values. Additionally, qualitative analysis of both perturbed and unperturbed dynamical systems is conducted using bifurcation and chaos theory. In bifurcation analysis, we analyze the detailed parameter analysis near fixed points of the unperturbed system. An external periodic force is applied to perturb the system, leading to an investigation of its chaotic behavior. Chaos detection tools are employed to predict the behavior of the perturbed dynamical system, with results validated through visual representations.Multistability analysis is conducted under varying initial conditions to identify multiple stable states in the perturbed dynamical system, contributing to chaotic behavior. Also, sensitivity analysis of the Hamiltonian system is performed for different initial conditions. The novelty of this work lies in the significance of the obtained results, which have not been previously explored for the considered equation. These findings offer noteworthy insights into the behavior of the complex cubic NLSE with δ-potential and its applications in fields such as nonlinear optics, quantum mechanics and Bose–Einstein condensates.展开更多
This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations(SDDEs).A delayed stochastic model is formulated by dividing the population into five distinct compartme...This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations(SDDEs).A delayed stochastic model is formulated by dividing the population into five distinct compartments:susceptible,exposed,infected,environmental irritants,and recovered individuals.The model undergoes thorough analytical examination,addressing key dynamical properties including positivity,boundedness,existence,and uniqueness of solutions.Local and global stability around the equilibrium points is studied with respect to the basic reproduction number.The existence of a unique global positive solution for the stochastic delayed model is established.In addition,a stochastic nonstandard finite difference scheme is developed,which is shown to be dynamically consistent and convergent toward the equilibrium states.The scheme preserves the essential qualitative features of the model and demonstrates improved performance when compared to existing numerical methods.Finally,the impact of time delays and stochastic fluctuations on the susceptible and infected populations is analyzed.展开更多
Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers e...Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
In this study,FeCr_(x)MnAlCu(x=0,0.5,1.0,1.5,2.0)high-entropy alloys were fabricated using vacuum arc melting,and the corrosion behavior of these alloys in 3.5wt%NaCl solution at room temperature was investigated by e...In this study,FeCr_(x)MnAlCu(x=0,0.5,1.0,1.5,2.0)high-entropy alloys were fabricated using vacuum arc melting,and the corrosion behavior of these alloys in 3.5wt%NaCl solution at room temperature was investigated by electrochemical dynamic potential polarization curves and immersion experiments.The microstructure results show that the high-entropy alloy with x=0 has a body-centered cubic phase structure,whereas the high-entropy alloys with x=0.5–2.0 have a mixed face-centered cubic+body-centered cubic dual-phase structure.The corrosion results show that the corrosion resistance of the high-entropy alloy is increased with the increase in Cr content.Among them,the high-entropy alloy with x=2.0 exhibits the optimal corrosion resistance:the highest self-corrosion potential(E_(corr)=−0.354 V vs.Ag/AgCl),the smallest self-corrosion current density(I_(corr)=1.991×10^(−6)A·cm^(−2)),and the smallest corrosion rate(0.0292 mm/a).The composite passivation film of oxides and hydroxides is formed on the surface of the corroded high-entropy alloys,and the Cr_(2)O_(3)content is increased with the increase in Cr content,which effectively improves the stability and protective properties of the passivation film.展开更多
In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar perce...In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.展开更多
To investigate the effect of solution treatment and aging process parameters on the microstructure and mechanical properties of TB18 titanium alloy,process optimization research was conducted based on the mixed-level ...To investigate the effect of solution treatment and aging process parameters on the microstructure and mechanical properties of TB18 titanium alloy,process optimization research was conducted based on the mixed-level orthogonal experiment design of factor levels.Results show that through range analysis,the significance order of process parameters is determined as follows:solution cooling method>solution temperature>aging time>aging temperature>solution time.Considering the strength-ductility matching and engineering application requirements,the benchmark parameters are selected as solution time of 1 h,solution cooling method of air cooling(AC),aging temperature of 525℃,and aging time of 4 h.Furthermore,the effects of solution temperature in the range of 790–870℃ on the impact toughness and micro-fracture characteristics of the alloy were studied.The results reveal that the larger the area of shear lip and fibrous zone,and the smaller the area of radiation zone,the better the toughness of the alloy.With the increase in solution temperature,the length of secondary cracks on the fracture surface increases,the number of dimples increases,and the toughness is enhanced.Based on the collaborative optimization of strength and toughness,the optimal heat treatment process for TB18 alloy is determined as 870℃/1 h,AC+525℃/4 h,AC.展开更多
Energy-regenerative suspension combined with piezoelectric and electromagnetic transduction has evolved into a core technological pathway in advancing automotive design paradigms.With the aim of improving energy harve...Energy-regenerative suspension combined with piezoelectric and electromagnetic transduction has evolved into a core technological pathway in advancing automotive design paradigms.With the aim of improving energy harvesting performance,time-delayed feedback control is widely used in an energy-regenerative suspension system under different external disturbances in this paper.Meanwhile,limited research has addressed the stochastic dynamics of time-delayed nonlinear energy-regenerative suspension systems.Different from previous studies,this work studies the stochastic response and P-bifurcation of the nonlinear energy-regenerative suspension system with time-delayed feedback control.Firstly,an approximately equivalent dimension reduction system is established by the variable transformation method,and then the stationary probability density function of amplitude is obtained by the stochastic averaging method.Secondly,the precision of the method used in this work is verified by comparing the numerical solutions with the analytical results.Finally,based on the stationary probability density function,the influence of system parameters on stochastic P-bifurcation and the mean output power is discussed.展开更多
In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solu...In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.展开更多
Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in a...Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in an algebra,then the solution(and also the control gain in many cases)is also in the same algebra.The main result is verified by a numerical simulation.展开更多
This study investigates the dimensionless quasi-geostrophic potential vorticity(QG-PV)equation with external sources.Employing the Gardner-Morikawa transformation and weakly nonlinear perturbation expansion,we derive ...This study investigates the dimensionless quasi-geostrophic potential vorticity(QG-PV)equation with external sources.Employing the Gardner-Morikawa transformation and weakly nonlinear perturbation expansion,we derive the nonlinear Boussinesq equation with external sources.We demonstrate the existence of explicit zero-order and first-order Wronskian solutions for the model equation whenα_4=0.Furthermore,using a modified Jacobi elliptic function method,we obtain soliton-like solutions for bothα_4=0 andα_4≠0.Analysis of these solutions reveals that the generalizedβ-plane approximation and shear flow are significant factors in inducing nonlinear Rossby waves,and that external sources play a crucial role in influencing Rossby wave behavior.展开更多
A stochastic predator-prey system with Markov switching is explored.We have developed a new chasing technique to efficiently solve the Fokker-Planck-Kolmogorov and backward Kolmogorov equations.Dynamic balance and rel...A stochastic predator-prey system with Markov switching is explored.We have developed a new chasing technique to efficiently solve the Fokker-Planck-Kolmogorov and backward Kolmogorov equations.Dynamic balance and reliability of the switching system are evaluated via stationary probability density function and first-passage failure theory,taking into account factors such as switching frequencies,noise intensities,and initial conditions.Results reveal that Markov switching leads to stochastic P-bifurcation,enhancing dynamic balance and reducing white-noise-induced oscillations.But frequent switching can heighten initial value dependence,harming reliability.Further,the influence of the subsystem on the switching system is not proportional to its action probabilities.Monte Carlo simulations validate the findings,offering an in-depth exploration of these dynamics.展开更多
Predator–prey interactions are fundamental to understanding ecosystem stability and biodiversity.In this study,we propose and analyze a stochastic predator–prey model that incorporates two critical ecological factor...Predator–prey interactions are fundamental to understanding ecosystem stability and biodiversity.In this study,we propose and analyze a stochastic predator–prey model that incorporates two critical ecological factors:prey refuge and harvesting.The model also integrates disease transmission within the predator population,adding an important layer of realism.Using rigorous mathematical techniques,we demonstrate the existence and uniqueness of a global positive solution,thereby confirming the model's biological feasibility.We further derive sufficient conditions for two key ecological scenarios:stochastic permanence,which ensures the sustained co-existence of prey and predators over time,and extinction,where one or both populations decline to zero.The interplay between prey refuge and harvesting is thoroughly examined to understand their combined impact on population dynamics.All theoretical results are validated by detailed numerical simulations,highlighting the applicability of the model to real-world ecological systems.From the simulation results,we observed that with an adequate level of prey refuge and predator harvesting,the susceptible predator and prey coexist with extensive oscillations,while the infected predator population was moving towards extinction.In addition,we have investigated the effect of disease transmission on system dynamics.Our results show that,as the transmission rate of disease increases,the susceptible predator approaches extinction,whereas,on the other hand,when it declines,the susceptible predator shows robust oscillations while the infected approaches extinction.In both cases,the prey population demonstrates robust stability due to the prey refuge.Our findings show that the management of harvesting and the prey refuge can be effective ecological tactics for disease control and species protection under stochastic environmental effects.展开更多
Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challeng...Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.展开更多
We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity(i.e.random violation of Newton's third law)and then investigate its statistical behaviors,including fluctuations ...We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity(i.e.random violation of Newton's third law)and then investigate its statistical behaviors,including fluctuations of velocity and position,time evolution of probability distribution functions,energy gain,and entropy production.The effective temperature of this two-body system immersed in a thermal bath is also derived.Furthermore,we heuristically present an extremely minimal model where the relative motion adheres to the same rules as in classical mechanics,while the effect of stochastically broken reciprocity only manifests in the fluctuating motion of the center of mass.展开更多
In this paper,we study a predator-prey model with additional food for predator.By using white noise to perturb the natural growth rates and introduce a jump process,we model the corresponding stochastic differential e...In this paper,we study a predator-prey model with additional food for predator.By using white noise to perturb the natural growth rates and introduce a jump process,we model the corresponding stochastic differential equations.The effect of fear and prey refuge on population dynamics is also considered.First,we use Itô's formula to prove the existence and uniqueness of a global positive solution and its boundedness.Next,sufficient conditions for the extinction and persistence of both species have been given.Then the stochastic permanence of our system is investigated under some conditions.Our main results demonstrate that sufficiently large white noise could drive both species to extinction.However,Lévy noise enhances the survival of both prey and predator species.Our analytical derivations are justified through numerical simulations which show the reliability of the model from the ecological point of view.In addition,we have investigated the impact of fear effect,prey refuge and the additional food biomass on this model by numerical simulation.展开更多
基金Supported by the National Natural Science Foundation of China(10671182)。
文摘The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.
基金Supported by NSFC(Nos.10671182,12061020)NSF of Guizhou Province(Nos.QKH[2019]1123,QKHKY[2021]088,QKHKY[2022]301,QKH-ZK[2021]331)the Ph.D.Project of Guizhou Education University(No.2021BS005)。
文摘A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positive solution.Second,by selecting an appropriate Lyapunov function,we provide the sufficient condition for the existence of a positive T-periodic solution.Finally,numerical simulations illustrate our theoretical results,which show that the impulse or the white noises can result in the extinction of the predator in a certain condition.
基金Supported by the National Natural Science Foundation of China(12171247)。
文摘In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.
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Supporting Project under Grant No.RSP2025R472,King Saud University,Riyadh,Saudi Arabia。
文摘The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian process. The investigation begins with the derivation of stochastic solitary wave solutions using the modified exp(-Ψ(ξ)) expansion method. To illustrate the noise effects, 3D and 2D visualizations are displayed for different non-negative values of noise parameter under suitable parameter values. Additionally, qualitative analysis of both perturbed and unperturbed dynamical systems is conducted using bifurcation and chaos theory. In bifurcation analysis, we analyze the detailed parameter analysis near fixed points of the unperturbed system. An external periodic force is applied to perturb the system, leading to an investigation of its chaotic behavior. Chaos detection tools are employed to predict the behavior of the perturbed dynamical system, with results validated through visual representations.Multistability analysis is conducted under varying initial conditions to identify multiple stable states in the perturbed dynamical system, contributing to chaotic behavior. Also, sensitivity analysis of the Hamiltonian system is performed for different initial conditions. The novelty of this work lies in the significance of the obtained results, which have not been previously explored for the considered equation. These findings offer noteworthy insights into the behavior of the complex cubic NLSE with δ-potential and its applications in fields such as nonlinear optics, quantum mechanics and Bose–Einstein condensates.
基金supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R899)Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabiasupported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia(KFU252831)。
文摘This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations(SDDEs).A delayed stochastic model is formulated by dividing the population into five distinct compartments:susceptible,exposed,infected,environmental irritants,and recovered individuals.The model undergoes thorough analytical examination,addressing key dynamical properties including positivity,boundedness,existence,and uniqueness of solutions.Local and global stability around the equilibrium points is studied with respect to the basic reproduction number.The existence of a unique global positive solution for the stochastic delayed model is established.In addition,a stochastic nonstandard finite difference scheme is developed,which is shown to be dynamically consistent and convergent toward the equilibrium states.The scheme preserves the essential qualitative features of the model and demonstrates improved performance when compared to existing numerical methods.Finally,the impact of time delays and stochastic fluctuations on the susceptible and infected populations is analyzed.
文摘Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Gansu Provincial Science and Technology Major Special Program(24ZDWA008)Fourth Batch of Top Leading Talents Fund Projects in Gansu Province(ZZ2023G50100013)。
文摘In this study,FeCr_(x)MnAlCu(x=0,0.5,1.0,1.5,2.0)high-entropy alloys were fabricated using vacuum arc melting,and the corrosion behavior of these alloys in 3.5wt%NaCl solution at room temperature was investigated by electrochemical dynamic potential polarization curves and immersion experiments.The microstructure results show that the high-entropy alloy with x=0 has a body-centered cubic phase structure,whereas the high-entropy alloys with x=0.5–2.0 have a mixed face-centered cubic+body-centered cubic dual-phase structure.The corrosion results show that the corrosion resistance of the high-entropy alloy is increased with the increase in Cr content.Among them,the high-entropy alloy with x=2.0 exhibits the optimal corrosion resistance:the highest self-corrosion potential(E_(corr)=−0.354 V vs.Ag/AgCl),the smallest self-corrosion current density(I_(corr)=1.991×10^(−6)A·cm^(−2)),and the smallest corrosion rate(0.0292 mm/a).The composite passivation film of oxides and hydroxides is formed on the surface of the corroded high-entropy alloys,and the Cr_(2)O_(3)content is increased with the increase in Cr content,which effectively improves the stability and protective properties of the passivation film.
基金Supported by the Doctoral Research Start-up Project of Yuncheng University(YQ-2023067)Project of Shanxi Natural Science Foundation(202303021211189)+1 种基金Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Provinces(20220036)Shanxi ProvinceIntelligent Optoelectronic Sensing Application Technology Innovation Center and Shanxi Province Optoelectronic Information Science and TechnologyLaboratory,Yuncheng University.
文摘In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.
基金Key Program of National Natural Science Foundation of China(52431001)。
文摘To investigate the effect of solution treatment and aging process parameters on the microstructure and mechanical properties of TB18 titanium alloy,process optimization research was conducted based on the mixed-level orthogonal experiment design of factor levels.Results show that through range analysis,the significance order of process parameters is determined as follows:solution cooling method>solution temperature>aging time>aging temperature>solution time.Considering the strength-ductility matching and engineering application requirements,the benchmark parameters are selected as solution time of 1 h,solution cooling method of air cooling(AC),aging temperature of 525℃,and aging time of 4 h.Furthermore,the effects of solution temperature in the range of 790–870℃ on the impact toughness and micro-fracture characteristics of the alloy were studied.The results reveal that the larger the area of shear lip and fibrous zone,and the smaller the area of radiation zone,the better the toughness of the alloy.With the increase in solution temperature,the length of secondary cracks on the fracture surface increases,the number of dimples increases,and the toughness is enhanced.Based on the collaborative optimization of strength and toughness,the optimal heat treatment process for TB18 alloy is determined as 870℃/1 h,AC+525℃/4 h,AC.
基金Project supported by the National Natural Science Foundation of China(Grant No.12002089)the Science and Technology Projects in Guangzhou(Grant No.2023A04J1323)UKRI Horizon Europe Guarantee(Marie SklodowskaCurie Fellowship)(Grant No.EP/Y016130/1)。
文摘Energy-regenerative suspension combined with piezoelectric and electromagnetic transduction has evolved into a core technological pathway in advancing automotive design paradigms.With the aim of improving energy harvesting performance,time-delayed feedback control is widely used in an energy-regenerative suspension system under different external disturbances in this paper.Meanwhile,limited research has addressed the stochastic dynamics of time-delayed nonlinear energy-regenerative suspension systems.Different from previous studies,this work studies the stochastic response and P-bifurcation of the nonlinear energy-regenerative suspension system with time-delayed feedback control.Firstly,an approximately equivalent dimension reduction system is established by the variable transformation method,and then the stationary probability density function of amplitude is obtained by the stochastic averaging method.Secondly,the precision of the method used in this work is verified by comparing the numerical solutions with the analytical results.Finally,based on the stationary probability density function,the influence of system parameters on stochastic P-bifurcation and the mean output power is discussed.
基金Supported by the National Natural Science Foundation of China(12226412)Natural Science Foundation of Jiangsu Province(BK20221339)。
文摘In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.
文摘Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in an algebra,then the solution(and also the control gain in many cases)is also in the same algebra.The main result is verified by a numerical simulation.
基金supported by the National Natural Science Foundation of China(Grant No.12362027)the Scientific Research Ability of Youth Teachers of Inner Mongolia Agricultural University(Grant No.BR230110)+3 种基金Inner Mongolia National Science Fund for Excellent Young Scholars(Grant No.2025YQ033)Foundation for Basic Science Research Initiation at Inner Mongolia Agricultural University(Grant No.JC2021001)The Natural Science Foundation of Inner Mongolia Autonomous Region(2025MS01020)Supported by the Basic and Applied Basic Research Science and Technology Program Projects of Hohhot(2025-rule-basic-60)。
文摘This study investigates the dimensionless quasi-geostrophic potential vorticity(QG-PV)equation with external sources.Employing the Gardner-Morikawa transformation and weakly nonlinear perturbation expansion,we derive the nonlinear Boussinesq equation with external sources.We demonstrate the existence of explicit zero-order and first-order Wronskian solutions for the model equation whenα_4=0.Furthermore,using a modified Jacobi elliptic function method,we obtain soliton-like solutions for bothα_4=0 andα_4≠0.Analysis of these solutions reveals that the generalizedβ-plane approximation and shear flow are significant factors in inducing nonlinear Rossby waves,and that external sources play a crucial role in influencing Rossby wave behavior.
基金Project supported by the National Natural Science Foundation of China(Grant No.12472033)。
文摘A stochastic predator-prey system with Markov switching is explored.We have developed a new chasing technique to efficiently solve the Fokker-Planck-Kolmogorov and backward Kolmogorov equations.Dynamic balance and reliability of the switching system are evaluated via stationary probability density function and first-passage failure theory,taking into account factors such as switching frequencies,noise intensities,and initial conditions.Results reveal that Markov switching leads to stochastic P-bifurcation,enhancing dynamic balance and reducing white-noise-induced oscillations.But frequent switching can heighten initial value dependence,harming reliability.Further,the influence of the subsystem on the switching system is not proportional to its action probabilities.Monte Carlo simulations validate the findings,offering an in-depth exploration of these dynamics.
基金supported by the National Natural Science Foundation of China(Grant No.32271554)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515011501)。
文摘Predator–prey interactions are fundamental to understanding ecosystem stability and biodiversity.In this study,we propose and analyze a stochastic predator–prey model that incorporates two critical ecological factors:prey refuge and harvesting.The model also integrates disease transmission within the predator population,adding an important layer of realism.Using rigorous mathematical techniques,we demonstrate the existence and uniqueness of a global positive solution,thereby confirming the model's biological feasibility.We further derive sufficient conditions for two key ecological scenarios:stochastic permanence,which ensures the sustained co-existence of prey and predators over time,and extinction,where one or both populations decline to zero.The interplay between prey refuge and harvesting is thoroughly examined to understand their combined impact on population dynamics.All theoretical results are validated by detailed numerical simulations,highlighting the applicability of the model to real-world ecological systems.From the simulation results,we observed that with an adequate level of prey refuge and predator harvesting,the susceptible predator and prey coexist with extensive oscillations,while the infected predator population was moving towards extinction.In addition,we have investigated the effect of disease transmission on system dynamics.Our results show that,as the transmission rate of disease increases,the susceptible predator approaches extinction,whereas,on the other hand,when it declines,the susceptible predator shows robust oscillations while the infected approaches extinction.In both cases,the prey population demonstrates robust stability due to the prey refuge.Our findings show that the management of harvesting and the prey refuge can be effective ecological tactics for disease control and species protection under stochastic environmental effects.
基金Supported by National Natural Science Foundation of China(Grant No.62173161).
文摘Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.
基金supported by the National Natural Science Foundation of China(Grant No.12475032)。
文摘We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity(i.e.random violation of Newton's third law)and then investigate its statistical behaviors,including fluctuations of velocity and position,time evolution of probability distribution functions,energy gain,and entropy production.The effective temperature of this two-body system immersed in a thermal bath is also derived.Furthermore,we heuristically present an extremely minimal model where the relative motion adheres to the same rules as in classical mechanics,while the effect of stochastically broken reciprocity only manifests in the fluctuating motion of the center of mass.
基金Supported by Guangxi Natural Science Foundation(2026GXNSFAA00641039)。
文摘In this paper,we study a predator-prey model with additional food for predator.By using white noise to perturb the natural growth rates and introduce a jump process,we model the corresponding stochastic differential equations.The effect of fear and prey refuge on population dynamics is also considered.First,we use Itô's formula to prove the existence and uniqueness of a global positive solution and its boundedness.Next,sufficient conditions for the extinction and persistence of both species have been given.Then the stochastic permanence of our system is investigated under some conditions.Our main results demonstrate that sufficiently large white noise could drive both species to extinction.However,Lévy noise enhances the survival of both prey and predator species.Our analytical derivations are justified through numerical simulations which show the reliability of the model from the ecological point of view.In addition,we have investigated the impact of fear effect,prey refuge and the additional food biomass on this model by numerical simulation.
