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
Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently so...Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.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 paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave so...In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.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
The(2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper,which describe optical solitons in birefringent fibers.Utilizing the Hirota bilinear...The(2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper,which describe optical solitons in birefringent fibers.Utilizing the Hirota bilinear method,we systematically construct single-and double-periodic lump solutions.To provide a detailed insight into the dynamic behavior of the nonlinear waves,we explore diverse mixed solutions,including bright-dark,W-shaped,multi-peak,and bright soliton solutions.Building upon single-periodic lump solutions,we analyze the dynamics of lump waves on both plane-wave and periodic backgrounds using the long-wave limit method.Moreover,we obtain the interaction solutions involving lumps,periodic lumps,and solitons.The interactions among two solitons,multiple lumps,and mixed waves are illustrated and analyzed.Comparative analysis reveals that these multi-lump solutions exhibit richer dynamical properties than conventional single-lump ones.These results contribute to a deeper understanding of nonlinear systems and may facilitate solving nonlinear problems in nature.展开更多
The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function.The constraint equati...The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function.The constraint equations and unknown parameters are redefined,and the numerical calculation process of the N-periodic wave solutions is derived.It has been verified that under certain conditions,the asymptotic relations between N-periodic wave solutions and N-soliton solutions can be established.Some numerical solutions of three-periodic wave are presented.Under the influence of the Grassmann variable,the three-periodic wave solutions will generate an influence band in the middle region,and the amplitude becomes bigger as the distance from the influence band increases.展开更多
The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of...The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.展开更多
In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the e...In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations are obtained.To illustrate the ab-stract result,a concrete example is given.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
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
The outbreak of infectious diseases is the result of a combination of various factors,including season,the movement of individuals,non-pharmaceutical interventions(NPIs)and the effectiveness and availability of vaccin...The outbreak of infectious diseases is the result of a combination of various factors,including season,the movement of individuals,non-pharmaceutical interventions(NPIs)and the effectiveness and availability of vaccines.Taking these key elements into consideration,an almost periodic SVEIR warning model in the patch environment is here proposed.First,in terms of reproduction numbers,our results imply that if the effective reproduction numbers are R_(e)<1,then the disease dies out;if R_(e)>1,then the disease spreads and leads to local outbreaks.Second,the relationships between R_(e)and C_(s1),C_(a1)(see Section 2)are given by numerical simulations.The numerical results show that even if all people are vaccinated,NPIs are still needed because of the potentially low efficacy of vaccines.Furthermore,the numerical results suggest that NPIs and the strengthening of the effective rate of vaccination are essential in order to achieve herd immunity.Theories involving this model effectively explain the transmission mechanism of most infectious diseases,and provide a valuable theoretical basis for analyzing new infectious diseases in the future.Moreover,this model is helpful for the prevention and control of infectious diseases and the formulation of public health safety policies.展开更多
This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic fie...This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar...Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar abort trajectory and leverages its advantageous properties to address the optimization design problem of abort trajectories.Initially,a solution set of all feasible abort trajectories,originating from an abort point on the nominal trajectory and complying with fundamental reentry constraints,is formulated through the introduction of two novel design parameters.Subsequently,the geometric characteristics of the solution set,as well as the distributional properties of key iterative constraint responses,including flight time and velocity increment,are analyzed.Finally,the characteristics exhibited in the solution set are employed to directly identify the design parameters of the abort trajectories with minimum flight time and velocity increment,thereby providing solutions to two distinct types of optimization problems.The simulation results for a variety of nominal trajectories,encompassing the reconstruction and redesign of the Apollo13 abort trajectory,validate the proposed method,demonstrating its ability to directly generate optimal abort trajectories.The method proposed in this paper investigates feasible abort trajectories from a global perspective,providing both a framework and convenience for mission planning and iterative optimization in abort trajectory design.展开更多
Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analyt...Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications.展开更多
Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development...Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development of mechanization,wide-row spacing substrate cultivation became an optimize mode of the greenhouse cucumber cultivation,aligning with the trend of intelligent agriculture.To determine the optimal nutrient solution supply amount(NS)and supply frequency(SF)for promoting the integrated growth of cucumber under wide-row spacing substrate cultivation,we explored the effects of substrate supply amount(SS),NS,and SF on cucumber yield,quality,and element utilization efficiency.A five-level quadratic orthogonal rotation combination design with three experimental factors(NS,SF,and SS)was implemented for 23 coupling treatments over three growing seasons,including spring(2022S and 2023S)and autumn(2022A).The technique for order preference by similarity to ideal solution(TOPSIS)combining weights based on game theory was applied to construct cucumber comprehensive growth evaluation model.Single and two experimental factors analyses revealed significant effects of single factors and the coupling of NS-SS,NS-SF and SS-SF on the integrated growth of cucumber for all three growing seasons.For the NS-SF-SS combination,the optimal parameters for comprehensive cucumber growth were determined as follows:levels of^(-1).68 for NS,-0.7 for SF,and^(-1).682 for SS in 2022A;-0.43 for NS,-0.06 for SF,and 0.34 for SS in 2022S;0.3 for NS,-0.02 for SF,and 0.04 for SS in 2023S.Furthermore,for SS ranges of 2.00-3.01,3.01-4.50,4.50-5.99,5.99-7.00(L·plant^(-1)),the corresponding NS and SF intervals maximizing cucumber integrated growth in spring were:0.28-0.30(L·plant^(-1))and 6(times·d^(-1)),0.26-0.30(L·plant^(-1))and 6(times·d^(-1)),0.25-0.30(L·plant^(-1))and 6(times·d^(-1)),0.23-0.30(L·plant^(-1))and 6(times·d^(-1)),respectively.With the same SS,the corresponding NS and SF intervals that maximized cucumber integrated growth in autumn were:0.10(L·plant^(-1))and 8(times·d^(-1)),0.18(L·plant^(-1))and 7(times·d^(-1)),0.30(L·plant^(-1))and 6(times·d^(-1)),0.49(L·plant^(-1))and 5(times·d^(-1)),respectively.The results provide a theoretical basis for solution management,and further in-depth research on cucumber cultivation.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 (No.12371378)NSF of Fujian Province (Nos.2024J01980,2023J01955)。
文摘Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.
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(12261050)Science and Technology Project of Department of Education of Jiangxi Province(GJJ2201612 and GJJ211027)Natural Science Foundation of Jiangxi Province of China(20212BAB202021)。
文摘In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
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.
基金supported by the Applied Basic Research Program of Shanxi Province,China(Grant Nos.202403021212253 and 202203021221217).
文摘The(2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper,which describe optical solitons in birefringent fibers.Utilizing the Hirota bilinear method,we systematically construct single-and double-periodic lump solutions.To provide a detailed insight into the dynamic behavior of the nonlinear waves,we explore diverse mixed solutions,including bright-dark,W-shaped,multi-peak,and bright soliton solutions.Building upon single-periodic lump solutions,we analyze the dynamics of lump waves on both plane-wave and periodic backgrounds using the long-wave limit method.Moreover,we obtain the interaction solutions involving lumps,periodic lumps,and solitons.The interactions among two solitons,multiple lumps,and mixed waves are illustrated and analyzed.Comparative analysis reveals that these multi-lump solutions exhibit richer dynamical properties than conventional single-lump ones.These results contribute to a deeper understanding of nonlinear systems and may facilitate solving nonlinear problems in nature.
基金supported by the National Natural Science Foundation of China(Grant Nos.12101572 and 12371256)2024 Shanxi Province Graduate Innovation Project(Grant No.2024KY615)the Fundamental Research Program of Shanxi Province of China(Grant No.202403021211002)。
文摘The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function.The constraint equations and unknown parameters are redefined,and the numerical calculation process of the N-periodic wave solutions is derived.It has been verified that under certain conditions,the asymptotic relations between N-periodic wave solutions and N-soliton solutions can be established.Some numerical solutions of three-periodic wave are presented.Under the influence of the Grassmann variable,the three-periodic wave solutions will generate an influence band in the middle region,and the amplitude becomes bigger as the distance from the influence band increases.
基金supported by the National Natural Science Foundation of China under Grant No.12375006the Weimu Technology Company Limited of Hangzhou of China under Grant No.KYY-HX-20240495。
文摘The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.
基金Supported by the National Natural Science Foundation of China(11226337)the Science and Technology Research Projects of Henan Education Committee(22B110017).
文摘In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations are obtained.To illustrate the ab-stract result,a concrete example is given.
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 NSFC(11501269)and the Natural Science Foundation of Gansu Province(23JRRA1041).
文摘The outbreak of infectious diseases is the result of a combination of various factors,including season,the movement of individuals,non-pharmaceutical interventions(NPIs)and the effectiveness and availability of vaccines.Taking these key elements into consideration,an almost periodic SVEIR warning model in the patch environment is here proposed.First,in terms of reproduction numbers,our results imply that if the effective reproduction numbers are R_(e)<1,then the disease dies out;if R_(e)>1,then the disease spreads and leads to local outbreaks.Second,the relationships between R_(e)and C_(s1),C_(a1)(see Section 2)are given by numerical simulations.The numerical results show that even if all people are vaccinated,NPIs are still needed because of the potentially low efficacy of vaccines.Furthermore,the numerical results suggest that NPIs and the strengthening of the effective rate of vaccination are essential in order to achieve herd immunity.Theories involving this model effectively explain the transmission mechanism of most infectious diseases,and provide a valuable theoretical basis for analyzing new infectious diseases in the future.Moreover,this model is helpful for the prevention and control of infectious diseases and the formulation of public health safety policies.
基金supported by the National Natural Science Foundation of China(12401279,12371219)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027).
文摘This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
文摘Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar abort trajectory and leverages its advantageous properties to address the optimization design problem of abort trajectories.Initially,a solution set of all feasible abort trajectories,originating from an abort point on the nominal trajectory and complying with fundamental reentry constraints,is formulated through the introduction of two novel design parameters.Subsequently,the geometric characteristics of the solution set,as well as the distributional properties of key iterative constraint responses,including flight time and velocity increment,are analyzed.Finally,the characteristics exhibited in the solution set are employed to directly identify the design parameters of the abort trajectories with minimum flight time and velocity increment,thereby providing solutions to two distinct types of optimization problems.The simulation results for a variety of nominal trajectories,encompassing the reconstruction and redesign of the Apollo13 abort trajectory,validate the proposed method,demonstrating its ability to directly generate optimal abort trajectories.The method proposed in this paper investigates feasible abort trajectories from a global perspective,providing both a framework and convenience for mission planning and iterative optimization in abort trajectory design.
基金supported by the National Natural Science Foundation of China(No.41941018)Shanghai Gaofeng Discipline Construction Funding.
文摘Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications.
基金supported by the China Agriculture Research System(Grant No.CARS-23-D06)the Key Research and Development Program of Shaanxi Province(Grant Nos.2024NC2-GJHX-29 and 2024NC-ZDCYL-05-08)Shaanxi Agricultural Collaborative Innovation and Extension Alliance Project(Grant No.LMZD202202).
文摘Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development of mechanization,wide-row spacing substrate cultivation became an optimize mode of the greenhouse cucumber cultivation,aligning with the trend of intelligent agriculture.To determine the optimal nutrient solution supply amount(NS)and supply frequency(SF)for promoting the integrated growth of cucumber under wide-row spacing substrate cultivation,we explored the effects of substrate supply amount(SS),NS,and SF on cucumber yield,quality,and element utilization efficiency.A five-level quadratic orthogonal rotation combination design with three experimental factors(NS,SF,and SS)was implemented for 23 coupling treatments over three growing seasons,including spring(2022S and 2023S)and autumn(2022A).The technique for order preference by similarity to ideal solution(TOPSIS)combining weights based on game theory was applied to construct cucumber comprehensive growth evaluation model.Single and two experimental factors analyses revealed significant effects of single factors and the coupling of NS-SS,NS-SF and SS-SF on the integrated growth of cucumber for all three growing seasons.For the NS-SF-SS combination,the optimal parameters for comprehensive cucumber growth were determined as follows:levels of^(-1).68 for NS,-0.7 for SF,and^(-1).682 for SS in 2022A;-0.43 for NS,-0.06 for SF,and 0.34 for SS in 2022S;0.3 for NS,-0.02 for SF,and 0.04 for SS in 2023S.Furthermore,for SS ranges of 2.00-3.01,3.01-4.50,4.50-5.99,5.99-7.00(L·plant^(-1)),the corresponding NS and SF intervals maximizing cucumber integrated growth in spring were:0.28-0.30(L·plant^(-1))and 6(times·d^(-1)),0.26-0.30(L·plant^(-1))and 6(times·d^(-1)),0.25-0.30(L·plant^(-1))and 6(times·d^(-1)),0.23-0.30(L·plant^(-1))and 6(times·d^(-1)),respectively.With the same SS,the corresponding NS and SF intervals that maximized cucumber integrated growth in autumn were:0.10(L·plant^(-1))and 8(times·d^(-1)),0.18(L·plant^(-1))and 7(times·d^(-1)),0.30(L·plant^(-1))and 6(times·d^(-1)),0.49(L·plant^(-1))and 5(times·d^(-1)),respectively.The results provide a theoretical basis for solution management,and further in-depth research on cucumber cultivation.
