The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix sp...The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.展开更多
In this paper,we present a circuit model of single-quantum-well InGaN/GaN light-emitting diodes based on the standard rate equations.Two rate equations describe carrier transport processes occurring in sep-arate confi...In this paper,we present a circuit model of single-quantum-well InGaN/GaN light-emitting diodes based on the standard rate equations.Two rate equations describe carrier transport processes occurring in sep-arate confinement heterostructure and quantum well respectively,and the third equation describes the varied photons in quantum well.By using the presented model,impacts of quantum well thickness on the static and dynamic performances are investigated.Simulated results show that LED with 4 nm well exhibits better lightcurrent(L-I)performance,but LED with 3 nm well presents wider 3 dB modulation bandwidth.It reveals that high carrier density in quantum well is detrimental to the static performance,but beneficial to the dynamic performance.展开更多
In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
The hot compression deformation behavior of Mg-6Zn-1Mn-0.5Ca(ZM61-0.5Ca)and Mg-6Zn-1Mn-2Sn-0.5Ca(ZMT612-0.5Ca)alloys was investigated at deformation temperatures ranging from 250℃to 400℃and strain rates varying from...The hot compression deformation behavior of Mg-6Zn-1Mn-0.5Ca(ZM61-0.5Ca)and Mg-6Zn-1Mn-2Sn-0.5Ca(ZMT612-0.5Ca)alloys was investigated at deformation temperatures ranging from 250℃to 400℃and strain rates varying from 0.001 s^(-1) to 1 s^(-1).The results show that the addition of Sn promotes dynamic recrystallization(DRX),and CaMgSn phases can act as nucleation sites during the compression deformation.Flow stress increases with increasing the strain rate and decreasing the temperature.Both the ZM61-0.5Ca and ZMT612-0.5Ca alloys exhibit obvious DRX characteristics.CaMgSn phases can effectively inhibit dislocation motion with the addition of Sn,thus increasing the peak fl ow stress of the alloy.The addition of Sn increases the hot deformation activation energy of the ZM61-0.5Ca alloy from 199.654 kJ/mol to 276.649 kJ/mol,thus improving the thermal stability of the alloy.For the ZMT612-0.5Ca alloy,the optimal hot deformation parameters are determined to be a deformation temperature range of 350–400℃and a strain rate range of 0.001–0.01 s^(-1).展开更多
Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,...Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.展开更多
The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly couple...The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.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 article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equ...In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.展开更多
This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit...This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.展开更多
With a perspective of interest in the modeling of dynamic processes, here we investigate various types of basic growth equations, which in their formulation quantify the change of the variables, the state, or the inde...With a perspective of interest in the modeling of dynamic processes, here we investigate various types of basic growth equations, which in their formulation quantify the change of the variables, the state, or the independent one, using balance equations in which the counts(aggregation-reduction) are of the multiplicative type. We enter the context of the “differential” equations typical of non-Newtonian calculations, such as geometric calculus, bi-geometric calculus, or the lesser-known logarithmic calculus, when we take the step to the limit. In these new possibilities of dynamic laws, we highlight the interpretive aspects. A particular case is to review the equivalents of the logistic equation of the standard calculation in the new accounting calculations, where we make graphical and semantic comparisons. Finally, the construction of a geometric type equation is exemplified, with applications inherent to the financial mathematics.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 existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong ...The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.展开更多
The variation laws of runoff and sediment load under different climate,vegetation,and human activity scenarios are significantly different.Exploring the impacts of climate change and human activities on runoff and sed...The variation laws of runoff and sediment load under different climate,vegetation,and human activity scenarios are significantly different.Exploring the impacts of climate change and human activities on runoff and sediment load dynamics can provide a profound understanding of the mechanism of runoff and sediment load variability in basins,which is crucial for the sustainable development of regional ecosystems.This study investigates the Tao River Basin(TRB)on the Tibetan Plateau,as well as the Zuli River Basin(ZRB)and Jing River Basin(JRB)on the Loess Plateau,to differentiate the impacts of climate change and human activities on runoff and sediment load dynamics.The runoff and sediment load of the three watersheds have shown a decreasing trend over the past 40 years,and combined with the DMC(Dual mass curve)method,it was found that the slope of the runoff sediment gradually tends to flatten out.After the time period was divided,the CA(Cumulative anomaly)method was used for verification,which revealed good correspondence between the two before 2000 and then gradual deviations.The power function best represents the relationship between runoff and sediment load.During the initial period,climate had a significant impact on runoff variation in the TRB and JRB,with contribution rates of-54.93%and-63.02%,respectively.In the later period,human activities became the dominant influence,contributing more than-60%of the runoff variation.In the ZRB,human activities consistently dominated runoff variation,with contribution rates of-72.72%and-55.66%during both periods.In the early stages of research,the impact of climate change on sediment load was more severe in the TRB and JRB,and human activities played a significant role in the later stages.However,in the ZRB,human activities have always been the main contributor.Based on the actual local situation,runoff and sediment load in the TRB are influenced primarily by engineering measures,and vegetation and check dams exert greater impacts on the ZRB and JRB.This study explores the attribution of water and sediment load changes in different ecological geographic regions from a comparative perspective,providing a valuable theoretical basis and reference for understanding global runoff and sediment transport changes in similar areas.展开更多
Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in ...Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.展开更多
Signal transduction in a cell is mostly mediated with biochemical reactions which are noisy and often modeled with chemical master equations or Langevin type of dynamics.Thus stochastic simulation constitutes a major ...Signal transduction in a cell is mostly mediated with biochemical reactions which are noisy and often modeled with chemical master equations or Langevin type of dynamics.Thus stochastic simulation constitutes a major part of computation in cell signaling.Nevertheless,the presence of a wide span of time scales or molecular numbers in various pathways may lead to trouble in computation efficiency or accuracy.To avoid this problem,the commonly employed variational method evolves the whole probability distribution and reduces the stochastic equations to deterministic ones of only a few parameters.However,the design of the left variational basis is essential for its successful application,especially to large networks.In this paper,we extend the conventional polynomial basis to the Fourier and further the Gaussian basis,much facilitating description of multi-peaked or localized non-Gaussian distributions and at the same time avoiding numerical instability and computational complexity frequently encountered with conventional basis.The extension here is demonstrated in several typical biochemical signaling networks and achieves similar accuracy as the benchmark Gillespie algorithm,but with much less running time,which seems to open new opportunities in the variational approach to efficient analysis of noisy dynamics.展开更多
This paper aims to develop a unified Bayesian approach for clustered data analysis when observations are subject to missingness at random.The authors consider a general framework in which the parameters of interest ar...This paper aims to develop a unified Bayesian approach for clustered data analysis when observations are subject to missingness at random.The authors consider a general framework in which the parameters of interest are defined through estimating equations,and the probability of missingness follows a general parametric form.The generalized method of moments framework is employed to derive an optimal combination of inverse-probability-weighted estimating equations for the parameters of interest and score equations for propensity score.Using this framework,the authors develop a quasi-Bayesian analysis for clustered samples with missing values.A unified model selection approach is also proposed to compare models characterized by different moment conditions.The authors systematically evaluate the large-sample properties of the proposed quasi-posterior density with both fixed and shrinking priors and establish the selection consistency of the proposed model selection criterion.The proposed results are valid under very mild conditions and offer significant advantages for parameters defined through non-smooth estimating functions.Extensive numerical studies demonstrate that the proposed method performs exceptionally well in finite samples.展开更多
In this article,the authors explore the online updating estimation for general estimating equations(EEs)in heterogeneous streaming data settings.The framework is based on more conservative model assumptions,leading to...In this article,the authors explore the online updating estimation for general estimating equations(EEs)in heterogeneous streaming data settings.The framework is based on more conservative model assumptions,leading to more robust estimations and preventing misspecification.The authors establish the standard renewable estimation under blockwise heterogeneity assumption,which can correctly specify model in some sense.To mitigate heterogeneity and enhance estimation accuracy,the authors propose two novel online detection and fusion strategies,with corresponding algorithms provided.Theoretical properties of the proposed methods are demonstrated in the context of small block sizes.Extensive numerical experiments validate the theoretical findings.Real data analysis of the Ford Gobike docked bike-sharing dataset verifies the feasibility and robustness of the proposed methods.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
基金The National Natural Science Foundations of China (12202219)the Natural Science Foundations of Ningxia (2024AAC02009, 2023AAC05001)the Ningxia Youth Top Talents Training Project。
文摘The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.
文摘In this paper,we present a circuit model of single-quantum-well InGaN/GaN light-emitting diodes based on the standard rate equations.Two rate equations describe carrier transport processes occurring in sep-arate confinement heterostructure and quantum well respectively,and the third equation describes the varied photons in quantum well.By using the presented model,impacts of quantum well thickness on the static and dynamic performances are investigated.Simulated results show that LED with 4 nm well exhibits better lightcurrent(L-I)performance,but LED with 3 nm well presents wider 3 dB modulation bandwidth.It reveals that high carrier density in quantum well is detrimental to the static performance,but beneficial to the dynamic performance.
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金Sichuan Science and Technology Program(2025ZNSFSC1341)Fundamental Research Funds for the Central Universities(J2022-090,25CAFUC04087)。
文摘The hot compression deformation behavior of Mg-6Zn-1Mn-0.5Ca(ZM61-0.5Ca)and Mg-6Zn-1Mn-2Sn-0.5Ca(ZMT612-0.5Ca)alloys was investigated at deformation temperatures ranging from 250℃to 400℃and strain rates varying from 0.001 s^(-1) to 1 s^(-1).The results show that the addition of Sn promotes dynamic recrystallization(DRX),and CaMgSn phases can act as nucleation sites during the compression deformation.Flow stress increases with increasing the strain rate and decreasing the temperature.Both the ZM61-0.5Ca and ZMT612-0.5Ca alloys exhibit obvious DRX characteristics.CaMgSn phases can effectively inhibit dislocation motion with the addition of Sn,thus increasing the peak fl ow stress of the alloy.The addition of Sn increases the hot deformation activation energy of the ZM61-0.5Ca alloy from 199.654 kJ/mol to 276.649 kJ/mol,thus improving the thermal stability of the alloy.For the ZMT612-0.5Ca alloy,the optimal hot deformation parameters are determined to be a deformation temperature range of 350–400℃and a strain rate range of 0.001–0.01 s^(-1).
文摘Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.
基金Supported by National Natural Science Foundation of China Under Grant(12401647)Supported by Fundamental Research Program of Shanxi Province(202203021212336)+2 种基金Taiyuan Institute of Technology Scientific Research Initial Funding(2023KJ057,2024KJ007,2024LJ005)Supported by Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2024L358)Youth Program of Taiyuan University(24TYQN10)。
文摘The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
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Supported by the National Natural Science Foundation of China(12001424,12271324)the Natural Science Basic research program of Shaanxi Province(2021JZ-21)+1 种基金the China Postdoctoral Science Foundation(2020M673332)Xi’an University,Xi’an Science and Technology Plan Wutongshu Technology Transfer Action Innovation Team(25WTZD07)。
文摘In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.
文摘This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.
文摘With a perspective of interest in the modeling of dynamic processes, here we investigate various types of basic growth equations, which in their formulation quantify the change of the variables, the state, or the independent one, using balance equations in which the counts(aggregation-reduction) are of the multiplicative type. We enter the context of the “differential” equations typical of non-Newtonian calculations, such as geometric calculus, bi-geometric calculus, or the lesser-known logarithmic calculus, when we take the step to the limit. In these new possibilities of dynamic laws, we highlight the interpretive aspects. A particular case is to review the equivalents of the logistic equation of the standard calculation in the new accounting calculations, where we make graphical and semantic comparisons. Finally, the construction of a geometric type equation is exemplified, with applications inherent to the financial mathematics.
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.
文摘The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.
基金funding from the Natural Science Foundation of Shanxi Province(202403021222245,20240302121217)。
文摘The variation laws of runoff and sediment load under different climate,vegetation,and human activity scenarios are significantly different.Exploring the impacts of climate change and human activities on runoff and sediment load dynamics can provide a profound understanding of the mechanism of runoff and sediment load variability in basins,which is crucial for the sustainable development of regional ecosystems.This study investigates the Tao River Basin(TRB)on the Tibetan Plateau,as well as the Zuli River Basin(ZRB)and Jing River Basin(JRB)on the Loess Plateau,to differentiate the impacts of climate change and human activities on runoff and sediment load dynamics.The runoff and sediment load of the three watersheds have shown a decreasing trend over the past 40 years,and combined with the DMC(Dual mass curve)method,it was found that the slope of the runoff sediment gradually tends to flatten out.After the time period was divided,the CA(Cumulative anomaly)method was used for verification,which revealed good correspondence between the two before 2000 and then gradual deviations.The power function best represents the relationship between runoff and sediment load.During the initial period,climate had a significant impact on runoff variation in the TRB and JRB,with contribution rates of-54.93%and-63.02%,respectively.In the later period,human activities became the dominant influence,contributing more than-60%of the runoff variation.In the ZRB,human activities consistently dominated runoff variation,with contribution rates of-72.72%and-55.66%during both periods.In the early stages of research,the impact of climate change on sediment load was more severe in the TRB and JRB,and human activities played a significant role in the later stages.However,in the ZRB,human activities have always been the main contributor.Based on the actual local situation,runoff and sediment load in the TRB are influenced primarily by engineering measures,and vegetation and check dams exert greater impacts on the ZRB and JRB.This study explores the attribution of water and sediment load changes in different ecological geographic regions from a comparative perspective,providing a valuable theoretical basis and reference for understanding global runoff and sediment transport changes in similar areas.
基金Supported by the Development and Application Project of Ship CAE Software.
文摘Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.
基金supported by the National Natural Science Foundation of China under Grants No.12375030。
文摘Signal transduction in a cell is mostly mediated with biochemical reactions which are noisy and often modeled with chemical master equations or Langevin type of dynamics.Thus stochastic simulation constitutes a major part of computation in cell signaling.Nevertheless,the presence of a wide span of time scales or molecular numbers in various pathways may lead to trouble in computation efficiency or accuracy.To avoid this problem,the commonly employed variational method evolves the whole probability distribution and reduces the stochastic equations to deterministic ones of only a few parameters.However,the design of the left variational basis is essential for its successful application,especially to large networks.In this paper,we extend the conventional polynomial basis to the Fourier and further the Gaussian basis,much facilitating description of multi-peaked or localized non-Gaussian distributions and at the same time avoiding numerical instability and computational complexity frequently encountered with conventional basis.The extension here is demonstrated in several typical biochemical signaling networks and achieves similar accuracy as the benchmark Gillespie algorithm,but with much less running time,which seems to open new opportunities in the variational approach to efficient analysis of noisy dynamics.
基金supported by the National Key R&D Program of China under Grant No.2022YFA1003701the National Natural Science Foundation of China under Grant Nos.12331009 and 12071416the Yunnan Fundamental Research Projects under Grant No.202201AV070006。
文摘This paper aims to develop a unified Bayesian approach for clustered data analysis when observations are subject to missingness at random.The authors consider a general framework in which the parameters of interest are defined through estimating equations,and the probability of missingness follows a general parametric form.The generalized method of moments framework is employed to derive an optimal combination of inverse-probability-weighted estimating equations for the parameters of interest and score equations for propensity score.Using this framework,the authors develop a quasi-Bayesian analysis for clustered samples with missing values.A unified model selection approach is also proposed to compare models characterized by different moment conditions.The authors systematically evaluate the large-sample properties of the proposed quasi-posterior density with both fixed and shrinking priors and establish the selection consistency of the proposed model selection criterion.The proposed results are valid under very mild conditions and offer significant advantages for parameters defined through non-smooth estimating functions.Extensive numerical studies demonstrate that the proposed method performs exceptionally well in finite samples.
基金supported in part by the National Natural Science Foundation of China under Grant No.12471281in part by the National Statistical Science Research Project under Grant No.2022LD03。
文摘In this article,the authors explore the online updating estimation for general estimating equations(EEs)in heterogeneous streaming data settings.The framework is based on more conservative model assumptions,leading to more robust estimations and preventing misspecification.The authors establish the standard renewable estimation under blockwise heterogeneity assumption,which can correctly specify model in some sense.To mitigate heterogeneity and enhance estimation accuracy,the authors propose two novel online detection and fusion strategies,with corresponding algorithms provided.Theoretical properties of the proposed methods are demonstrated in the context of small block sizes.Extensive numerical experiments validate the theoretical findings.Real data analysis of the Ford Gobike docked bike-sharing dataset verifies the feasibility and robustness of the proposed methods.
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.
