In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the ...We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the distribution of the lengths of these intervals is relatively light compared to the distribution of the increments of the random walks,we derive the asymptotic tail distribution of the partial maximum sum over the random time interval.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
In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asy...In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asymptotic stability of the trivial solution and the positive periodic solution.Finally,numerical simulations are presented to validate our results.Our results show that age-selective harvesting is more conducive to sustainable population survival than non-age-selective harvesting.展开更多
With the rapid development of artificial intelligence,intelligent air combat maneuver decision-making(ACMD)has garnered global attention.Although deep reinforcement learning provides a promising approach to ACMD,exist...With the rapid development of artificial intelligence,intelligent air combat maneuver decision-making(ACMD)has garnered global attention.Although deep reinforcement learning provides a promising approach to ACMD,existing methods often suffer from rigid reward functions and limited adaptability to evolving adversarial strategies.Moreover,most research assumes open airspace,overlooking the influence of potential obstacles.In this paper,we address one-on-one within-visual-range ACMD in obstructed environments,and propose an improved Soft Actor-Critic(SAC)algorithm trained under a curriculum self-play framework.A maneuver strategy mirroring inference module is integrated to estimate each other's likely positions when visual obstruction occurs.By leveraging curriculum learning to guide progressive experience accumulation and self-play for adversarial evolution,our method enhances both training efficiency and tactical diversity.We further integrate an attention mechanism that dynamically adjusts the weights of sub-rewards,enabling the learned policy to adapt to rapidly changing air combat situations.Numerical simulations demonstrate that our enhanced SAC converges more quickly and achieves higher win rates than other baseline methods.An animation is available at bilibili.com/video/BV1BHVszHE98 for better illustration.展开更多
As carrier aircraft sortie frequency and flight deck operational density increase,autonomous dispatch trajectory planning for carrier-based vehicles demands efficient,safe,and kinematically feasible solutions.This pap...As carrier aircraft sortie frequency and flight deck operational density increase,autonomous dispatch trajectory planning for carrier-based vehicles demands efficient,safe,and kinematically feasible solutions.This paper presents an Iterative Safe Dispatch Corridor(iSDC)framework,addressing the suboptimality of the traditional SDC method caused by static corridor construction and redundant obstacle exploration.First,a Kinodynamic-Informed-Bidirectional Rapidly-exploring Random Tree Star(KIBRRT^(*))algorithm is proposed for the front-end coarse planning.By integrating bidirectional tree expansion,goal-biased elliptical sampling,and artificial potential field guidance,it reduces unnecessary exploration near concave obstacles and generates kinematically admissible paths.Secondly,the traditional SDC is implemented in an iterative manner,and the obtained trajectory in the current iteration is fed into the next iteration for corridor generation,thus progressively improving the quality of withincorridor constraints.For tractors,a reverse-motion penalty function is incorporated into the back-end optimizer to prioritize forward driving,aligning with mechanical constraints and human operational preferences.Numerical validations on the data of Gerald R.Ford-class carrier demonstrate that the KIBRRT^(*)reduces average computational time by 75%and expansion nodes by 25%compared to conventional RRT^(*)algorithms.Meanwhile,the iSDC framework yields more time-efficient trajectories for both carrier aircraft and tractors,with the dispatch time reduced by 31.3%and tractor reverse motion proportion decreased by 23.4%relative to traditional SDC.The presented framework offers a scalable solution for autonomous dispatch in confined and safety-critical environment,and an illustrative animation is available at bilibili.com/video/BV1tZ7Zz6Eyz.Moreover,the framework can be easily extended to three-dimension scenarios,and thus applicable for trajectory planning of aerial and underwater vehicles.展开更多
In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation ...In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.展开更多
In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained f...In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.展开更多
In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergen...In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.展开更多
For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial...For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.展开更多
This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
For every integer 4≤d≤11,an explicit construction of infinite families of 2d-regular unique-neighbor expanders is presented,which is a generalization of the 6-regular unique-neighbors initially developed by Alon and...For every integer 4≤d≤11,an explicit construction of infinite families of 2d-regular unique-neighbor expanders is presented,which is a generalization of the 6-regular unique-neighbors initially developed by Alon and Capalbo.Additionally,for values of d greater than 11,a sufficient condition is established for employing the same construction method.Our construction method involves the“line product”of large bipartite Ramanujan graphs and a sufficiently good unique-neighbor expander(a small gadget).展开更多
This paper investigates ruin,capital injection,and dividends for a two-dimensional risk model.The model posits that surplus levels of insurance companies are governed by a perturbed composite Poisson risk model.This m...This paper investigates ruin,capital injection,and dividends for a two-dimensional risk model.The model posits that surplus levels of insurance companies are governed by a perturbed composite Poisson risk model.This model introduces a dependence between the two surplus levels,present in both the associated perturbations and the claims resulting from common shocks.Critical levels of capital injection and dividends are established for each of the two risks.The surplus levels are observed discretely at fixed intervals,guiding decisions on capital injection,dividends,and ruin at these junctures.This study employs a two-dimensional Fourier cosine series expansion method to approximate the finite time expected discounted operating cost until ruin.The ensuing approximation error is also quantified.The validity and accuracy of the method are corroborated through numerical examples.Furthermore,the research delves into the optimal capital allocation problem.展开更多
Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_...Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.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
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
A generalization of the linguistic aggregation functions （or operators） is presented by using generalized and quasiarithmetic means. Firstly, the linguistic weighted generalized mean （LWGM） and the linguistic gene...A generalization of the linguistic aggregation functions （or operators） is presented by using generalized and quasiarithmetic means. Firstly, the linguistic weighted generalized mean （LWGM） and the linguistic generalized ordered weighted averaging （LGOWA） operator are introduced. These aggregation functions use linguistic information and generalized means in the weighted average （WA） and in the ordered weighted averaging （OWA） function. They are very useful for uncertain situations where the available information cannot be assessed with numerical values but it is possible to use linguistic assessments. These aggregation operators generalize a wide range of aggregation operators that use linguistic information such as the linguistic generalized mean （LGM）, the linguistic OWA （LOWA） operator and the linguistic or- dered weighted quadratic averaging （LOWQA） operator. We also introduce a further generalization by using quasi-arithmetic means instead of generalized means obtaining the quasi-LWA and the quasi-LOWA operator. Finally, we develop an application of the new approach where we analyze a decision making problem regarding the selection of strategies.展开更多
Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic diffe...Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.展开更多
In this article, the authors obtain some theoretical results for 2_(IV)^(m-p) designs to have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear...In this article, the authors obtain some theoretical results for 2_(IV)^(m-p) designs to have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2_(IV)^(m-p) designs with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration.展开更多
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
基金supported by Xinjiang Normal University Outstanding Young Teacher Research Launch Fund Project(Grant No.XJNU202116)。
文摘We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the distribution of the lengths of these intervals is relatively light compared to the distribution of the increments of the random walks,we derive the asymptotic tail distribution of the partial maximum sum over the random time interval.
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 the National Natural Science Foundation of China(12261018)Universities Key Laboratory of Mathematical Modeling and Data Mining in Guizhou Province(2023013)。
文摘In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asymptotic stability of the trivial solution and the positive periodic solution.Finally,numerical simulations are presented to validate our results.Our results show that age-selective harvesting is more conducive to sustainable population survival than non-age-selective harvesting.
基金support of the National Key Research and Development Plan(No.2021YFB3302501)the financial support of the National Science Foundation of China(No.12161076)the financial support of the Fundamental Research Funds for the Central Universities(No.DUT25GF207).
文摘With the rapid development of artificial intelligence,intelligent air combat maneuver decision-making(ACMD)has garnered global attention.Although deep reinforcement learning provides a promising approach to ACMD,existing methods often suffer from rigid reward functions and limited adaptability to evolving adversarial strategies.Moreover,most research assumes open airspace,overlooking the influence of potential obstacles.In this paper,we address one-on-one within-visual-range ACMD in obstructed environments,and propose an improved Soft Actor-Critic(SAC)algorithm trained under a curriculum self-play framework.A maneuver strategy mirroring inference module is integrated to estimate each other's likely positions when visual obstruction occurs.By leveraging curriculum learning to guide progressive experience accumulation and self-play for adversarial evolution,our method enhances both training efficiency and tactical diversity.We further integrate an attention mechanism that dynamically adjusts the weights of sub-rewards,enabling the learned policy to adapt to rapidly changing air combat situations.Numerical simulations demonstrate that our enhanced SAC converges more quickly and achieves higher win rates than other baseline methods.An animation is available at bilibili.com/video/BV1BHVszHE98 for better illustration.
基金support of the National Key Research and Development Plan(Grant No.2021YFB3302501)the financial support of the National Science Foundation of China(Grant No.12161076)the financial support of the Fundamental Research Funds for the Central Universities(Grant No.DUT24LAB129).
文摘As carrier aircraft sortie frequency and flight deck operational density increase,autonomous dispatch trajectory planning for carrier-based vehicles demands efficient,safe,and kinematically feasible solutions.This paper presents an Iterative Safe Dispatch Corridor(iSDC)framework,addressing the suboptimality of the traditional SDC method caused by static corridor construction and redundant obstacle exploration.First,a Kinodynamic-Informed-Bidirectional Rapidly-exploring Random Tree Star(KIBRRT^(*))algorithm is proposed for the front-end coarse planning.By integrating bidirectional tree expansion,goal-biased elliptical sampling,and artificial potential field guidance,it reduces unnecessary exploration near concave obstacles and generates kinematically admissible paths.Secondly,the traditional SDC is implemented in an iterative manner,and the obtained trajectory in the current iteration is fed into the next iteration for corridor generation,thus progressively improving the quality of withincorridor constraints.For tractors,a reverse-motion penalty function is incorporated into the back-end optimizer to prioritize forward driving,aligning with mechanical constraints and human operational preferences.Numerical validations on the data of Gerald R.Ford-class carrier demonstrate that the KIBRRT^(*)reduces average computational time by 75%and expansion nodes by 25%compared to conventional RRT^(*)algorithms.Meanwhile,the iSDC framework yields more time-efficient trajectories for both carrier aircraft and tractors,with the dispatch time reduced by 31.3%and tractor reverse motion proportion decreased by 23.4%relative to traditional SDC.The presented framework offers a scalable solution for autonomous dispatch in confined and safety-critical environment,and an illustrative animation is available at bilibili.com/video/BV1tZ7Zz6Eyz.Moreover,the framework can be easily extended to three-dimension scenarios,and thus applicable for trajectory planning of aerial and underwater vehicles.
基金Supported by the Jiangsu Higher School Undergraduate Innovation and Entrepreneurship Training Program(202311117078Y)。
文摘In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.
基金Supported by the National Natural Science Foundation of China(11971458,11471310)。
文摘In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.
基金supported by the National Social Science Fundation(Grant No.21BTJ040)the Project of Outstanding Young People in University of Anhui Province(Grant Nos.2023AH020037,SLXY2024A001).
文摘In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.
基金Supported by Projects from Chongqing Municipal Science and Technology Commission(CSTB2022NSCQ-MSX0445)。
文摘For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
文摘For every integer 4≤d≤11,an explicit construction of infinite families of 2d-regular unique-neighbor expanders is presented,which is a generalization of the 6-regular unique-neighbors initially developed by Alon and Capalbo.Additionally,for values of d greater than 11,a sufficient condition is established for employing the same construction method.Our construction method involves the“line product”of large bipartite Ramanujan graphs and a sufficiently good unique-neighbor expander(a small gadget).
基金supported by the Shihezi University High-Level Talents Research Startup Project(Project No.RCZK202521)the National Natural Science Foundation of China(Grant Nos.12271066,11871121,12171405)+1 种基金the Chongqing Natural Science Foundation Joint Fund for Innovation and Development Project(Project No.CSTB2024NSCQLZX0085)the Chongqing Normal University Foundation(Grant No.23XLB018).
文摘This paper investigates ruin,capital injection,and dividends for a two-dimensional risk model.The model posits that surplus levels of insurance companies are governed by a perturbed composite Poisson risk model.This model introduces a dependence between the two surplus levels,present in both the associated perturbations and the claims resulting from common shocks.Critical levels of capital injection and dividends are established for each of the two risks.The surplus levels are observed discretely at fixed intervals,guiding decisions on capital injection,dividends,and ruin at these junctures.This study employs a two-dimensional Fourier cosine series expansion method to approximate the finite time expected discounted operating cost until ruin.The ensuing approximation error is also quantified.The validity and accuracy of the method are corroborated through numerical examples.Furthermore,the research delves into the optimal capital allocation problem.
基金supported by the National Key Research and Development Program of China(2023YFA1010200,2020YFA0713100)the National Natural Science Foundation of China(12071453)the Innovation Program for Quantum Science and Technology(2021ZD0302902).
文摘Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.
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.
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 Spanish Ministry of Education(JC2009-00189)the Spanish Ministry of Foreign Affairs(A/023879/09)+1 种基金the National Natural Science Foundation of China(71071002)Academic Innovation Team of Anhui University(KJTD001B,SKTD007B)
文摘A generalization of the linguistic aggregation functions （or operators） is presented by using generalized and quasiarithmetic means. Firstly, the linguistic weighted generalized mean （LWGM） and the linguistic generalized ordered weighted averaging （LGOWA） operator are introduced. These aggregation functions use linguistic information and generalized means in the weighted average （WA） and in the ordered weighted averaging （OWA） function. They are very useful for uncertain situations where the available information cannot be assessed with numerical values but it is possible to use linguistic assessments. These aggregation operators generalize a wide range of aggregation operators that use linguistic information such as the linguistic generalized mean （LGM）, the linguistic OWA （LOWA） operator and the linguistic or- dered weighted quadratic averaging （LOWQA） operator. We also introduce a further generalization by using quasi-arithmetic means instead of generalized means obtaining the quasi-LWA and the quasi-LOWA operator. Finally, we develop an application of the new approach where we analyze a decision making problem regarding the selection of strategies.
基金Project(06JJ30024) supported by the Natural Science Foundation of Hunan Province, ChinaProject(2004CB619206) supported by the Major State Basic Research and Development Program of China+1 种基金Project(50321402) supported by the National Science Fund for Innovative Research Groups of ChinaProject(06B052) supported by the Scientific Research Fund of Hunan Provincial Education Department of China
文摘Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.
基金Research supported by the NNSF of China (10301015: 10571093)the SRFDP of China (20050055038)the China Portdoctoral Science Foundation (20060390169)Liu and Zhang's research was also supported by the Visiting Scholar Program at Chern Institute of Mathematics.
文摘In this article, the authors obtain some theoretical results for 2_(IV)^(m-p) designs to have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2_(IV)^(m-p) designs with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration.
