A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element m...A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers.展开更多
Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region....Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.展开更多
In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the...In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.展开更多
This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for th...In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.展开更多
Abstract A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.
This paper is concerned with the existence, uniqueness, comparison and dynamics problem of a functional reaction-diffusion problem. The existence and uniqueness of the global C1,2 strong solution to the problem is der...This paper is concerned with the existence, uniqueness, comparison and dynamics problem of a functional reaction-diffusion problem. The existence and uniqueness of the global C1,2 strong solution to the problem is derived using Schauder fixed point theorem in Banach space instead of the Ascoli-Arzela theorem in the unbounded region, meanwhile, the maximal and minimal solutions are also presented by the monotone iteration method with a pair of supper and lower solutions as the initial iteration.展开更多
This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incr...This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.展开更多
We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） ...We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） quenches at the originx = 0 at the same time ＇1＇ （see Theorem 4.3）. We also tind various other conditions tor the solution to quench in a finite time and obtain the corresponding decay rate of the solution near the quenching time.展开更多
In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed ...In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters. The asymptotic solutions of the problem are given.展开更多
A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary ...A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.展开更多
Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission i...Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission is investigated.We aim to study the existence,nonexistence and minimum wave speed of traveling wave solutions to the model.The results show that the existence and nonexistence of traveling wave solutions are fully determined by the threshold values,which are,the basic reproduction number R0 and critical wave speed c^(*)>0.Specifically,when R0>1 and the wave speed c≥c^(*),the existence of the traveling wave solution is obtained by using Schauder's fixed point theorem and Lyapunov functional.It is proven that the model has no nontrivial traveling wave solutions for R0≤1 or R0>1 and 0<c<c^(*)by employing comparison principle and limit theory.As a consequence,we conclude that the critical wave speed c^(*)is the minimum wave speed of the model.Finally,numerical simulations are carried out to illustrate the effects of several important parameters on the minimum wave speed.展开更多
In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Bot...In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous.We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise.The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method.展开更多
In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof ar...In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .展开更多
This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate ...This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.展开更多
The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion eq...The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion equation was solved. Under suitable conditions, the formal asymptotic solutions were constructed using the method of two-step expansions and the uniform validity of the solutions was proved using the differential inequality.展开更多
With the development of technology,diffusion model-based solvers have shown significant promise in solving Combinatorial Optimization(CO)problems,particularly in tackling Non-deterministic Polynomial-time hard(NP-hard...With the development of technology,diffusion model-based solvers have shown significant promise in solving Combinatorial Optimization(CO)problems,particularly in tackling Non-deterministic Polynomial-time hard(NP-hard)problems such as the Traveling Salesman Problem(TSP).However,existing diffusion model-based solvers typically employ a fixed,uniform noise schedule(e.g.,linear or cosine annealing)across all training instances,failing to fully account for the unique characteristics of each problem instance.To address this challenge,we present GraphGuided Diffusion Solvers(GGDS),an enhanced method for improving graph-based diffusion models.GGDS leverages Graph Neural Networks(GNNs)to capture graph structural information embedded in node coordinates and adjacency matrices,dynamically adjusting the noise levels in the diffusion model.This study investigates the TSP by examining two distinct time-step noise generation strategies:cosine annealing and a Neural Network(NN)-based approach.We evaluate their performance across different problem scales,particularly after integrating graph structural information.Experimental results indicate that GGDS outperforms previous methods with average performance improvements of 18.7%,6.3%,and 88.7%on TSP-500,TSP-100,and TSP-50,respectively.Specifically,GGDS demonstrates superior performance on TSP-500 and TSP-50,while its performance on TSP-100 is either comparable to or slightly better than that of previous methods,depending on the chosen noise schedule and decoding strategy.展开更多
This study examines the mediating role of positive psychological capital and the moderating role of ethnicity in the relationship between mindfulness and internalizing/externalizing problems among adolescents.The stud...This study examines the mediating role of positive psychological capital and the moderating role of ethnicity in the relationship between mindfulness and internalizing/externalizing problems among adolescents.The study sample comprized Chinese adolescents(N=637 ethnic minority;females=40.97%,meam age=12.68,SD=0.49 years;N=636 Han;females=49.06%,mean age=12.71,SD=0.47 years).The participants completed the Child and Adolescent Mindfulness Measure,the Positive Psycap Questionnaire,and the Youth Self-Report.Results from the moderated mediation analysis showed mindfulness was negatively associated with both internalizing and externalizing problems.Ethnicity moderated the relationship between mindfulness and internalizing problems to be stronger for Han adolescents compared to ethnic minority adolescents.Psychological capital mediated the relationship between mindfulness and internalizing problems in both groups,with a negative direction.Findings support the Conservation of Resources theory and highlight mindfulness as a personal resource fostering adolescent well-being in multicultural contexts.展开更多
Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund...Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.展开更多
The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a coll...The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a collaborative scheduling problem inherent to the operational processes of carrier aircraft,where launch and recovery tasks are conducted concurrently on the flight deck.The objective is to minimize the cumulative weighted waiting time in the air for recovering aircraft and the cumulative weighted delay time for launching aircraft.To tackle this challenge,a multiple population self-adaptive differential evolution(MPSADE)algorithm is proposed.This method features a self-adaptive parameter updating mechanism that is contingent upon population diversity,an asynchronous updating scheme,an individual migration operator,and a global crossover mechanism.Additionally,comprehensive experiments are conducted to validate the effectiveness of the proposed model and algorithm.Ultimately,a comparative analysis with existing operation modes confirms the enhanced efficiency of the collaborative operation mode.展开更多
文摘A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers.
基金supported by the Educational Department Foundation of Fujian Province of China(Nos. JA08140 and A0610025)the Scientific Research Foundation of Zhejiang University of Scienceand Technology (No. 2008050)the National Natural Science Foundation of China (No. 50679074)
文摘Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.
文摘In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
基金The first author was supported by Hungarian National Research Fund OTKA No.K67819the second author was partially supported by Hungarian National Research Fund OTKA No.K67819the first and the third authors were supported by Jedlik project “ReCoMend”2008-2011。
文摘In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.
文摘Abstract A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.
基金supported by the NSF of Shandong Province (No.ZR2010AL013, Y2008A31)
文摘This paper is concerned with the existence, uniqueness, comparison and dynamics problem of a functional reaction-diffusion problem. The existence and uniqueness of the global C1,2 strong solution to the problem is derived using Schauder fixed point theorem in Banach space instead of the Ascoli-Arzela theorem in the unbounded region, meanwhile, the maximal and minimal solutions are also presented by the monotone iteration method with a pair of supper and lower solutions as the initial iteration.
文摘This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.
基金supported by NSFC(11201380)the Fundamental Research Funds for the Central Universities(XDJK2012B007)+1 种基金Doctor Fund of Southwest University(SWU111021)Educational Fund of Southwest University(2010JY053)
文摘We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） quenches at the originx = 0 at the same time ＇1＇ （see Theorem 4.3）. We also tind various other conditions tor the solution to quench in a finite time and obtain the corresponding decay rate of the solution near the quenching time.
基金supported by the National Natural Science Foundation of China (Nos. 40676016, 40876010)the Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+1 种基金the LASG State Key Laboratory Special Fundthe E-Institute of Shanghai Municipal Education Commission (No. E03004)
文摘In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters. The asymptotic solutions of the problem are given.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12275065,12275064,12475203)the Natural Science Foundation of Hebei Province(Grant Nos.A2021201010 and A2024201020)+3 种基金Interdisciplinary Research Program of Natural Science of Hebei University(Grant No.DXK202108)Hebei Provincial Central Government Guiding Local Science and Technology Development Funds(Grant No.236Z1501G)Scientific Research and Innovation Team Foundation of Hebei University(Grant No.IT2023B03)the Excellent Youth Research Innovation Team of Hebei University(Grant No.QNTD202402)。
文摘A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.
基金supported by the National Natural Science Foundation of China(12271317,11871316)。
文摘Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission is investigated.We aim to study the existence,nonexistence and minimum wave speed of traveling wave solutions to the model.The results show that the existence and nonexistence of traveling wave solutions are fully determined by the threshold values,which are,the basic reproduction number R0 and critical wave speed c^(*)>0.Specifically,when R0>1 and the wave speed c≥c^(*),the existence of the traveling wave solution is obtained by using Schauder's fixed point theorem and Lyapunov functional.It is proven that the model has no nontrivial traveling wave solutions for R0≤1 or R0>1 and 0<c<c^(*)by employing comparison principle and limit theory.As a consequence,we conclude that the critical wave speed c^(*)is the minimum wave speed of the model.Finally,numerical simulations are carried out to illustrate the effects of several important parameters on the minimum wave speed.
文摘In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous.We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise.The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method.
基金supported by the NSFC(12271141)supported by the Fundamental Research Funds for the Central Universities(B240205026)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX24_0821).
文摘In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .
基金supported by the National Natural Science Foundation of China(No.12271399)the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.
基金Project supported by National Natural Science Foundation ofChina(Grant No .10071048)
文摘The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion equation was solved. Under suitable conditions, the formal asymptotic solutions were constructed using the method of two-step expansions and the uniform validity of the solutions was proved using the differential inequality.
基金supported by the National Science and Technology Council,Taiwan,under grant no.NSTC 114-2221-E-197-005-MY3.
文摘With the development of technology,diffusion model-based solvers have shown significant promise in solving Combinatorial Optimization(CO)problems,particularly in tackling Non-deterministic Polynomial-time hard(NP-hard)problems such as the Traveling Salesman Problem(TSP).However,existing diffusion model-based solvers typically employ a fixed,uniform noise schedule(e.g.,linear or cosine annealing)across all training instances,failing to fully account for the unique characteristics of each problem instance.To address this challenge,we present GraphGuided Diffusion Solvers(GGDS),an enhanced method for improving graph-based diffusion models.GGDS leverages Graph Neural Networks(GNNs)to capture graph structural information embedded in node coordinates and adjacency matrices,dynamically adjusting the noise levels in the diffusion model.This study investigates the TSP by examining two distinct time-step noise generation strategies:cosine annealing and a Neural Network(NN)-based approach.We evaluate their performance across different problem scales,particularly after integrating graph structural information.Experimental results indicate that GGDS outperforms previous methods with average performance improvements of 18.7%,6.3%,and 88.7%on TSP-500,TSP-100,and TSP-50,respectively.Specifically,GGDS demonstrates superior performance on TSP-500 and TSP-50,while its performance on TSP-100 is either comparable to or slightly better than that of previous methods,depending on the chosen noise schedule and decoding strategy.
基金supported by the Guizhou Provincial Science and Technology Projects[Basic Science of Guizhou-[2024]Youth 309,Guizhou Platform Talents[2021]1350-046]Zunyi Science and Technology Cooperation[HZ(2024)311]+3 种基金Funding of the Chinese Academy of Social Sciences(2024SYZH005)Peking University Longitudinal Scientific Research Technical Service Project(G-252)Guizhou Provincial Graduate Student Research Fund Project(2024YJSKYJJ339)Zunyi Medical University Graduate Research Fund Project(ZYK206).
文摘This study examines the mediating role of positive psychological capital and the moderating role of ethnicity in the relationship between mindfulness and internalizing/externalizing problems among adolescents.The study sample comprized Chinese adolescents(N=637 ethnic minority;females=40.97%,meam age=12.68,SD=0.49 years;N=636 Han;females=49.06%,mean age=12.71,SD=0.47 years).The participants completed the Child and Adolescent Mindfulness Measure,the Positive Psycap Questionnaire,and the Youth Self-Report.Results from the moderated mediation analysis showed mindfulness was negatively associated with both internalizing and externalizing problems.Ethnicity moderated the relationship between mindfulness and internalizing problems to be stronger for Han adolescents compared to ethnic minority adolescents.Psychological capital mediated the relationship between mindfulness and internalizing problems in both groups,with a negative direction.Findings support the Conservation of Resources theory and highlight mindfulness as a personal resource fostering adolescent well-being in multicultural contexts.
文摘Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.
文摘The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a collaborative scheduling problem inherent to the operational processes of carrier aircraft,where launch and recovery tasks are conducted concurrently on the flight deck.The objective is to minimize the cumulative weighted waiting time in the air for recovering aircraft and the cumulative weighted delay time for launching aircraft.To tackle this challenge,a multiple population self-adaptive differential evolution(MPSADE)algorithm is proposed.This method features a self-adaptive parameter updating mechanism that is contingent upon population diversity,an asynchronous updating scheme,an individual migration operator,and a global crossover mechanism.Additionally,comprehensive experiments are conducted to validate the effectiveness of the proposed model and algorithm.Ultimately,a comparative analysis with existing operation modes confirms the enhanced efficiency of the collaborative operation mode.
