A new type of Galerkin finite element for first-order initial-value problems(IVPs)is proposed.Both the trial and test functions employ the same m-degreed polynomials.The adjoint equation is used to eliminate one degre...A new type of Galerkin finite element for first-order initial-value problems(IVPs)is proposed.Both the trial and test functions employ the same m-degreed polynomials.The adjoint equation is used to eliminate one degree of freedom(DOF)from the test function,and then the so-called condensed test function and its consequent condensed Galerkin element are constructed.It is mathematically proved and numerically verified that the condensed element produces the super-convergent nodal solutions of O(h^(2m+2)),which is equivalent to the order of accuracy by the conventional element of degree m+1.Some related properties are addressed,and typical numerical examples of both linear and nonlinear IVPs of both a single equation and a system of equations are presented to show the validity and effectiveness of the proposed element.展开更多
A fractal approximation algorithm is developed to obtain approximate solutions to an inverse initial-value problem IVP(inverse IVP) for the differential equation. Numerical computational results are presented to demon...A fractal approximation algorithm is developed to obtain approximate solutions to an inverse initial-value problem IVP(inverse IVP) for the differential equation. Numerical computational results are presented to demonstrate the effectiveness of this algorithm for solving inverse IVP for a class of specific differential equations.展开更多
Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a ...Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.展开更多
Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to...Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in uncomfortably many numerical operations and high memory requirements. It is shown in this work that performance is substantially enhanced by the introduction of algorithms for temporal and spatial subdomains in combination with sparse matrix methods. The accuracy and efficiency of the recently developed time spectral, generalized weighted residual method (GWRM) are compared to that of the explicit Lax-Wendroff and implicit Crank-Nicolson methods. Three initial-value PDEs are employed as model problems;the 1D Burger equation, a forced 1D wave equation and a coupled system of 14 linearized ideal magnetohydrodynamic (MHD) equations. It is found that the GWRM is more efficient than the time-stepping methods at high accuracies. The advantageous scalings Nt<sup style="margin-left:-6px;">1.0Ns<sup style="margin-left:-6px;">1.43 and Nt<sup style="margin-left:-6px;">0.0Ns<sup style="margin-left:-6px;">1.08 were obtained for CPU time and memory requirements, respectively, with Nt and Ns denoting the number of temporal and spatial subdomains. For time-averaged solution of the two-time-scales forced wave equation, GWRM performance exceeds that of the finite difference methods by an order of magnitude both in terms of CPU time and memory requirement. Favorable subdomain scaling is demonstrated for the MHD equations, indicating a potential for efficient solution of advanced initial-value problems in, for example, fluid mechanics and MHD.展开更多
A time-spectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this general...A time-spectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this generalized weighted residual method (GWRM). The approximate solutions obtained are thus analytical, finite order multivariate polynomials. The method avoids time step limitations. To determine the spectral coefficients, a system of algebraic equations is solved iteratively. A root solver, with excellent global convergence properties, has been developed. Accuracy and efficiency are controlled by the number of included Chebyshev modes and by use of temporal and spatial subdomains. As examples of advanced application, stability problems within ideal and resistive magnetohydrodynamics (MHD) are solved. To introduce the method, solutions to a stiff ordinary differential equation are demonstrated and discussed. Subsequently, the GWRM is applied to the Burger and forced wave equations. Comparisons with the explicit Lax-Wendroff and implicit Crank-Nicolson finite difference methods show that the method is accurate and efficient. Thus the method shows potential for advanced initial value problems in fluid mechanics and MHD.展开更多
Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisatio...Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.展开更多
Let K_(j)/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τ_(kj)^(K_(j))(n)be the divisor function associated to Dedekind zeta function SK_(j)(s).In this paper,we consider a multid...Let K_(j)/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τ_(kj)^(K_(j))(n)be the divisor function associated to Dedekind zeta function SK_(j)(s).In this paper,we consider a multidimensional general divisor problem related to the τ_(kj)^(K_(j))(n)involving several number fields over square integers,by establishing the corresponding asymptotic formula.As an application,we also obtain the asymptotic formula of variance of these coefi icients.展开更多
This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theo...This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.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
This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural condit...This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).展开更多
In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can student...In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can students truly experience the importance of teamwork and the impact of organizational structure on project complexity?To answer these questions,we introduce the requirement-driven organization structure(R-DOS)approach,which tightly couples software requirements with the actual development process.By extending problem-frames modeling and focusing on requirements,R-DOS allows educators and students to(1)diagnose structural flaws early,(2)prescribe role-level and communication fixes,and(3)observe-in real time-how poor structure can derail a project while good structure accelerates learning and delivery.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
Background:The growing parenting stress among Chinese mothers in recent years raises concerns about its impact on adolescent internalizing problems.The purpose of this study was to examine the curvilinear relationship...Background:The growing parenting stress among Chinese mothers in recent years raises concerns about its impact on adolescent internalizing problems.The purpose of this study was to examine the curvilinear relationship between maternal parenting stress and internalizing problems in adolescents,and further explore the moderating effects of family socioeconomic status(SES)and adolescent gender.Methods:Data were collected from 405 mothers and adolescents(203 boys,Meanage=12.23)across five cities(Beijing,Hebei,Shanxi,Shenzhen,and Shandong)in China,who completed self-report measures of maternal parenting stress and internalizing problems.Descriptive statistics and multiple regression analyses were conducted using SPSS 27.0.Results:Multiple regression analyses indicated that the association between maternal parenting stress2 and adolescents’internalizing problems was moderated by the interaction between gender and SES(b=−0.03,p<0.01).Specifically,a significant U-shaped relationship was observed among high-SES boys(b=0.12,t=3.89,p<0.001),with internalizing problems peaking at both low and high levels of maternal parenting stress,whereas the moderating effect of SES was not significant among girls.Conclusion:The study highlights that moderate maternal parenting stress is associated with lower internalizing problems among adolescents,particularly among high-SES boys,indicating that interventions should consider the optimal balance of parental stress and account for family socioeconomic and adolescent gender differences.展开更多
Sensitivity of observational data is important in the study of Glacial Isostatic Adjustment(GIA).However,depending on whether sensitivity is used for the Inverse Problem or the Forward Problem,the final formulation an...Sensitivity of observational data is important in the study of Glacial Isostatic Adjustment(GIA).However,depending on whether sensitivity is used for the Inverse Problem or the Forward Problem,the final formulation and display of the sensitivity kernel will be different.Unfortunately,in the past,both perspectives give the same name to their quantity computed/displayed,and that has caused some confusion.To distinguish between the two,their perspective should be added to the names.This paper focuses only on the perspective of the Forward Problem where the input parameters are known.The Perturbation method has been successfully used in the computation of the sensitivity kernels of observations on 1D and 3D viscosity variations from the Forward perspective.One aim of this paper is to review and clarify the physics of the Perturbation method and bring out some important aspects of this method that have been misunderstood or neglected.Another aim is to present sensitivity kernels from the Perturbation method using 3D(both radially and laterally heterogeneous)Earth models with realistic ice history.These new results are now suitable for future comparison with those from new methods using the Forward perspective.Finally,the sensitivity computations for realistic ice histories on a 3D Earth is reviewed and used to search for optimal locations of new GIA observations.展开更多
Cubic-shaped magnetic particles subjected to a dimensionless uniaxial anisotropy(Q=0.1)aligned with one of the crystallographic axes provide an ideal system for investigating magnetic equilibrium states.In this system...Cubic-shaped magnetic particles subjected to a dimensionless uniaxial anisotropy(Q=0.1)aligned with one of the crystallographic axes provide an ideal system for investigating magnetic equilibrium states.In this system,three fundamental magnetization configurations are identified:(i)the flower state,(ii)the twisted flower state,and(iii)the vortex state.This problem corresponds to standard problem No.3 proposed by the NIST Micromagnetics Modeling Group,widely adopted as a benchmark for validating computational micromagnetics methods.In this work,we approach the problem using a computational method based on direct dipolar interactions,in contrast to conventional techniques that typically compute the demagnetizing field via finite difference-based fast Fourier transform(FFT)methods,tensor grid approaches,or finite element formulations.Our results are compared with established literature data,focusing on the dimensionless parameterλ=L/l_(ex),where L is the cube edge length and l_(ex)is the exchange length of the material.To analyze equilibrium state transitions,we systematically varied the size L as a function of the simulation cell number N and intercellular spacing a,determining the criticalλvalue associated with configuration changes.Our simulations reveal that the transition between the twisted flower and vortex states occurs atλ≈8.45,consistent with values reported in the literature,validating our code(Grupo de Física da Matéeria Condensada-UFJF),and shows that this standard problem can be resolved using only interaction dipolar of a direct way without the need for sophisticated additional calculations.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
Backgrounds:Somatization and eating-related problems in adolescents living in residential care may be shaped by the interplay of risk and protective factors,including gender,relational trauma,attachment patterns,emoti...Backgrounds:Somatization and eating-related problems in adolescents living in residential care may be shaped by the interplay of risk and protective factors,including gender,relational trauma,attachment patterns,emotional intelligence,and perceived social support.This study examined how gender,relational trauma,attachment dimensions,resilience,and emotional intelligence contribute to the presence of somatic and eating difficulties in this population.Methods:The sample included 46 adolescents(63%female;ages 12–17,Mean=14.85,Standard Deviation(SD)=1.49)residing in child protection institutions in Uruguay.Participants completed self-report measures assessing childhood relational trauma(CaMir),attachment dimensions(anxiety and avoidance),resilience,emotional intelligence(adaptability and stress management),social support(MOS),and psychosocial adjustment(SENA subscales of somatization and eating problems).Using a fuzzy-set Qualitative Comparative Analysis(fsQCA)approach,distinct configurations of risk and protective factors associated with elevated levels of somatization and eating problems were identified.Results:Relational trauma and attachment anxiety showed moderate associations with both somatization and eating problems(r=0.52–0.57,p<0.01),whereas stress management was negatively associated with both outcomes(r=−0.37 to−0.47,p<0.05).FsQCA revealed multiple configurations of risk and protective factors explaining 81–90%of cases,with solution consistencies ranging from 0.83 to 0.87.Results suggest that relational trauma and attachment anxiety are key risk conditions,whereas resilience,emotional regulation,and perceived social support function as protective factors.Conclusions:Findings highlight the importance of considering multifactorial patterns of vulnerability and protection rather than single predictors and underscore the need for tailored interventions that strengthen resilience and emotional skills while addressing the impact of early relational trauma.展开更多
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer...In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.展开更多
The airplane refueling problem can be stated as follows.We are given n airplanes which can refuel one another during the flight.Each airplane has a reservoir volume wj(liters)and a consumption rate pj(liters per kilom...The airplane refueling problem can be stated as follows.We are given n airplanes which can refuel one another during the flight.Each airplane has a reservoir volume wj(liters)and a consumption rate pj(liters per kilometer).As soon as one airplane runs out of fuel,it is dropping out of the flight.The problem asks for finding a refueling scheme such that the last plane in the air reach a maximal distance.An equivalent version is the n-vehicle exploration problem.The computational complexity of this non-linear combinatorial optimization problem is open so far.This paper employs the neighborhood exchange method of single-machine scheduling to study the precedence relations of jobs,so as to improve the necessary and sufficiency conditions of optimal solutions,and establish an efficient heuristic algorithm which is a generalization of several existing special algorithms.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.51878383 and51378293)。
文摘A new type of Galerkin finite element for first-order initial-value problems(IVPs)is proposed.Both the trial and test functions employ the same m-degreed polynomials.The adjoint equation is used to eliminate one degree of freedom(DOF)from the test function,and then the so-called condensed test function and its consequent condensed Galerkin element are constructed.It is mathematically proved and numerically verified that the condensed element produces the super-convergent nodal solutions of O(h^(2m+2)),which is equivalent to the order of accuracy by the conventional element of degree m+1.Some related properties are addressed,and typical numerical examples of both linear and nonlinear IVPs of both a single equation and a system of equations are presented to show the validity and effectiveness of the proposed element.
文摘A fractal approximation algorithm is developed to obtain approximate solutions to an inverse initial-value problem IVP(inverse IVP) for the differential equation. Numerical computational results are presented to demonstrate the effectiveness of this algorithm for solving inverse IVP for a class of specific differential equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.
文摘Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in uncomfortably many numerical operations and high memory requirements. It is shown in this work that performance is substantially enhanced by the introduction of algorithms for temporal and spatial subdomains in combination with sparse matrix methods. The accuracy and efficiency of the recently developed time spectral, generalized weighted residual method (GWRM) are compared to that of the explicit Lax-Wendroff and implicit Crank-Nicolson methods. Three initial-value PDEs are employed as model problems;the 1D Burger equation, a forced 1D wave equation and a coupled system of 14 linearized ideal magnetohydrodynamic (MHD) equations. It is found that the GWRM is more efficient than the time-stepping methods at high accuracies. The advantageous scalings Nt<sup style="margin-left:-6px;">1.0Ns<sup style="margin-left:-6px;">1.43 and Nt<sup style="margin-left:-6px;">0.0Ns<sup style="margin-left:-6px;">1.08 were obtained for CPU time and memory requirements, respectively, with Nt and Ns denoting the number of temporal and spatial subdomains. For time-averaged solution of the two-time-scales forced wave equation, GWRM performance exceeds that of the finite difference methods by an order of magnitude both in terms of CPU time and memory requirement. Favorable subdomain scaling is demonstrated for the MHD equations, indicating a potential for efficient solution of advanced initial-value problems in, for example, fluid mechanics and MHD.
文摘A time-spectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this generalized weighted residual method (GWRM). The approximate solutions obtained are thus analytical, finite order multivariate polynomials. The method avoids time step limitations. To determine the spectral coefficients, a system of algebraic equations is solved iteratively. A root solver, with excellent global convergence properties, has been developed. Accuracy and efficiency are controlled by the number of included Chebyshev modes and by use of temporal and spatial subdomains. As examples of advanced application, stability problems within ideal and resistive magnetohydrodynamics (MHD) are solved. To introduce the method, solutions to a stiff ordinary differential equation are demonstrated and discussed. Subsequently, the GWRM is applied to the Burger and forced wave equations. Comparisons with the explicit Lax-Wendroff and implicit Crank-Nicolson finite difference methods show that the method is accurate and efficient. Thus the method shows potential for advanced initial value problems in fluid mechanics and MHD.
文摘Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.
基金Supported in part by NSFC(Nos.12401011,12201214)National Key Research and Development Program of China(No.2021YFA1000700)+3 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics(No.23JSQ053)Science and Technology Program for Youth New Star of Shaanxi Province(No.2025ZC-KJXX-29)Natural Science Basic Research Program of Shaanxi Province(No.2025JC-YBQN-091)Scientific Research Foundation for Young Talents of WNU(No.2024XJ-QNRC-01)。
文摘Let K_(j)/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τ_(kj)^(K_(j))(n)be the divisor function associated to Dedekind zeta function SK_(j)(s).In this paper,we consider a multidimensional general divisor problem related to the τ_(kj)^(K_(j))(n)involving several number fields over square integers,by establishing the corresponding asymptotic formula.As an application,we also obtain the asymptotic formula of variance of these coefi icients.
基金Supported by the National Natural Science Foundation of China(11361047)Fundamental Research Program of Shanxi Province(20210302124529)。
文摘This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.
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.
基金Supported by the National Natural Science Foundation of China(Grant No.12371110).
文摘This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).
基金supported by the National Natural Science Foundation of China(No.62362006)Guangxi Science and Technology Project(Key Research&Development)(No.GuiKeAB24010343)+1 种基金Guangxi“Bagui Scholar”Teams for Innovation and Research,Innovation Project of Guangxi Graduate Education(No.YCSW2025193)Guangxi Collaborative Innovation Center of Multi-source Information Integration and Intelligent Processing.
文摘In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can students truly experience the importance of teamwork and the impact of organizational structure on project complexity?To answer these questions,we introduce the requirement-driven organization structure(R-DOS)approach,which tightly couples software requirements with the actual development process.By extending problem-frames modeling and focusing on requirements,R-DOS allows educators and students to(1)diagnose structural flaws early,(2)prescribe role-level and communication fixes,and(3)observe-in real time-how poor structure can derail a project while good structure accelerates learning and delivery.
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.
基金supported by the National Natural Science Foundation of China(32171069).
文摘Background:The growing parenting stress among Chinese mothers in recent years raises concerns about its impact on adolescent internalizing problems.The purpose of this study was to examine the curvilinear relationship between maternal parenting stress and internalizing problems in adolescents,and further explore the moderating effects of family socioeconomic status(SES)and adolescent gender.Methods:Data were collected from 405 mothers and adolescents(203 boys,Meanage=12.23)across five cities(Beijing,Hebei,Shanxi,Shenzhen,and Shandong)in China,who completed self-report measures of maternal parenting stress and internalizing problems.Descriptive statistics and multiple regression analyses were conducted using SPSS 27.0.Results:Multiple regression analyses indicated that the association between maternal parenting stress2 and adolescents’internalizing problems was moderated by the interaction between gender and SES(b=−0.03,p<0.01).Specifically,a significant U-shaped relationship was observed among high-SES boys(b=0.12,t=3.89,p<0.001),with internalizing problems peaking at both low and high levels of maternal parenting stress,whereas the moderating effect of SES was not significant among girls.Conclusion:The study highlights that moderate maternal parenting stress is associated with lower internalizing problems among adolescents,particularly among high-SES boys,indicating that interventions should consider the optimal balance of parental stress and account for family socioeconomic and adolescent gender differences.
文摘Sensitivity of observational data is important in the study of Glacial Isostatic Adjustment(GIA).However,depending on whether sensitivity is used for the Inverse Problem or the Forward Problem,the final formulation and display of the sensitivity kernel will be different.Unfortunately,in the past,both perspectives give the same name to their quantity computed/displayed,and that has caused some confusion.To distinguish between the two,their perspective should be added to the names.This paper focuses only on the perspective of the Forward Problem where the input parameters are known.The Perturbation method has been successfully used in the computation of the sensitivity kernels of observations on 1D and 3D viscosity variations from the Forward perspective.One aim of this paper is to review and clarify the physics of the Perturbation method and bring out some important aspects of this method that have been misunderstood or neglected.Another aim is to present sensitivity kernels from the Perturbation method using 3D(both radially and laterally heterogeneous)Earth models with realistic ice history.These new results are now suitable for future comparison with those from new methods using the Forward perspective.Finally,the sensitivity computations for realistic ice histories on a 3D Earth is reviewed and used to search for optimal locations of new GIA observations.
基金CAPES,CNPq,and FAPEMIG(Brazilian Agencies)for their financial support。
文摘Cubic-shaped magnetic particles subjected to a dimensionless uniaxial anisotropy(Q=0.1)aligned with one of the crystallographic axes provide an ideal system for investigating magnetic equilibrium states.In this system,three fundamental magnetization configurations are identified:(i)the flower state,(ii)the twisted flower state,and(iii)the vortex state.This problem corresponds to standard problem No.3 proposed by the NIST Micromagnetics Modeling Group,widely adopted as a benchmark for validating computational micromagnetics methods.In this work,we approach the problem using a computational method based on direct dipolar interactions,in contrast to conventional techniques that typically compute the demagnetizing field via finite difference-based fast Fourier transform(FFT)methods,tensor grid approaches,or finite element formulations.Our results are compared with established literature data,focusing on the dimensionless parameterλ=L/l_(ex),where L is the cube edge length and l_(ex)is the exchange length of the material.To analyze equilibrium state transitions,we systematically varied the size L as a function of the simulation cell number N and intercellular spacing a,determining the criticalλvalue associated with configuration changes.Our simulations reveal that the transition between the twisted flower and vortex states occurs atλ≈8.45,consistent with values reported in the literature,validating our code(Grupo de Física da Matéeria Condensada-UFJF),and shows that this standard problem can be resolved using only interaction dipolar of a direct way without the need for sophisticated additional calculations.
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.
文摘Backgrounds:Somatization and eating-related problems in adolescents living in residential care may be shaped by the interplay of risk and protective factors,including gender,relational trauma,attachment patterns,emotional intelligence,and perceived social support.This study examined how gender,relational trauma,attachment dimensions,resilience,and emotional intelligence contribute to the presence of somatic and eating difficulties in this population.Methods:The sample included 46 adolescents(63%female;ages 12–17,Mean=14.85,Standard Deviation(SD)=1.49)residing in child protection institutions in Uruguay.Participants completed self-report measures assessing childhood relational trauma(CaMir),attachment dimensions(anxiety and avoidance),resilience,emotional intelligence(adaptability and stress management),social support(MOS),and psychosocial adjustment(SENA subscales of somatization and eating problems).Using a fuzzy-set Qualitative Comparative Analysis(fsQCA)approach,distinct configurations of risk and protective factors associated with elevated levels of somatization and eating problems were identified.Results:Relational trauma and attachment anxiety showed moderate associations with both somatization and eating problems(r=0.52–0.57,p<0.01),whereas stress management was negatively associated with both outcomes(r=−0.37 to−0.47,p<0.05).FsQCA revealed multiple configurations of risk and protective factors explaining 81–90%of cases,with solution consistencies ranging from 0.83 to 0.87.Results suggest that relational trauma and attachment anxiety are key risk conditions,whereas resilience,emotional regulation,and perceived social support function as protective factors.Conclusions:Findings highlight the importance of considering multifactorial patterns of vulnerability and protection rather than single predictors and underscore the need for tailored interventions that strengthen resilience and emotional skills while addressing the impact of early relational trauma.
基金supported by the National Natural Science Foundation of China(11601525)the Natural Science Foundation of Hunan Province(2024JJ5412),the Changsha Municipal Natural Science Foundation(kq2402193).
文摘In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.
基金Supported by Natural Science Foundation of Henan Province(Grant Nos.232300421218 and 252300421483).
文摘The airplane refueling problem can be stated as follows.We are given n airplanes which can refuel one another during the flight.Each airplane has a reservoir volume wj(liters)and a consumption rate pj(liters per kilometer).As soon as one airplane runs out of fuel,it is dropping out of the flight.The problem asks for finding a refueling scheme such that the last plane in the air reach a maximal distance.An equivalent version is the n-vehicle exploration problem.The computational complexity of this non-linear combinatorial optimization problem is open so far.This paper employs the neighborhood exchange method of single-machine scheduling to study the precedence relations of jobs,so as to improve the necessary and sufficiency conditions of optimal solutions,and establish an efficient heuristic algorithm which is a generalization of several existing special algorithms.
