The fabrication of high-precision panels for the compact antenna test range (CATR) with a sandwich construction of two aluminum skin-plates and one aluminum middle plate,which are bonded to two aluminum honeycomb core...The fabrication of high-precision panels for the compact antenna test range (CATR) with a sandwich construction of two aluminum skin-plates and one aluminum middle plate,which are bonded to two aluminum honeycomb core-layers poses a lot of tricky problems. Of them,the force analysis of individual skin-layers and the springback calculation of sandwich are of utmost importance. Under reasonable assumptions,by using Fourier expansion of stress function and power series expansion of deflection function,two boun...展开更多
In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered in...In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.展开更多
Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In ...Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.展开更多
By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive soluti...By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.展开更多
In this paper, the equations of motion and all boundary conditions as well as the energy equation for non_local asymmetric elasticity are derived together from the complete principles of virtual work and virtual power...In this paper, the equations of motion and all boundary conditions as well as the energy equation for non_local asymmetric elasticity are derived together from the complete principles of virtual work and virtual power as well as the generalized Piola theorem. Adding the boundary conditions presented here to the results by Gao Jian and Dai Tianmin,the mixed boundary_value problem of the non_local asymmetric linear elasticity are formulated.展开更多
Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + ...Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.展开更多
This note is concerned with an iterative method for the solution of singular boundary value problems. It can be considered as a predictor-corrector method. Sufficient conditions for the convergence of the method are i...This note is concerned with an iterative method for the solution of singular boundary value problems. It can be considered as a predictor-corrector method. Sufficient conditions for the convergence of the method are introduced. A number of numerical examples are used to study the applicability of the method.展开更多
we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line{δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0. u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）, u（x,0）=f（x）,δtu（x,0）=δx...we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line{δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0. u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）, u（x,0）=f（x）,δtu（x,0）=δxh（x）.The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data （f, h, h1, h2） belong to the product spaceH^5（R^＋）×H^s-1（R^＋）×H^s/2＋1/4（R^＋）×H^s/2＋1/4（R^＋） 1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered.展开更多
In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approxim...In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.展开更多
The nonlocal theory which confiders interatomic long-range interaction in materials is one of the generalized continuum theories which involve the microstructure characteristic of material media. The basic equations o...The nonlocal theory which confiders interatomic long-range interaction in materials is one of the generalized continuum theories which involve the microstructure characteristic of material media. The basic equations of linear, homogeneous, isotropic, nonlocal elastic solids展开更多
The paper is concerned with the existence and multiplicity of positive solutions for a nonlinear m-point boundary value problem. The proofs are based on a fixed-point theorem and a fixed-point index theorem in cones.
An initial boundary-value problem for the Hirota equation on the half-line,0<x<∞, t>0, is analysed by expressing the solution q(x, t) in terms of the solution of a matrix Riemann-Hilbert(RH) problem in the c...An initial boundary-value problem for the Hirota equation on the half-line,0<x<∞, t>0, is analysed by expressing the solution q(x, t) in terms of the solution of a matrix Riemann-Hilbert(RH) problem in the complex k-plane. This RH problem has explicit(x, t) dependence and it involves certain functions of k referred to as the spectral functions. Some of these functions are defined in terms of the initial condition q(x,0) = q0(x), while the remaining spectral functions are defined in terms of the boundary values q(0, t) = g0(t), qx(0, t) = g1(t) and qxx(0, t) = g2(t). The spectral functions satisfy an algebraic global relation which characterizes, say, g2(t) in terms of {q0(x), g0(t), g1(t)}.The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.展开更多
We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize...We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.展开更多
In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem...In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem. Nonlinear term may be singular at t= 0 and/or t - 1 and x =0.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
In this article,we consider a domain consisting of two cavities linked by a hole of small size.We derive a numerical method to compute an approximation of the eigenvalues of an elliptic operator without refining in th...In this article,we consider a domain consisting of two cavities linked by a hole of small size.We derive a numerical method to compute an approximation of the eigenvalues of an elliptic operator without refining in the neighborhood of the hole.Several convergence rates are obtained and illustrated by numerical simulations.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
基金National Natural Science Foundation of China (10477001, 60673056)
文摘The fabrication of high-precision panels for the compact antenna test range (CATR) with a sandwich construction of two aluminum skin-plates and one aluminum middle plate,which are bonded to two aluminum honeycomb core-layers poses a lot of tricky problems. Of them,the force analysis of individual skin-layers and the springback calculation of sandwich are of utmost importance. Under reasonable assumptions,by using Fourier expansion of stress function and power series expansion of deflection function,two boun...
文摘In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.
基金Project supported by the National Natural Science Foundation of China (Nos.10372016 and 10672022)
文摘Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.
文摘By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.
文摘In this paper, the equations of motion and all boundary conditions as well as the energy equation for non_local asymmetric elasticity are derived together from the complete principles of virtual work and virtual power as well as the generalized Piola theorem. Adding the boundary conditions presented here to the results by Gao Jian and Dai Tianmin,the mixed boundary_value problem of the non_local asymmetric linear elasticity are formulated.
文摘Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.
文摘This note is concerned with an iterative method for the solution of singular boundary value problems. It can be considered as a predictor-corrector method. Sufficient conditions for the convergence of the method are introduced. A number of numerical examples are used to study the applicability of the method.
基金Supported by National Natural Science Foundation of China (Grant No. 10931007)Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6090158)
文摘we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line{δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0. u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）, u（x,0）=f（x）,δtu（x,0）=δxh（x）.The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data （f, h, h1, h2） belong to the product spaceH^5（R^＋）×H^s-1（R^＋）×H^s/2＋1/4（R^＋）×H^s/2＋1/4（R^＋） 1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered.
基金partially supported by the NASA Nebraska Space Grant Program and UCRCA at the University of Nebraska at Omaha.
文摘In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.
基金Project supported by the National Natural Science Foundation of China
文摘The nonlocal theory which confiders interatomic long-range interaction in materials is one of the generalized continuum theories which involve the microstructure characteristic of material media. The basic equations of linear, homogeneous, isotropic, nonlocal elastic solids
基金Supported by the NSFC(10271095).GG-110-10736-1003,NWNU-KJCXGC-212the Foundation of Major Project of Science and Technology of Chinese Education Ministry
文摘Let ξ i ∈ (0, 1) with 0 < ξ1 < ξ2 < ··· < ξ m?2 < 1, a i , b i ∈ [0,∞) with and . We consider the m-point boundary-value problem
基金The paper is supported by NNSFC (10471155)SRFDP (20020558092) SFGD (031608).
文摘The paper is concerned with the existence and multiplicity of positive solutions for a nonlinear m-point boundary value problem. The proofs are based on a fixed-point theorem and a fixed-point index theorem in cones.
基金supported by the China Postdoctoral Science Foundation(No.2015M580285).
文摘An initial boundary-value problem for the Hirota equation on the half-line,0<x<∞, t>0, is analysed by expressing the solution q(x, t) in terms of the solution of a matrix Riemann-Hilbert(RH) problem in the complex k-plane. This RH problem has explicit(x, t) dependence and it involves certain functions of k referred to as the spectral functions. Some of these functions are defined in terms of the initial condition q(x,0) = q0(x), while the remaining spectral functions are defined in terms of the boundary values q(0, t) = g0(t), qx(0, t) = g1(t) and qxx(0, t) = g2(t). The spectral functions satisfy an algebraic global relation which characterizes, say, g2(t) in terms of {q0(x), g0(t), g1(t)}.The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.
基金supported by the program"Leading Scientific Schools"supported by RFBR
文摘We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971179)the Natural Science Foundation of Liaocheng University (Grant No. 31805)
文摘In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem. Nonlinear term may be singular at t= 0 and/or t - 1 and x =0.
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 French National Research Agency under grant No.ANR-08-SYSC-001.
文摘In this article,we consider a domain consisting of two cavities linked by a hole of small size.We derive a numerical method to compute an approximation of the eigenvalues of an elliptic operator without refining in the neighborhood of the hole.Several convergence rates are obtained and illustrated by numerical simulations.
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.
