We present a new exactly solvable quantum problem for which the Schrtidinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two-Coulomb-center prob...We present a new exactly solvable quantum problem for which the Schrtidinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two-Coulomb-center problem for the case of an imaginary intercenter parameter and complex conjugate charges are considered. Since the potential is defined by the two-sheeted mapping whose singularities are concentrated on a circle rather than at separate points, there arise additional possibilities in the choice of boundary conditions. A detailed classification of the various types of boundary-value problems is given. The quasi-radial equation leads to a new type of boundary value problem which has never been considered before. Results of the numerical calculations, which allow conclusions to be drawn about the structure of the energy spectrum, are shown. Possible physical applications are discussed.展开更多
For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessa...For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.展开更多
The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy ran...The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy randomized adaptive search procedure with path-relinking （GRASP/PR） algorithm for the p-center problem, which combines both GRASP and path-relinking. Each iteration of GRASP/PR consists of the construction of a randomized greedy solution, followed by a tabu search procedure. The resulting solution is combined with one of the elite solutions by path-relinking, which consists in exploring trajectories that connect high-quality solutions. Experiments show that GRASP/PR is competitive with the state-of-the-art algorithms in the literature in terms of both solution quality and computational efficiency. Specifically, it virtually improves the previous best known results for 10 out of 40 large instances while matching the best known results for others.展开更多
This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls...This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls(2020)and the one by Zhou(2020),respectively.The proofs in this paper are much simpler than the previous ones.展开更多
The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we giv...The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we give new centers for s = 6, 7 a linear center perturbed by They are completely classified these results for s = 2, 3, 4, 5,展开更多
Consider the polynomial differential system of degree m of the form x=-y(1+μ(a_(2)x-a_(1)y))+x(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),y=x(1+μ(a_(2)x-a_(1)y))+y(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),whereμandνare real numbers s...Consider the polynomial differential system of degree m of the form x=-y(1+μ(a_(2)x-a_(1)y))+x(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),y=x(1+μ(a_(2)x-a_(1)y))+y(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),whereμandνare real numbers such that(μ^(2)+v^(2))(μ+v(m-2))(a_(1)^(2)+a_(2)^(2))≠m>2 andΩ_(m−1)(x,y)is a homogenous polynomial of degree m−1.A conjecture,stated in J.Differential Equations 2019,suggests that whenν=1,this differential system has a weak center at the origin if and only if after a convenient linear change of variable(x,y)→(X,Y)the system is invariant under the transformation(X,Y,t)→(−X,Y,−t).For every degree m we prove the extension of this conjecture to any value ofνexcept for a finite set of values ofμ.展开更多
In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techn...In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence.To prove the convergence in a simply way,we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space.Thus,the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions.Numerical results show that the new algorithm has better convergence than the existing algorithms.展开更多
With the popularity of Computer Assisted Language Learning(CALL),autonomous language learning centers have been established in the universities throughout the country.However,there are many problems exist in the pract...With the popularity of Computer Assisted Language Learning(CALL),autonomous language learning centers have been established in the universities throughout the country.However,there are many problems exist in the practice of the autonomous language learning center.This essay tries to discuss the problems and its countermeasures with an aim of improving College English learning and teaching by the example of autonomous language learning center in Nanyang Institute of Technology.展开更多
Under the current new situation, the core principle of the reform of the education and teaching in the military academies is the ＂problem center＂ . In the center of the teaching mode, the ＂problem＂ is the core of...Under the current new situation, the core principle of the reform of the education and teaching in the military academies is the ＂problem center＂ . In the center of the teaching mode, the ＂problem＂ is the core of teaching, the teaching process is carried out around the ＂problem＂ . Based on the analysis of the status of ＂problem＂ problem centered teaching mode based on the proposed worked in education and teaching, setting principles and strategies, on the teaching reform of the post education has a certain guiding significance.展开更多
In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of ...In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.展开更多
文摘We present a new exactly solvable quantum problem for which the Schrtidinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two-Coulomb-center problem for the case of an imaginary intercenter parameter and complex conjugate charges are considered. Since the potential is defined by the two-sheeted mapping whose singularities are concentrated on a circle rather than at separate points, there arise additional possibilities in the choice of boundary conditions. A detailed classification of the various types of boundary-value problems is given. The quasi-radial equation leads to a new type of boundary value problem which has never been considered before. Results of the numerical calculations, which allow conclusions to be drawn about the structure of the energy spectrum, are shown. Possible physical applications are discussed.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10831003 and 10771196）
文摘For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.
基金The research was supported by the National Natural Science Foundation of China under Grant Nos. 61370183 and 61262011.
文摘The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy randomized adaptive search procedure with path-relinking （GRASP/PR） algorithm for the p-center problem, which combines both GRASP and path-relinking. Each iteration of GRASP/PR consists of the construction of a randomized greedy solution, followed by a tabu search procedure. The resulting solution is combined with one of the elite solutions by path-relinking, which consists in exploring trajectories that connect high-quality solutions. Experiments show that GRASP/PR is competitive with the state-of-the-art algorithms in the literature in terms of both solution quality and computational efficiency. Specifically, it virtually improves the previous best known results for 10 out of 40 large instances while matching the best known results for others.
基金Supported by NSFC(Grant Nos.12171491 and 12071006)。
文摘This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls(2020)and the one by Zhou(2020),respectively.The proofs in this paper are much simpler than the previous ones.
基金The author is partially supported by a DGICYT grant number BFM 2002-04236-C02-01 by DURSI of Government of Catalonia"Distincióde la Generalitat de Catalunya per a la promocióde la recerca universitària"
文摘The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we give new centers for s = 6, 7 a linear center perturbed by They are completely classified these results for s = 2, 3, 4, 5,
基金Supported by Grant NNSF of China(Grant No.12171491)the Ministerio de Ciencia,Innovación y Universidades,Agencia Estatal de Investigación grants MTM2016-77278-P(FEDER)and PID2019-104658GB-I00(FEDER)+1 种基金the Agència de Gestiód’Ajuts Universitaris i de Recerca grant 2017SGR1617the H2020 European Research Council grant MSCA-RISE-2017-777911。
文摘Consider the polynomial differential system of degree m of the form x=-y(1+μ(a_(2)x-a_(1)y))+x(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),y=x(1+μ(a_(2)x-a_(1)y))+y(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),whereμandνare real numbers such that(μ^(2)+v^(2))(μ+v(m-2))(a_(1)^(2)+a_(2)^(2))≠m>2 andΩ_(m−1)(x,y)is a homogenous polynomial of degree m−1.A conjecture,stated in J.Differential Equations 2019,suggests that whenν=1,this differential system has a weak center at the origin if and only if after a convenient linear change of variable(x,y)→(X,Y)the system is invariant under the transformation(X,Y,t)→(−X,Y,−t).For every degree m we prove the extension of this conjecture to any value ofνexcept for a finite set of values ofμ.
基金Supported by the NNSF of china(11171221)SuppoSed by the Shanghai Municipal Committee of Science and Technology(10550500800)
文摘In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence.To prove the convergence in a simply way,we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space.Thus,the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions.Numerical results show that the new algorithm has better convergence than the existing algorithms.
文摘With the popularity of Computer Assisted Language Learning(CALL),autonomous language learning centers have been established in the universities throughout the country.However,there are many problems exist in the practice of the autonomous language learning center.This essay tries to discuss the problems and its countermeasures with an aim of improving College English learning and teaching by the example of autonomous language learning center in Nanyang Institute of Technology.
文摘Under the current new situation, the core principle of the reform of the education and teaching in the military academies is the ＂problem center＂ . In the center of the teaching mode, the ＂problem＂ is the core of teaching, the teaching process is carried out around the ＂problem＂ . Based on the analysis of the status of ＂problem＂ problem centered teaching mode based on the proposed worked in education and teaching, setting principles and strategies, on the teaching reform of the post education has a certain guiding significance.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11403013 and 11672126)the Fundamental Research Funds for the Central Universities (Nos. 56XAA14093 and 56YAH12036)the Postdoctoral Foundation of Jiangsu Province (No. 1301029B)
文摘In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.
