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
The approach of word problems is adopted to study the centers of nonautonomous cubic equations.We answer various questions that arise from this investigation. In particular.we demonstrate that a recent condition for t...The approach of word problems is adopted to study the centers of nonautonomous cubic equations.We answer various questions that arise from this investigation. In particular.we demonstrate that a recent condition for the existence of a center is not necessary.展开更多
In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any orde...In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any order derivative of h(x) at x=0 and obtain the focus value of each order. The new method in this paper avoids the recurence operation and reduces the work in calculating the focus value.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
Virtual Machine（VM） allocation for multiple tenants is an important and challenging problem to provide efficient infrastructure services in cloud data centers. Tenants run applications on their allocated VMs, and th...Virtual Machine（VM） allocation for multiple tenants is an important and challenging problem to provide efficient infrastructure services in cloud data centers. Tenants run applications on their allocated VMs, and the network distance between a tenant＇s VMs may considerably impact the tenant＇s Quality of Service（Qo S）. In this study, we define and formulate the multi-tenant VM allocation problem in cloud data centers, considering the VM requirements of different tenants, and introducing the allocation goal of minimizing the sum of the VMs＇ network diameters of all tenants. Then, we propose a Layered Progressive resource allocation algorithm for multi-tenant cloud data centers based on the Multiple Knapsack Problem（LP-MKP）. The LP-MKP algorithm uses a multi-stage layered progressive method for multi-tenant VM allocation and efficiently handles unprocessed tenants at each stage. This reduces resource fragmentation in cloud data centers, decreases the differences in the Qo S among tenants, and improves tenants＇ overall Qo S in cloud data centers. We perform experiments to evaluate the LP-MKP algorithm and demonstrate that it can provide significant gains over other allocation algorithms.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
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.
文摘The approach of word problems is adopted to study the centers of nonautonomous cubic equations.We answer various questions that arise from this investigation. In particular.we demonstrate that a recent condition for the existence of a center is not necessary.
文摘In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any order derivative of h(x) at x=0 and obtain the focus value of each order. The new method in this paper avoids the recurence operation and reduces the work in calculating the focus value.
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supported in part by the National Key Basic Research and Development (973) Program of China (No. 2011CB302600)the National Natural Science Foundation of China (No. 61222205)+1 种基金the Program for New Century Excellent Talents in Universitythe Fok Ying-Tong Education Foundation (No. 141066)
文摘Virtual Machine（VM） allocation for multiple tenants is an important and challenging problem to provide efficient infrastructure services in cloud data centers. Tenants run applications on their allocated VMs, and the network distance between a tenant＇s VMs may considerably impact the tenant＇s Quality of Service（Qo S）. In this study, we define and formulate the multi-tenant VM allocation problem in cloud data centers, considering the VM requirements of different tenants, and introducing the allocation goal of minimizing the sum of the VMs＇ network diameters of all tenants. Then, we propose a Layered Progressive resource allocation algorithm for multi-tenant cloud data centers based on the Multiple Knapsack Problem（LP-MKP）. The LP-MKP algorithm uses a multi-stage layered progressive method for multi-tenant VM allocation and efficiently handles unprocessed tenants at each stage. This reduces resource fragmentation in cloud data centers, decreases the differences in the Qo S among tenants, and improves tenants＇ overall Qo S in cloud data centers. We perform experiments to evaluate the LP-MKP algorithm and demonstrate that it can provide significant gains over other allocation algorithms.
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.
