要证明“1+1”等数学命题,需建立一个新数学模型 — pn 阶准素数模型。该模型具有方便于研究的阶梯性、周期性、对称性、可递推性、宏观均匀性等等。其隐含的递推机制是:每层 pi 筛网对 pi?1阶准素数中,每支同相位、等间距准素数的有效...要证明“1+1”等数学命题,需建立一个新数学模型 — pn 阶准素数模型。该模型具有方便于研究的阶梯性、周期性、对称性、可递推性、宏观均匀性等等。其隐含的递推机制是:每层 pi 筛网对 pi?1阶准素数中,每支同相位、等间距准素数的有效筛除,都是每隔 ( pi ?1)p ?1个、便精准地筛掉1个;存留率为 ipi 。于是,小于 x 的素数及“特定素数n pi ?1对”数目,便有了误差δn (x) 占比小且趋于0的、连续函数计算式:π n (x) = x ? ∏ p +δi=1 i n (x) 等。可证得 δn (x) ≤ n ;可算得任意x x x偶数 的“1+1”数目之底线为 limλ(x) ≥x→∝ 4 ;小于 x 的“孪生素数对”数目之底线为 lim R(x) ≥x→∝ 2 。且当 x 增至16后,该两个底线已蜕变为: λ(x) ≥ x ; R(x) ≥ x4 2 。这两个底线皆为 x 的递增函数,就是证明哥德巴赫猜想命题“1+1”及孪生素数无穷性的、无懈可击之数学证据。展开更多
The constriction factor method (CFM) is a new variation of the basic particle swarm optimization (PSO), which has relatively better convergent nature. The effects of the major parameters on CFM were systematically inv...The constriction factor method (CFM) is a new variation of the basic particle swarm optimization (PSO), which has relatively better convergent nature. The effects of the major parameters on CFM were systematically investigated based on some benchmark functions. The constriction factor, velocity constraint, and population size all have significant impact on the per- formance of CFM for PSO. The constriction factor and velocity constraint have optimal values in practical application, and im- proper choice of these factors will lead to bad results. Increasing population size can improve the solution quality, although the computing time will be longer. The characteristics of CFM parameters are described and guidelines for determining parameter values are given in this paper.展开更多
Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)...Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).展开更多
The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The pote...The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.展开更多
Multi-quasiparticle states and rotational bands in neutron-rich erbium isotopes have been investigated by the configuration- constrained pairing-deformation-frequency self-consistent total-Routhian-surface （TRS） met...Multi-quasiparticle states and rotational bands in neutron-rich erbium isotopes have been investigated by the configuration- constrained pairing-deformation-frequency self-consistent total-Routhian-surface （TRS） method with particle-number-conserved pairing. Specifically, the recently observed Kπ = 4- bands in 168,170,172Er have been found to experience a configuration change in our calculation. Some other multi-quasiparticle states with uncertain configuration assignments have been reinvestigated by calculating their collective rotations. The configuration-constrained TRS calculation can reproduce experimental data consistently.展开更多
This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether ce...This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.展开更多
In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthdn type inter- action is considered to describe the a-a, t-a He and t=3 H systems. By exploiting the phase function method, scatt...In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthdn type inter- action is considered to describe the a-a, t-a He and t=3 H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELb -- 100 MeV for the a-a system and ELab = 15 MeV for a-3He and a-3H systems. The S-wave phase shift 5o for the system tends to 2n and 53/2_ for thea-3He system tends to n, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2- states of a-3He and a-3H systems, With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2- states. We have also compared our results with the convenient Born approximations.展开更多
文摘要证明“1+1”等数学命题,需建立一个新数学模型 — pn 阶准素数模型。该模型具有方便于研究的阶梯性、周期性、对称性、可递推性、宏观均匀性等等。其隐含的递推机制是:每层 pi 筛网对 pi?1阶准素数中,每支同相位、等间距准素数的有效筛除,都是每隔 ( pi ?1)p ?1个、便精准地筛掉1个;存留率为 ipi 。于是,小于 x 的素数及“特定素数n pi ?1对”数目,便有了误差δn (x) 占比小且趋于0的、连续函数计算式:π n (x) = x ? ∏ p +δi=1 i n (x) 等。可证得 δn (x) ≤ n ;可算得任意x x x偶数 的“1+1”数目之底线为 limλ(x) ≥x→∝ 4 ;小于 x 的“孪生素数对”数目之底线为 lim R(x) ≥x→∝ 2 。且当 x 增至16后,该两个底线已蜕变为: λ(x) ≥ x ; R(x) ≥ x4 2 。这两个底线皆为 x 的递增函数,就是证明哥德巴赫猜想命题“1+1”及孪生素数无穷性的、无懈可击之数学证据。
基金Project (No. 20276063) supported by the National Natural Sci-ence Foundation of China
文摘The constriction factor method (CFM) is a new variation of the basic particle swarm optimization (PSO), which has relatively better convergent nature. The effects of the major parameters on CFM were systematically investigated based on some benchmark functions. The constriction factor, velocity constraint, and population size all have significant impact on the per- formance of CFM for PSO. The constriction factor and velocity constraint have optimal values in practical application, and im- proper choice of these factors will lead to bad results. Increasing population size can improve the solution quality, although the computing time will be longer. The characteristics of CFM parameters are described and guidelines for determining parameter values are given in this paper.
文摘Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).
基金Project(200550)supported by the Foundation for the Author of National Excellent Doctoral Dissertation of ChinaProject(200631878557)supported by West Traffic of Science and Technology of China
文摘The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.
基金the National Key Basic Research Program of China (Grant No. 2013CB834400)the National Natural Science Foundation of China (Grant No. 11235001)
文摘Multi-quasiparticle states and rotational bands in neutron-rich erbium isotopes have been investigated by the configuration- constrained pairing-deformation-frequency self-consistent total-Routhian-surface （TRS） method with particle-number-conserved pairing. Specifically, the recently observed Kπ = 4- bands in 168,170,172Er have been found to experience a configuration change in our calculation. Some other multi-quasiparticle states with uncertain configuration assignments have been reinvestigated by calculating their collective rotations. The configuration-constrained TRS calculation can reproduce experimental data consistently.
基金supported by a National Key Basic Research Project of ChinaNSFC
文摘This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.
文摘In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthdn type inter- action is considered to describe the a-a, t-a He and t=3 H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELb -- 100 MeV for the a-a system and ELab = 15 MeV for a-3He and a-3H systems. The S-wave phase shift 5o for the system tends to 2n and 53/2_ for thea-3He system tends to n, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2- states of a-3He and a-3H systems, With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2- states. We have also compared our results with the convenient Born approximations.
