In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（...In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.展开更多
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y）...We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.展开更多
The Woods-Saxon-Gaussian （WSG） potential is proposed as a new phenomenological potential to sys- tematically describe the level scheme, electromagnetic transitions, and alpha-decay half-lives of tile alpha-cluster s...The Woods-Saxon-Gaussian （WSG） potential is proposed as a new phenomenological potential to sys- tematically describe the level scheme, electromagnetic transitions, and alpha-decay half-lives of tile alpha-cluster structures in various alpha ＋ closed shell nuclei. It modifies the original Woods Saxon （WS） potential with a shifted Gaussian factor centered at the nuclear surface. The free parameters in the WSG potential are determined by reproducing the correct level scheme of ^212Po=^208Pb＋α. It is found that the resulting WSG potential matches the NI3Y double-folding potential at tile surface region and makes corrections to the inner part of the cluster-core l）otential. It was also determined that the WSG potential, with nearly identical parameters to that of ^212Po （except for a rescale（l radius）, could also be used to describe alpha-cluster structures in ^20Ne=^16O＋α and ^44Ti = ^40Ca＋α. In all lhrec cases, the calculated values of the level schemes, electromagnetic transitions, and alpha-decay half-lives agree with the experimental data. which indicates that the WSG potential could indeed capture many important features of the alpha-cluster structures in alpha ＋ closed shell nuclei. This study is a useful complement to the existing cluster-core potentials ill literature. The Gaussian form factor centered at the nuclear surface might also help to improve our understailding of the alpha-cluster formation, which occurs in the same general region.展开更多
Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension...Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method： Grobner-Shirshov basis method. We develop the GrSbner-Shirshov basis theory of differential difference al- gebras, and of finitely generated modules over differential difference algebras, respectively. Then, via GrSbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.展开更多
This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant fo...This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123211171119)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211009)
文摘In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.
文摘We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.
基金Supported by the National Natural Science Foundation of China(11535004,11761161001,11375086,11120101005,11175085,11235001)the National Key R&D Program of China(2018YFA0404403,2016YFE0129300)the Science and Technology Development Fund of Macao(008/2017/AFJ)
文摘The Woods-Saxon-Gaussian （WSG） potential is proposed as a new phenomenological potential to sys- tematically describe the level scheme, electromagnetic transitions, and alpha-decay half-lives of tile alpha-cluster structures in various alpha ＋ closed shell nuclei. It modifies the original Woods Saxon （WS） potential with a shifted Gaussian factor centered at the nuclear surface. The free parameters in the WSG potential are determined by reproducing the correct level scheme of ^212Po=^208Pb＋α. It is found that the resulting WSG potential matches the NI3Y double-folding potential at tile surface region and makes corrections to the inner part of the cluster-core l）otential. It was also determined that the WSG potential, with nearly identical parameters to that of ^212Po （except for a rescale（l radius）, could also be used to describe alpha-cluster structures in ^20Ne=^16O＋α and ^44Ti = ^40Ca＋α. In all lhrec cases, the calculated values of the level schemes, electromagnetic transitions, and alpha-decay half-lives agree with the experimental data. which indicates that the WSG potential could indeed capture many important features of the alpha-cluster structures in alpha ＋ closed shell nuclei. This study is a useful complement to the existing cluster-core potentials ill literature. The Gaussian form factor centered at the nuclear surface might also help to improve our understailding of the alpha-cluster formation, which occurs in the same general region.
文摘Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method： Grobner-Shirshov basis method. We develop the GrSbner-Shirshov basis theory of differential difference al- gebras, and of finitely generated modules over differential difference algebras, respectively. Then, via GrSbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.
基金supported by the NSFC(11072125 and 11272175)the NSF of Jiangsu Province(SBK201140044)the Specialized Research Fund for Doctoral Program of Higher Education(20130002110044)
文摘This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.
