In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypers...In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda.展开更多
Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for d...Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for determining theexistence of transversal homoclinic and heteroclinic orbits are presented. By exploitingthese criteria the existence of the transversal homoclinic orbits and so, of thetransversal homoclinic tangle .phenomenon in the near-integrable circular planarrestricted three-body problem with sufficiently small mass ratio of the two primaries isproven. Under some assumptions, the existence of the transversal heleroclinic orbits isproven. The global qualitative phase diagram is also illustrated.展开更多
Unconventional fermions in the immensely studied topological semimetals are the source for rich exotic topological properties.Here,using symmetry analysis and first-principles calculations,we propose the coexistence o...Unconventional fermions in the immensely studied topological semimetals are the source for rich exotic topological properties.Here,using symmetry analysis and first-principles calculations,we propose the coexistence of multiple topological nodal structure in LaSb_(2),including topological nodal surfaces,nodal lines and in particular eightfold degenerate nodal points,which have been scarcely observed in a single material.Further,utilizing angle-resolved photoemission spectroscopy,we confirm the existence of nodal surfaces and eightfold degenerate nodal points in LaSb_(2).The intriguing multiple topological nodal structure might play a crucial role in giving rise to the large linear magnetoresistance.Our work renews the insights into the exotic topological phenomena in LaSb_(2).展开更多
The interacting boson model with S U(3) higher-order interactions offers a new route to enhance our understanding onγ-soft rotation.In this paper, U(5) -like and O(6) -like newγ-softness are observed,in which the co...The interacting boson model with S U(3) higher-order interactions offers a new route to enhance our understanding onγ-soft rotation.In this paper, U(5) -like and O(6) -like newγ-softness are observed,in which the corresponding energy levels in the ground and quasi-γbands can be exactly degenerate and have a partial O(5) dynamical symmetry.The spherical-likeγ-softness is not related to the classical O(6) dynamical symmetry.The transitional behaviors of B(E2) values of the low-lying levels and quadrupole moment of the 2^(+)_(1) state are also discussed.Spherical-likeγ-softness can be used to explain the low-lying spectra and B(E2) values in ^(110)Cd normal states.展开更多
文摘In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda.
文摘Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for determining theexistence of transversal homoclinic and heteroclinic orbits are presented. By exploitingthese criteria the existence of the transversal homoclinic orbits and so, of thetransversal homoclinic tangle .phenomenon in the near-integrable circular planarrestricted three-body problem with sufficiently small mass ratio of the two primaries isproven. Under some assumptions, the existence of the transversal heleroclinic orbits isproven. The global qualitative phase diagram is also illustrated.
基金supported by the National Key R&D Program of China(Grant No.2023YFA1406304)the National Natural Science Foundation of China(Grant Nos.U2032208,12222413,11874264,12074181,11834006,and 12104217)+9 种基金the Natural Science Foundation of Shanghai(Grant Nos.23ZR1482200,22ZR1473300,and 14ZR1447600)the Shanghai Science and Technology Innovation Action Plan(Grant No.21JC1402000)the Open Projects from State Key Laboratory of Functional Materials for Informatics(Grant No.SKL2022)the Double First-Class Initiative Fund of Shanghai Tech Universitythe fund of Science and Technology on Surface Physics and Chemistry Laboratory(Grant No.6142A02200102)supported by ME2Project(Grant No.11227902)from the National Natural Science Foundation of Chinasupported by the National Key Projects for Research and Development of China(Grant No.2021YFA1400400)the Fundamental Research Funds for the Central Universities(Grant No.020414380185)the Natural Science Foundation of Jiangsu Province(Grant No.BK20200007)the Fok Ying-Tong Education Foundation of China(Grant No.161006)。
文摘Unconventional fermions in the immensely studied topological semimetals are the source for rich exotic topological properties.Here,using symmetry analysis and first-principles calculations,we propose the coexistence of multiple topological nodal structure in LaSb_(2),including topological nodal surfaces,nodal lines and in particular eightfold degenerate nodal points,which have been scarcely observed in a single material.Further,utilizing angle-resolved photoemission spectroscopy,we confirm the existence of nodal surfaces and eightfold degenerate nodal points in LaSb_(2).The intriguing multiple topological nodal structure might play a crucial role in giving rise to the large linear magnetoresistance.Our work renews the insights into the exotic topological phenomena in LaSb_(2).
基金Supported by Science and Technology Research Planning Project of Education Department of Jilin Province(JJKH20210526KJ)。
文摘The interacting boson model with S U(3) higher-order interactions offers a new route to enhance our understanding onγ-soft rotation.In this paper, U(5) -like and O(6) -like newγ-softness are observed,in which the corresponding energy levels in the ground and quasi-γbands can be exactly degenerate and have a partial O(5) dynamical symmetry.The spherical-likeγ-softness is not related to the classical O(6) dynamical symmetry.The transitional behaviors of B(E2) values of the low-lying levels and quadrupole moment of the 2^(+)_(1) state are also discussed.Spherical-likeγ-softness can be used to explain the low-lying spectra and B(E2) values in ^(110)Cd normal states.
