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The manuscripts published below have been examined by the peer-review process and have been accepted for publication. A “Just Accepted” manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Higher Education Press (HEP) provides “Just Accepted” as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an Online First article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall HEP be held responsible for errors or consequences arising from the use of any information contained in these “Just Accepted” manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI(r)), which is identical for all formats of publication.
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  • Proof of Some Congruence Conjectures of Z.-H. Sun
    Guoshuai Mao, Zhengkai Zhao
    Frontiers of Mathematics, https://doi.org/10.1007/s11464-024-0111-8

    In this paper, we mainly prove some conjectural congruences of Z.-H. Sun involving Almkvist–Zudilin numbers

    b n = ∑ k = 0 ⌊ n 3 ⌋ ( 2 k k ) ( 3 k k ) ( n 3 k ) ( n + k k ) ( − 3 ) n − 3 k .

    Let p > 3 be a prime. If p ≡ 3 (mod 4), then

  • Periodic Orbits and Homoclinic Orbits of Second-order Hamiltonian Systems with Mild Superquadratic Growth
    Xiaofei Zhang, Chungen Liu, Benxing Zhou
    Frontiers of Mathematics, https://doi.org/10.1007/s11464-023-0084-z

    Using the saddle point theorem and the mountain pass theorem with Morse index estimate, the existence of periodic solutions for second-order Hamiltonian systems with mild superquadratic growth is proved in this paper. Meanwhile the existence result of homoclinic orbits for this kind of Hamiltonian systems is also obtained by the local convergence of a sequence of subharmonic solutions.

  • Dynkin Indices, Casimir Elements and Branching Rules
    Yongzhi Luan
    Frontiers of Mathematics, https://doi.org/10.1007/s11464-022-0038-x

    The Dynkin index is introduced by E. B. Dynkin in his famous work on the classification of semisimple subalgebras of semisimple Lie algebras in 1952. Dynkin index offers a way to study the different embeddings of a simple subalgebra into a complex simple Lie algebra, and the Dynkin index is also used in the Wess–Zumino–Witten (WZW) model of the conformal field theory. In this paper, we work on the Dynkin indices of representations of

    A D E
    -type complex simple Lie algebras, as well as some non-
    A D E
    -type Lie algebras. As an application of computational Lie theory, we work on the branching rules from the complex simple exceptional Lie algebras to
    s l ( 3 , C )
     and
    g 2
    . As a result, we get the Dynkin indices of
    s l ( 3 , C )
     and
    g 2
     in the exceptional Lie algebras. In this process, we find a new Dynkin index of
    g 2
     in
    e 8
    , i.e., 4. This number is not listed in Dynkin’s paper of 1952.