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    20 August 2024
    Volume 59 Issue 8
    A note on fractional S-acts
    Xingliang LIANG,Yuhang LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  1-8.  doi:10.6040/j.issn.1671-9352.0.2023.362
    Abstract ( 169 )   HTML ( 8 )   PDF (460KB) ( 216 )   Save
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    Let S be a commutative monoid, in the category of S-acts, by the injectivity and surjectivity of the mapping of pullback diagrams, a new proof that fractional functors (the category of S-acts to the category of fractional S-acts) preserve flatness properties is given. The relationship between fractional functors and directed colimits is investigated. A sufficient condition for fractional S-acts having a cover is presented.

    Influence of SS-quasinormal subgroups on p-nilpotence of finite groups
    Jianling GAO,Yuemei MAO,Chenchen CAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  9-14.  doi:10.6040/j.issn.1671-9352.0.2023.321
    Abstract ( 152 )   HTML ( 6 )   PDF (343KB) ( 210 )   Save
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    Let G be a finite group. A subgroup H is called SS-quasinormal in G if there is a subgroup B of G such that G=HB, and HP=PH holds for all prime pπ(B) and P∈Sylp(B). The structures of finite groups with SS-quasinormality of primary subgroups are studied. Some new criteria of p-nilpotent group are given by using induction on the order of G and counterexample of minimal order.

    Influence of second maximal subgroups with given properties on structure of groups
    Xiaohong ZHANG,Wei LIU,Hongzhi WANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  15-19, 27.  doi:10.6040/j.issn.1671-9352.0.2023.404
    Abstract ( 116 )   HTML ( 4 )   PDF (383KB) ( 96 )   Save
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    A subgroup A of a finite group G is said to be NS-supplemented in G, if there exists a subgroup B of G such that G=AB and whenever X is a normal subgroup of A and pπ(B). There exists a Sylow p-subgroup Bp of B, such that XBp=BpX. In this paper, we explore the structure of finite groups by utilizing the properties of NS-supplement and cover-avoidance of second maximal subgroups in specific sets, and characterize the related classes of groups.

    Sharp constant for reverse fractional Hardy inequality on higher-dimensional product spaces
    Xiaoyu LIU,Mingquan WEI,Pengchao SONG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  20-27.  doi:10.6040/j.issn.1671-9352.0.2023.331
    Abstract ( 104 )   HTML ( 3 )   PDF (390KB) ( 133 )   Save
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    The conditions for the validity of the reverse fractional Hardy inequality in power-weighted Lebesgue spaces are studied, and the sharp constant for the inequality is given.

    Zero distribution of one class of complex differential-difference polynomials
    Jiale CHANG,Xianfeng SU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  28-33.  doi:10.6040/j.issn.1671-9352.0.2023.280
    Abstract ( 102 )   HTML ( 2 )   PDF (340KB) ( 94 )   Save
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    By using the theory of Nevanlinna's meromorphic functions value distribution and the idea of common zeros and common poles, the zero distribution problems of a class of complex differential-difference polynomials are generalized and improved, and some accurate results are obtained.

    Numerical radius of operator in Hilbert space
    Yongfeng PANG,Ben LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  34-41.  doi:10.6040/j.issn.1671-9352.0.2023.282
    Abstract ( 113 )   HTML ( 0 )   PDF (370KB) ( 165 )   Save
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    Let B(H) be the algebra of all bounded linear operators on a Hilbert space H, I be the identity operator on H, TB(H). Let N(·) be an arbitrary norm on B(H). An extension of the numerical radius based on the approximate D-orthogonality by $w_{N-D-\varepsilon}(T)=\sup \left\{|\zeta|: \zeta \in \mathbf{C}, I \perp_{D-\varepsilon}^N(T-\zeta I)\right\}$ is given. It is proved that wN-D-ε(·) is a semi-norm on B(H). It is also given a necessary and sufficient condition that wN-D-ε(·) is a norm on B(H). When wN-D-ε(·) is a norm, the geometry and related properties of the normed linear space (B(H), wN-D-ε(·)) are investigated.

    Existence number of solutions for impulsive equations involving p-Laplacian operator with nonhomogeneous Neumann boundary conditions
    Guoping YANG,Jian LIU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  42-47.  doi:10.6040/j.issn.1671-9352.0.2023.062
    Abstract ( 108 )   HTML ( 0 )   PDF (342KB) ( 123 )   Save
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    The sufficient condition of the existence of nontrivial solutions for some p-Laplacian impulsive differential equations with nonhomogeneous Neumann boundary conditions is obtained. We get two theorems on the numbers of nontrivial solutions via variational methods and corresponding critical points theory when nonlinear terms satisfying the L1-Carathéodory condition and applying the Newton-iterative method into concrete examples to illustrate the obtained conclusions.

    Normalized solutions for a class of fractional critical Choquard equations with perturbation
    Yanbin SANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  48-55,66.  doi:10.6040/j.issn.1671-9352.0.2023.543
    Abstract ( 98 )   HTML ( 3 )   PDF (418KB) ( 138 )   Save
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    The normalized solutions for a class of fractional Choquard equations are studied, where Hardy-Littlewood-Sobolev critical exponent and mass supercritical nonlocal term with the parameter are contained in nonlinearites. By analyzing the properties of Pohozaev manifold, the compact condition of Palais-Smale sequences for the energy functional corresponding to above equations is established. When the coefficient of perturbation is large enough, the existence of normalized ground state solutions is obtained.

     
    Identification of nonlinear heat transfer law of heat conduction equation
    Le DU,Liu YANG,Tao ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  56-66.  doi:10.6040/j.issn.1671-9352.0.2023.232
    Abstract ( 133 )   HTML ( 3 )   PDF (468KB) ( 106 )   Save
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    The identification of temperature-dependent heat transfer coefficients in heat conduction equations by boundary control is considered. Based on the optimal control theory, the general heat conduction equation parameter inversion problem is transformed into a variational problem, and then the existence and necessary conditions of the minimum value are discussed. Finally, by using the energy norm estimation method, the uniqueness and stability of the minimum value are proved under the assumption that the terminal time is small.

    Barycentric interpolation collocation method for solving the small-amplitude long-wave scheme generalized BBM-KdV equation
    Xiumin LYU,Qian GE,Jin LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  67-76.  doi:10.6040/j.issn.1671-9352.0.2023.341
    Abstract ( 135 )   HTML ( 0 )   PDF (4459KB) ( 50 )   Save
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    The barycentric interpolation collocation method is applied to solve the small-amplitude long-wave scheme generalized Benjamin-Bona-Mahony(BBM)-Korteweg-de Vries (KdV) equation in the small amplitude long wave scheme. By the direct linearization method, the nonlinear term ηpηx in the equation is converted into a linear term. Unknown functions of BBM-KdV equation is approximated by the barycentric interpolation basis function. The matrix equation of the generalized BBM-KdV equation is obtained by discretized the generalized BBM-KdV equation in the space-time domain, and the convergence analysis is carried out. The effectiveness and numerical accuracy of the barycentric interpolation collocation method is verified by numerical example, and the calculation accuracy can reach the order of 10-8.

    Iterated fractional Tikhonov method for simultaneous inversion of the source term and initial data in time-fractional diffusion equations
    Wenhui DU,Xiangtuan XIONG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  77-83.  doi:10.6040/j.issn.1671-9352.0.2022.626
    Abstract ( 91 )   HTML ( 0 )   PDF (374KB) ( 116 )   Save
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    The inverse problem of identifying the space-dependent source term and the initial value simultaneously for a time-fractional diffusion equation is investigated. This inverse problem is reformulated on the basis of Fourier method as operator equations of the first kind. An iterative fractional Tikhonov regularization method is proposed to solve this inverse problem. In addition, a prior regularization parameter choice rule is given and the corresponding convergence estimation is proved.

    A class of two-state quantum walk based on Hadamard walk with the same eigenvalues and continuous spectrum
    Pingtao LYU,Caishi WANG,Jijun ZHAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  84-93.  doi:10.6040/j.issn.1671-9352.0.2023.123
    Abstract ( 99 )   HTML ( 0 )   PDF (1143KB) ( 15 )   Save
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    In this paper, we generalize the Wojcik model to make the whole model contain two parameters ε and ω. Especially, although the extended model adds one parameter ε, the eigenvalue does not change, i.e., it does not depend on the newly added parameter. At the same time, we compare the eigenvalue distribution of the extended model on the unit circle with the region of Hadamard walk continuous spectrum, and obtain relevant conclusions.

    Creditrisk assessment based on Logistic regression and credit strategy optimization modeling of small and medium-sized enterprises
    Zhongfeng QU,Honghua WU,Fanjun LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  94-102.  doi:10.6040/j.issn.1671-9352.0.2023.206
    Abstract ( 225 )   HTML ( 2 )   PDF (1260KB) ( 207 )   Save
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    In order to facilitate banks to assess the credit risk of small and medium-sized enterprises, and formulate the optimal credit strategy, an indicator system composed of four primary risk assessment indicators, namely, business income ability, profitability, customer stability, and transaction vitality, is constructed by using the bank flow information of enterprises with upstream and downstream partners. The enterprise credit risk is predicted based on Logistic regression, and compares it with error back-propagation neural network. Combining the probability of default and the retention rate under different interest rates, taking the maximum expected return of banks on small and medium-sized enterprises as the objective function, the credit strategy optimization model is established. In order to verify the effectiveness of the model, the credit risk assessment and credit strategy optimization models are empirically analyzed. The results indicate that Logistic regression has high accuracy and recall, and the area under the curve of receiver operating characteristic reaches 0.964, which is suitable for credit risk prediction and assessment of small and medium-sized enterprises. The credit strategy optimization model can determine the loan amount and loan interest rate of each lending enterprise, and maximize the expected return of the bank.

    Multi-particle short-distance teleportation in noisy environment with weak measurement
    Miao LIU,Jiayin PENG,Jiangang TANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  103-112.  doi:10.6040/j.issn.1671-9352.0.2023.007
    Abstract ( 101 )   HTML ( 0 )   PDF (1981KB) ( 72 )   Save
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    Using a three-particle maximally entangled state and an auxiliary particle in the ground state |0? as the quantum channel, a new deterministic scheme for transmitting an unknown three-particle GHZ (Greenberger-Horne-Zeilinger) state is proposing. In this scheme, the sender and the receiver share the auxiliary particle at the same time, and both parties need to perform quantum gate operation on the shared auxiliary particle. The results show that the scheme saves quantum entanglement resources but shortens the teleportation distance, and can be extended to the teleportation of multi-particle GHZ state. Furthermore, taking the amplitude damping channel as an example, the influence of quantum noise on the scheme is discussed, and the fidelity of teleportation is obtained. The influence of weak measurement and its reversal measurement on the noise scheme is analyzed. It is found that for a specific GHZ state, the weak measurement and its reversal measurement will suppress or deteriorate the degradation of the fidelity of its teleportation caused by noise.

    Integral inequality of Wulff curvature for plane convex bodies
    Yaling WANG,Xu DONG,Chunna ZENG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  113-117, 126.  doi:10.6040/j.issn.1671-9352.0.2023.033
    Abstract ( 101 )   HTML ( 0 )   PDF (756KB) ( 48 )   Save
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    In this paper, we mainly study the integral inequality of Wulff curvature in the case of Wulff flow on the plane. By using Green-Osher inequality and Wulff-Steiner polynomials, we obtain the Wulff curvature integral inequality of any power of symmetric and nonsymmetric convex bodies. Specifically, when one of the convex bodies is an unit circle, the curvature integral inequality of any powers of the plane convex curve is obtained.

    An efficient outlier detection method based on multi-factor fusion
    Zhiqiang YANG,Shan FENG,Yi YIN,Huijia WU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(8):  118-126.  doi:10.6040/j.issn.1671-9352.0.2023.250
    Abstract ( 110 )   HTML ( 4 )   PDF (937KB) ( 97 )   Save
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    Based on granularity characteristics of relative ratio of object neighborhood and importance of objects in neighborhood rough sets, an improved outlier detection method (neighborhood rough entropy-based outlier, NREOD) based on neighborhood rough entropy and multi-factor fusion is proposed. Comparison experiments on standard data sets in University of CaliforniaIrvine (UCI) databases show that the NREOD algorithm has a lower false positive rate for outlier detection in different types of data sets, and has better adaptability and effectiveness. This algorithm provides a new effective way for the research and application of outlier detection in mixed attribute data sets.