Table of Content

30 September 2024, Volume 39 Issue 3

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Italian Domination of Strong Product of Two Paths

WEI Li-yang, LI Feng

2024, 39(3):  221-234.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.001

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The domination problem of graphs is an important issue in the field of graph theory. This paper mainly considers the Italian domination number of the strong product between two paths. By constructing recursive Italian dominating functions, the upper bound of its Italian domination number is obtained, and then a partition method is proposed to prove its lower bound. Finally, this paper yields a sharp bound for the Italian domination number of the strong product of paths.

Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations

LI Xiang, YU Bo, TANG Qiong

2024, 39(3):  235-249.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.002

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We introduce a factorized Smith method (FSM) for solving large-scale highranked J-Stein equations within the banded-plus-low-rank structure framework. To effectively reduce both computational complexity and storage requirements, we develop techniques including deflation and shift, partial truncation and compression, as well as redesign the residual computation and termination condition. Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical
HODLR structured toolkit in terms of CPU time.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

LI Nan, ZHAO Hui-yan, XU Li-ping

2024, 39(3):  250-261.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.003

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 In this paper, we mainly focus on the following Choquard equation......

On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems

ZHANG Wen-wen, LI Ping-run

2024, 39(3):  262-269.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.004

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This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains.

Ostrowski’s Type Inequalities for Generalized (h,m)−Preinvex Functions with Its Applications

LI Ran, LIAN Tie-yan

2024, 39(3):  270-287.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.005

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A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed.

On the Weyl’s Lemma for Triharmonic Functions

ZHENG Run-jie, ZENG Jia-min, FANG Yi

2024, 39(3):  288-294.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.006

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In this paper, by choosing some appropriate test functions, we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.





Pseudo S-Asymptotically (ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type

MAO Hang-ning, CHANG Yong-kui

2024, 39(3):  295-306.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.007

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In this paper, we firstly recall some basic results on pseudo S-asymptotically (ω,c)-periodic functions and Sobolev type fractional differential equation. We secondly investigate some existence of pseudo S-asymptotically (ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type. We finally present a simple example.

Combinatorial Identities Concerning Harmonic Numbers

CHEN Yu-lei, GUO Dong-wei

2024, 39(3):  307-314.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.008

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In this paper, we firstly establish a combinatorial identity with a free parameter x, and then by means of derivative operation, several summation formulae concerning classical and generalized harmonic numbers, as well as binomial coefficients are derived.

The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms

WANG Ji-nan, SUN Da-wei

2024, 39(3):  315-323.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.009

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We study the existence of solutions for Kirchhoff-type equations. Firstly, we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum. Then, we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation when λ is small enough.

A Remark on the Affine Coordinates for KdV Tau-Functions

FU Zhi-peng

2024, 39(3):  324-330.  doi:10.13371/j.cnki.chin.q.j.m.2024.03.010

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We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.