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 Select 1. MAXIMAL $L^1$-REGULARITY OF GENERATORS FOR BOUNDED ANALYTIC SEMIGROUPS IN BANACH SPACES Myong-Hwan RI, Reinhard FARWIG 数学物理学报(英文版)    2022, 42 (4): 1261-1272.   DOI: 10.1007/s10473-022-0401-8 摘要 （91）      PDF       收藏 In this paper, we prove that the generator of any bounded analytic semigroup in $(\theta,1)$-type real interpolation of its domain and underlying Banach space has maximal $L^1$-regularity, using a duality argument combined with the result of maximal continuous regularity. As an application, we consider maximal $L^1$-regularity of the Dirichlet-Laplacian and the Stokes operator in inhomogeneous $B^s_{q,1}$-type Besov spaces on domains of $\mathbb R^n$, $n\geq 2$.
 Select 2. RELAXED INERTIAL METHODS FOR SOLVING SPLIT VARIATIONAL INEQUALITY PROBLEMS WITHOUT PRODUCT SPACE FORMULATION Grace Nnennaya OGWO, Chinedu IZUCHUKWU, Oluwatosin Temitope MEWOMO 数学物理学报(英文版)    2022, 42 (5): 1701-1733.   DOI: 10.1007/s10473-022-0501-5 摘要 （75）            收藏 Many methods have been proposed in the literature for solving the split variational inequality problem. Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space, or that the underlying operators are co-coercive. However, it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem. On the other hand, the co-coercive assumption of the underlying operators would preclude the potential applications of these methods. To avoid these setbacks, we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation, and for which the underlying operators are freed from the restrictive co-coercive assumption. The methods proposed, involve projections onto half-spaces only, and originate from an explicit discretization of a dynamical system, which combines both the inertial and relaxation techniques in order to achieve high convergence speed. Moreover, the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces. Furthermore, numerical implementations and comparisons are given to support our theoretical findings.
 Select 3. SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES 刘小松 数学物理学报(英文版)    2022, 42 (2): 454-466.   DOI: 10.1007/s10473-022-0202-0 摘要 （70）      PDF       收藏 In this paper, we first establish the sharp growth theorem and the distortion theorem of the Frechét derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cn with some restricted conditions. We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of Cn with an arbitrary norm and the unit polydisk in Cn under certain restricted assumptions. Finally we obtain the sharp Goluzin type distortion theorem for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cn with some additional conditions. The results derived all reduce to the corresponding classical results in one complex variable, and include some known results from the prior literature.
 Select 4. UNDERSTANDING SCHUBERT'S BOOK (III) 李绑河 数学物理学报(英文版)    2022, 42 (2): 437-453.   DOI: 10.1007/s10473-022-0201-1 摘要 （65）      PDF       收藏 In §13 of Schubert's famous book on enumerative geometry, he provided a few formulas called coincidence formulas, which deal with coincidence points where a pair of points coincide. These formulas play an important role in his method. As an application, Schubert utilized these formulas to give a second method for calculating the number of planar curves in a one dimensional system that are tangent to a given planar curve. In this paper, we give proofs for these formulas and justify his application to planar curves in the language of modern algebraic geometry. We also prove that curves that are tangent to a given planar curve is actually a condition in the space of planar curves and other relevant issues.
 Select 5. STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS 张立新 数学物理学报(英文版)    2022, 42 (2): 467-490.   DOI: 10.1007/s10473-022-0203-z 摘要 （53）      PDF       收藏 Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng[20]. We introduce a concept of extended negative dependence which is an extension of the kind of weak independence and the extended negative independence relative to classical probability that has appeared in the recent literature. Powerful tools such as moment inequality and Kolmogorov's exponential inequality are established for these kinds of extended negatively independent random variables, and these tools improve a lot upon those of Chen, Chen and Ng[1]. The strong law of large numbers and the law of iterated logarithm are also obtained by applying these inequalities.
 Select 6. GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION 晋雪婷, 肖跃龙, 于幻 数学物理学报(英文版)    2022, 42 (4): 1293-1309.   DOI: 10.1007/s10473-022-0403-6 摘要 （44）      PDF       收藏 In this paper, we prove the global well-posedness of the 2D Boussinesq equations with three kinds of partial dissipation; among these the initial data $(u_0,\theta_0)$ is required such that its own and the derivative of one of its directions $(x,y)$ are assumed to be $L^2(\mathbb R^2)$. Our results only need the lower regularity of the initial data, which ensures the uniqueness of the solutions.
 Select 7. MONOTONICITY FORMULAS FOR PARABOLIC FREE BOUNDARY PROBLEMS ON CONES Chung-Kwong Chan, Huichun Zhang, Xiping Zhu 数学物理学报(英文版)    2022, 42 (6): 2193-2203.   DOI: 10.1007/s10473-022-0601-2 摘要 （43）      PDF       收藏 Monotonicity formulas play a central role in the study of free boundary problems. In this note, we develop a Weiss-type monotonicity formula for solutions to parabolic free boundary problems on metric measure cones.
 Select 8. A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION* Jinbao Jian, Chen Zhang, Pengjie Liu 数学物理学报(英文版)    2023, 43 (1): 1-24.   DOI: 10.1007/s10473-023-0101-z 摘要 （41）      PDF       收藏 This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints. Based on the ideas of splitting and sequential quadratic optimization (SQO), a new feasible descent method for the discussed problem is proposed. First, we consider the problem of quadratic optimal (QO) approximation associated with the current feasible iteration point, and we split the QO into two small-scale QOs which can be solved in parallel. Second, a feasible descent direction for the problem is obtained and a new SQO-type method is proposed, namely, splitting feasible SQO (SF-SQO) method. Moreover, under suitable conditions, we analyse the global convergence, strong convergence and rate of superlinear convergence of the SF-SQO method. Finally, preliminary numerical experiments regarding the economic dispatch of a power system are carried out, and these show that the SF-SQO method is promising.
 Select 9. ON THE BOUNDS OF THE PERIMETER OF AN ELLIPSE 赵铁洪, 王淼坤, 褚玉明 数学物理学报(英文版)    2022, 42 (2): 491-501.   DOI: 10.1007/s10473-022-0204-y 摘要 （38）      PDF       收藏 In this paper, we present new bounds for the perimeter of an ellipse in terms of harmonic, geometric, arithmetic and quadratic means; these new bounds represent improvements upon some previously known results.
 Select 10. A GROUND STATE SOLUTION TO THE CHERN-SIMONS-SCHRÖDINGER SYSTEM Jin DENG, Benniao LI 数学物理学报(英文版)    2022, 42 (5): 1743-1764.   DOI: 10.1007/s10473-022-0503-3 摘要 （38）            收藏 In this paper, we consider the Chern-Simons-Schrödinger system \begin{equation*}\left\{\begin{array}{lll} - \Delta u+\left[e^{2}|\mathbf{A}|^{2}+\left(V(x)+2e A_{0}\right)+2\left(1+\frac{\kappa q}{2 }\right) N\right] u+ q |u|^{p-2}u=0, \\ -\Delta N+\kappa^{2} q^{2} N+q\left(1+\frac{\kappa q}{2}\right) u^{2}=0, \\ \kappa\left(\partial_{1} A_{2}-\partial_{2} A_{1}\right)= - e u^{2}, \, \, \partial_{1} A_{1}+\partial_{2} A_{2}=0, \\ \kappa \partial_{1} A_{0}= e^{2} A_{2} u^{2}, \, \, \kappa \partial_{2} A_{0}= - e^{2} A_{1} u^{2}, \, \, \end{array} \right.{\rm (P)} \end{equation*} where $u \in H^{1}(\mathbb{R}^{2})$, $p \in (2, 4)$, $A_{\alpha}: \mathbb{R}^{2} \rightarrow \mathbb{R}$ are the components of the gauge potential $(\alpha=0, 1, 2)$, $N: \mathbb{R}^{2} \rightarrow \mathbb{R}$ is a neutral scalar field, $V(x)$ is a potential function, the parameters $\kappa, q>0$ represent the Chern-Simons coupling constant and the Maxwell coupling constant, respectively, and $e>0$ is the coupling constant. In this paper, the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem. The ground state solution of the problem (P) is obtained by using the variational method.
 Select 11. WEIGHTED NORM INEQUALITIES FOR COMMUTATORS OF THE KATO SQUARE ROOT OF SECOND ORDER ELLIPTIC OPERATORS ON $\mathbb R^n$ 陈艳萍, 丁勇, 朱凯 数学物理学报(英文版)    2022, 42 (4): 1310-1332.   DOI: 10.1007/s10473-022-0404-5 摘要 （33）      PDF       收藏 Let $L=-\mathrm{div}(A\nabla)$ be a second order divergence form elliptic operator with bounded measurable coefficients in ${\Bbb R}^n$. We establish weighted $L^p$ norm inequalities for commutators generated by $\sqrt{L}$ and Lipschitz functions, where the range of $p$ is different from $(1,\infty)$, and we isolate the right class of weights introduced by Auscher and Martell. In this work, we use good-$\lambda$ inequality with two parameters through the weighted boundedness of Riesz transforms $\nabla L^{-1/2}$. Our result recovers, in some sense, a previous result of Hofmann.
 Select 12. PREFACE Gui-Qiang, G. CHEN, Bo LI, Zizhou TANG, Xiping ZHU 数学物理学报(英文版)    2022, 42 (6): 2189-2191.   DOI: 10.1007/s10473-022-0619-5 摘要 （33）            收藏
 Select 13. $\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS Anbalagan PRATAP, Ramachandran RAJA, 曹进德, 黃创霞, Chuangxia HUANG, Ovidiu BAGDASAR 数学物理学报(英文版)    2022, 42 (4): 1273-1292.   DOI: 10.1007/s10473-022-0402-7 摘要 （31）      PDF       收藏 This article explores the $\mathcal{O}(t^{-\beta})$ synchronization and asymptotic synchronization for fractional order BAM neural networks (FBAMNNs) with discrete delays, distributed delays and non-identical perturbations. By designing a state feedback control law and a new kind of fractional order Lyapunov functional, a new set of algebraic sufficient conditions are derived to guarantee the $\mathcal{O}(t^{-\beta})$ Synchronization and asymptotic synchronization of the considered FBAMNNs model; this can easily be evaluated without using a MATLAB LMI control toolbox. Finally, two numerical examples, along with the simulation results, illustrate the correctness and viability of the exhibited synchronization results.
 Select 14. GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY 王梅, 李自来, 郭真华 数学物理学报(英文版)    2022, 42 (2): 521-539.   DOI: 10.1007/s10473-022-0207-8 摘要 （27）      PDF       收藏 In this paper, we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosity μ is a positive constant and the bulk viscosity is λ(ρ) = ρβ with β > 2, which is a situation that was first introduced by Vaigant and Kazhikhov in [1]. The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω = {(r, z)|r = √x2 + y2, (x, y, z) ∈ R3, r ∈ I ⊂ (0, +∞), −∞ < z < +∞} is obtained. Here the initial density keeps a non-vacuum state p > 0 when z → ±∞. Our results also show that the solution will not develop the vacuum state in any finite time, provided that the initial density is uniformly away from the vacuum.
 Select 15. ITERATIVE ALGORITHMS FOR SYSTEM OF VARIATIONAL INCLUSIONS IN HADAMARD MANIFOLDS Qamrul Hasan ANSARI, Feeroz BABU, D. R. SAHU 数学物理学报(英文版)    2022, 42 (4): 1333-1356.   DOI: 10.1007/s10473-022-0405-4 摘要 （26）      PDF       收藏 In this paper, we consider system of variational inclusions and its several spacial cases, namely, alternating point problems, system of variational inequalities, etc., in the setting of Hadamard manifolds. We propose an iterative algorithm for solving system of variational inclusions and study its convergence analysis. Several special cases of the proposed algorithm and convergence result are also presented. We present application to constraints minimization problems for bifunctions in the setting of Hadamard manifolds. At the end, we illustrate proposed algorithms and convergence analysis by a numerical example. The algorithms and convergence results of this paper either improve or extend known algorithms and convergence results from linear structure to Hadamard manifolds.
 Select 16. TIME ANALYTICITY FOR THE HEAT EQUATION ON GRADIENT SHRINKING RICCI SOLITONS 吴加勇 数学物理学报(英文版)    2022, 42 (4): 1690-1700.   DOI: 10.1007/s10473-022-0424-1 摘要 （26）      PDF       收藏 On a complete non-compact gradient shrinking Ricci soliton, we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable. This growth condition is sharp. As an application, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.
 Select 17. TRAVELING WAVES IN A SIRH MODEL WITH SPATIO-TEMPORAL DELAY AND NONLOCAL DISPERSAL 杨璐, 杨赟瑞, 宋雪 数学物理学报(英文版)    2022, 42 (2): 715-736.   DOI: 10.1007/s10473-022-0218-5 摘要 （25）      PDF       收藏 This paper deals mainly with the existence and asymptotic behavior of traveling waves in a SIRH model with spatio-temporal delay and nonlocal dispersal based on Schauder's fixed-point theorem and analysis techniques, which generalize the results of nonlocal SIRH models without relapse and delay. In particular, the difficulty of obtaining the asymptotic behavior of traveling waves for the appearance of spatio-temporal delay is overcome by the use of integral techniques and analysis techniques. Finally, the more general nonexistence result of traveling waves is also included.
 Select 18. THE MULTIPLICITY AND CONCENTRATION OF POSITIVE SOLUTIONS FOR THE KIRCHHOFF-CHOQUARD EQUATION WITH MAGNETIC FIELDS 王莉, 程琨, 汪继秀 数学物理学报(英文版)    2022, 42 (4): 1453-1484.   DOI: 10.1007/s10473-022-0411-6 摘要 （24）      PDF       收藏 In this paper, we study the multiplicity and concentration of positive solutions for the following fractional Kirchhoff-Choquard equation with magnetic fields: \begin{equation*} (a\varepsilon^{2s}+b\varepsilon^{4s-3}[u]^2_{\varepsilon,A/\varepsilon}) (-\Delta)_{A/\varepsilon}^{s} u+V(x)u = \varepsilon^{-\alpha}(I_\alpha*F(|u|^2))f(|u|^2)u\ \ \text{in }\ \mathbb{R}^3. \end{equation*} Here $\varepsilon > 0$ is a small parameter, $a,b > 0$ are constants, $s \in (0% \frac{3} {4} ,1), (-\Delta)_{A}^{s}$ is the fractional magnetic Laplacian, $A: \mathbb{R}^3 \to \mathbb{R}^3$ is a smooth magnetic potential, $I_{\alpha}=\frac{\Gamma(\frac{3-\alpha}{2})}{2^{\alpha}\pi^{\frac{3}{2}}\Gamma(\frac{\alpha}{2})}\cdot\frac{1}{|x|^{\alpha} }$ is the Riesz potential, the potential $V$ is a positive continuous function having a local minimum, and $f: \mathbb{R} \to \mathbb{R}$ is a $C^1$ subcritical nonlinearity. Under some proper assumptions regarding $V$ and $f,$ we show the multiplicity and concentration of positive solutions with the topology of the set $M:= \{x \in \mathbb{R}^3 : V (x) = \inf V \}$ by applying the penalization method and Ljusternik-Schnirelmann theory for the above equation.
 Select 19. PHASE PORTRAITS OF THE LESLIE-GOWER SYSTEM Jaume LLIBRE, Claudia VALLS 数学物理学报(英文版)    2022, 42 (5): 1734-1742.   DOI: 10.1007/s10473-022-0502-4 摘要 （24）            收藏 In this paper we characterize the phase portraits of the Leslie-Gower model for competition among species. We give the complete description of their phase portraits in the Poincaré disc (i.e., in the compactification of $\mathbb{R}^2$ adding the circle $\mathbb{S}^1$ of the infinity) modulo topological equivalence.It is well-known that the equilibrium point of the Leslie-Gower model in the interior of the positive quadrant is a global attractor in this open quadrant, and in this paper we characterize where the orbits attracted by this equilibrium born.
 Select 20. A NONSMOOTH THEORY FOR A LOGARITHMIC ELLIPTIC EQUATION WITH SINGULAR NONLINEARITY 雷春雨, 廖家锋, 储昌木, 索洪敏 数学物理学报(英文版)    2022, 42 (2): 502-510.   DOI: 10.1007/s10473-022-0205-x 摘要 （22）      PDF       收藏 We consider the logarithmic elliptic equation with singular nonlinearity \begin{equation*} \begin{cases} \Delta u+u\log u^2 +\frac{\lambda}{u^\gamma}=0, &\rm \mathrm{in}\ \ \Omega, \\ u>0, &\rm \mathrm{in}\ \ \Omega, \\ u=0, &\rm \mathrm{on}\ \ \partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^N$ ($N\geq3$) is a bounded domain with a smooth boundary, $0<\gamma<1$ and $\lambda$ is a positive constant. By using a variational method and the critical point theory for a nonsmooth functional, we obtain the existence of two positive solutions. This result generalizes and improves upon recent results in the literature.