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GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES Min He, Maofa Wang, Jiale Chen Acta mathematica scientia,Series B    2025, 45 (2): 291-309.   DOI: 10.1007/s10473-025-0201-z Abstract （198）            Save In this paper, we study composition operators on weighted Bergman spaces of Dirichlet series. We first establish some Littlewood-type inequalities for generalized mean counting functions. Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series. The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained. Reference | Related Articles | Metrics

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LÉVY AREA ANALYSIS AND PARAMETER ESTIMATION FOR FOU PROCESSES VIA NON-GEOMETRIC ROUGH PATH THEORY* Zhongmin Qian, Xingcheng Xu Acta mathematica scientia,Series B    2024, 44 (5): 1609-1638.   DOI: 10.1007/s10473-024-0501-8 Abstract （158）            Save This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering. Reference | Related Articles | Metrics

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ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA* Zhanjie SONG, Jiaxing ZHANG Acta mathematica scientia,Series B    2024, 44 (5): 1984-1996.   DOI: 10.1007/s10473-024-0521-4 Abstract （116）            Save In this paper, we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field. By estimating the probability value of a time-stationary random field in a small range, we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region. It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1. In addition, we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs. Reference | Related Articles | Metrics

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APPROXIMATION PROBLEMS ON THE SMOOTHNESS CLASSES* Yongping LIU, Man LU Acta mathematica scientia,Series B    2024, 44 (5): 1721-1734.   DOI: 10.1007/s10473-024-0505-4 Abstract （106）            Save This paper investigates the relative Kolmogorov $n$-widths of $2\pi$-periodic smooth classes in $\widetilde{L}_{q}$. We estimate the relative widths of $\widetilde{W}^{r} H_{p}^{\omega}$ and its generalized class $K_{p}H^{\omega}(P_{r})$, where $K_{p}H^{\omega}(P_{r})$ is defined by a self-conjugate differential operator $P_{r}(D)$ induced by $P_{r}(t):= t^{\sigma} \Pi_{j=1}^{l}(t^{2}- t_{j}^{2}),~t_{j} > 0,~j=1, 2 ,\cdots, l,~l \geq 1,~\sigma \geq 1,~r=2l+\sigma .$ Also, the modulus of continuity of the $r$-th derivative, or $r$-th self-conjugate differential, does not exceed a given modulus of continuity $\omega$. Then we obtain the asymptotic results, especially for the case $p=\infty , 1\leq q \leq \infty$. Reference | Related Articles | Metrics

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CERTAIN OSCILLATING OPERATORS ON HERZ-TYPE HARDY SPACES Ziyao Liu, Dashan Fan Acta mathematica scientia,Series B    2025, 45 (2): 310-326.   DOI: 10.1007/s10473-025-0202-y Abstract （102）            Save Let $0 ＜p\leq1＜q＜\infty$, and $\omega_{1},\omega_{2}\in A_{1}$ (Muckenhoupt-class). We study an oscillating multiplier operator $T_{\gamma ,\beta }$ and obtain that it is bounded on the homogeneous weighted Herz-type Hardy spaces $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n};\omega _{1},\omega _{2})$ when $\gamma=\frac{n\beta }{2}, \alpha =n(1-1/q)$. Also, for the unweighted case, we obtain the $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n})$ boundedness of $T_{\gamma ,\beta }$ under certain conditions on $\gamma$. These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun. As an application, we prove the $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n})$ boundedness of the spherical average $S_{t}^{\delta}$ uniformly on $t>0$. Reference | Related Articles | Metrics

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HEAT KERNEL ON RICCI SHRINKERS (II)* Yu Li, Bing Wang Acta mathematica scientia,Series B    2024, 44 (5): 1639-1695.   DOI: 10.1007/s10473-024-0502-7 Abstract （102）            Save This paper is the sequel to our study of heat kernel on Ricci shrinkers [29]. In this paper, we improve many estimates in [29] and extend the recent progress of Bamler [2]. In particular, we drop the compactness and curvature boundedness assumptions and show that the theory of $\mathbb{F}$-convergence holds naturally on any Ricci flows induced by Ricci shrinkers. Reference | Related Articles | Metrics

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THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS* Yifang yang, Jinping wang Acta mathematica scientia,Series B    2024, 44 (5): 1787-1800.   DOI: 10.1007/s10473-024-0509-0 Abstract （101）            Save In this paper, we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit (BgOMP) algorithm in the $l_2$-bounded noise case. Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal, if the sensing matrix satisfies the the block restricted isometry property (block-RIP), then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations. Furthermore, we conjecture that this condition is sharp. Reference | Related Articles | Metrics

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THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS* Fatemeh Abtahi, Ali Rejali, Farshad Sayaf Acta mathematica scientia,Series B    2024, 44 (5): 1945-1954.   DOI: 10.1007/s10473-024-0518-z Abstract （96）            Save In this paper, $X$ is a locally compact Hausdorff space and ${\mathcal A}$ is a Banach algebra. First, we study some basic features of $C_0(X,\mathcal A)$ related to $\rm BSE$ concept, which are gotten from ${\mathcal A}$. In particular, we prove that if $C_0(X,\mathcal A)$ has the $\rm BSE$ property then $\mathcal A$ has so. We also establish the converse of this result, whenever $X$ is discrete and $\mathcal A$ has the BSE-norm property. Furthermore, we prove the same result for the $\rm BSE$ property of type I. Finally, we prove that $C_0(X,{\mathcal A})$ has the BSE-norm property if and only if $\mathcal A$ has so. Reference | Related Articles | Metrics

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VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES* Ziyi Zhou, Yi Jiang Acta mathematica scientia,Series B    2024, 44 (5): 1696-1706.   DOI: 10.1007/s10473-024-0503-6 Abstract （93）            Save For a general normed vector space, a special optimal value function called a maximal time function is considered. This covers the farthest distance function as a special case, and has a close relationship with the smallest enclosing ball problem. Some properties of the maximal time function are proven, including the convexity, the lower semicontinuity, and the exact characterizations of its subdifferential formulas. Reference | Related Articles | Metrics

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TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE* Lixia Feng, Yan Li, Zhiyu Wang, Liankuo Zhao Acta mathematica scientia,Series B    2024, 44 (5): 1707-1720.   DOI: 10.1007/s10473-024-0504-5 Abstract （88）            Save In this paper, by characterizing Carleson measures, we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békollé weights over the half-plane for all index choices. Reference | Related Articles | Metrics

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ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK* Shuxiong Zhang, Jie Xiong Acta mathematica scientia,Series B    2024, 44 (5): 2051-2072.   DOI: 10.1007/s10473-024-0525-0 Abstract （87）            Save Let $\{Z_n\}_{n\geq 0 }$ be a critical or subcritical $d$-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on $\mathbb{R}^d$. Denote by $R_n:=\sup\{u>0:Z_n(\{x\in\mathbb{R}^d:|x|<u\})=0\}$ the radius of the largest empty ball centered at the origin of $Z_n$. In this work, we prove that after suitable renormalization, $R_n$ converges in law to some non-degenerate distribution as $n\to\infty$. Furthermore, our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk. This completes the results of Révész [13] for the critical binary branching Wiener process. Reference | Related Articles | Metrics

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GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY* Xueli KE Acta mathematica scientia,Series B    2024, 44 (5): 1747-1765.   DOI: 10.1007/s10473-024-0507-2 Abstract （86）            Save We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data $(u_{0},B_{0})$ being located in the critical Besov space $\dot{B}_{p,1}^{-1+\frac{2}{p}}(\mathbb{R}^{2}) \,\, (1<p<2)$ and the initial density $\rho_{0}$ being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution. Reference | Related Articles | Metrics

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ON THE CAUCHY PROBLEM FOR THE GENERALIZED BOUSSINESQ EQUATION WITH A DAMPED TERM* Xiao SU, Shubin WANG Acta mathematica scientia,Series B    2024, 44 (5): 1766-1786.   DOI: 10.1007/s10473-024-0508-1 Abstract （85）            Save This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space. With the help of linear time-space estimates, we establish the local existence and uniqueness of solutions by means of the contraction mapping principle. The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained. Moreover, we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy. Reference | Related Articles | Metrics

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THE HÖOLDER CONTINUITY OF THE LYAPUNOV EXPONENT FOR A QUASI-PERIODIC SZEGÖ COCYCLE Bei ZHANG Acta mathematica scientia,Series B    2024, 44 (6): 2099-2110.   DOI: 10.1007/s10473-024-0603-3 Abstract （74）            Save In this paper, I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency. I extend the existing results about the regularity of the Lyapunov exponent from the Schrödinger cocycle in [24] to a Szegö cocycle. Reference | Related Articles | Metrics

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BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$* Yanyan CUI, Chaojun WANG, Yonghong XIE, Yuying QIAO Acta mathematica scientia,Series B    2024, 44 (5): 1837-1852.   DOI: 10.1007/s10473-024-0511-6 Abstract （67）            Save In this paper, conjugate $k$-holomorphic functions and generalized $k$-holomorphic functions are defined in the two-dimensional complex space, and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders. By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate $k$-holomorphic kernels, the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion, and the integral expressions of the solutions are obtained. Reference | Related Articles | Metrics

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GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY* Gonglin YUAN, Xiong ZHAO, Jiajia YU Acta mathematica scientia,Series B    2024, 44 (5): 1735-1746.   DOI: 10.1007/s10473-024-0506-3 Abstract （67）            Save A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems. The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption, which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method. Under some additional conditions, the method presented has a superlinear convergence rate, which can be regarded as an extension and supplement of BFGS-type methods with the projection technique. Finally, the effectiveness and application prospects of the proposed method are verified by numerical experiments. Reference | Related Articles | Metrics

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${C^{1, 1}}$ REGULARITY FOR SOLUTIONS TO THE DEGENERATE DUAL ORLICZ-MINKOWSKI PROBLEM Di Wu Acta mathematica scientia,Series B    2025, 45 (2): 327-337.   DOI: 10.1007/s10473-025-0203-x Abstract （67）            Save In this paper, $C^{1, 1}$ regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered. The dual Orlicz-Minkowski problem is a generalization of the $L_p$ dual Minkowski problem in convex geometry. The proof is adapted from Guan-Li [17] and Chen-Tu-Wu-Xiang [11]. Reference | Related Articles | Metrics

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EVOLUTION AND INTERACTION OF $\delta$-WAVES IN THE ZERO-PRESSURE GAS DYNAMICS SYSTEM* Abhishek Das, K. T. Joseph Acta mathematica scientia,Series B    2024, 44 (5): 1801-1836.   DOI: 10.1007/s10473-024-0510-7 Abstract （66）            Save Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system. In this paper, we study the initial value problem for one dimensional zero-pressure gas dynamics system. Here the first equation is the Burgers equation and the second one is the continuity equation. We consider the solution with initial data in the space of bounded Borel measures. First we prove a general existence result in the algebra of generalized functions of Colombeau. Then we study in detail special solutions with $\delta$-measures as initial data. We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves. This gives an understanding of plane-wave interactions in the multidimensional case. We use the vanishing viscosity method in our analysis as this gives the physical solution. Reference | Related Articles | Metrics

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ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS* Jun Chen, Xuemei Deng Acta mathematica scientia,Series B    2024, 44 (5): 1903-1915.   DOI: 10.1007/s10473-024-0515-2 Abstract （64）            Save We study equations in divergence form with piecewise $C^{\alpha }$ coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise $C^{1,\alpha }$ estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners. Reference | Related Articles | Metrics

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THE GLOBAL DYNAMICS OF A 3-DIMENSIONAL DIFFERENTIAL SYSTEM IN $\mathbb{R}^3$ VIA A DARBOUX INVARIANT Jaume Llibre, Claudia Valls Acta mathematica scientia,Series B    2025, 45 (2): 338-346.   DOI: 10.1007/s10473-025-0204-9 Abstract （64）            Save The differential system $\dot x= ax -y z, \ \dot y = -b y + x z, \ \dot z= -c z + x^2,$ where $a$, $b$ and $c$ are positive real parameters, has been studied numerically due to the big variety of strange attractors that it can exhibit. This system has a Darboux invariant when $c=2b$. Using this invariant and the Poincaré compactification technique we describe analytically its global dynamics. Reference | Related Articles | Metrics