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THE UNIQUENESS OF THE Lp MINKOWSKI PROBLEM FOR q-TORSIONAL RIGIDITY Guangling SUN, Lu XU, Ping ZHANG Acta mathematica scientia,Series B    2021, 41 (5): 1405-1416.   DOI: 10.1007/s10473-021-0501-x Abstract （200）      PDF       Save In this paper, we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p>1 and q>1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established. Reference | Related Articles | Metrics

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SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE Yong CHEN, Kei Ji IZUCHI, Kou Hei IZUCHI, Young Joo LEE Acta mathematica scientia,Series B    2021, 41 (3): 657-669.   DOI: 10.1007/s10473-021-0301-3 Abstract （83）      PDF       Save We consider Toeplitz operators $T_u$ with symbol $u$ on the Bergman space of the unit ball, and then study the convergences and summability for the sequences of powers of Toeplitz operators. We first charactreize analytic symbols $\varphi$ for which the sequence $T^{*k}_\varphi f$ or $T^{k}_\varphi f$ converges to 0 or $\infty$ as $k\to\infty$ in norm for every nonzero Bergman function $f$. Also, we characterize analytic symbols $\varphi$ for which the norm of such a sequence is summable or not summable. We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result. Reference | Related Articles | Metrics

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CONSTRUCTION OF IMPROVED BRANCHING LATIN HYPERCUBE DESIGNS Hao CHEN, Jinyu YANG, Min-Qian LIU Acta mathematica scientia,Series B    2021, 41 (4): 1023-1033.   DOI: 10.1007/s10473-021-0401-0 Abstract （62）      PDF       Save In this paper, we propose a new method, called the level-collapsing method, to construct branching Latin hypercube designs (BLHDs). The obtained design has a sliced structure in the third part, that is, the part for the shared factors, which is desirable for the qualitative branching factors. The construction method is easy to implement, and (near) orthogonality can be achieved in the obtained BLHDs. A simulation example is provided to illustrate the effectiveness of the new designs. Reference | Related Articles | Metrics

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ANALYTIC PHASE RETRIEVAL BASED ON INTENSITY MEASUREMENTS Wei QU, Tao QIAN, Guantie DENG, Youfa LI, Chunxu ZHOU Acta mathematica scientia,Series B    2021, 41 (6): 2123-2135.   DOI: 10.1007/s10473-021-0619-x Abstract （61）      PDF       Save This paper concerns the reconstruction of a function $f$ in the Hardy space of the unit disc $\mathbb{D}$ by using a sample value $f(a)$ and certain $n$-intensity measurements $|\langle f,E_{a_1\cdots a_n}\rangle|,$ where $a_1,\cdots,a_n\in \mathbb{D},$ and $E_{a_1\cdots a_n}$ is the $n$-th term of the Gram-Schmidt orthogonalization of the Szegökernels $k_{a_1},\cdots,k_{a_n},$ or their multiple forms. Three schemes are presented. The first two schemes each directly obtain all the function values $f(z).$ In the first one we use Nevanlinna's inner and outer function factorization which merely requires the $1$-intensity measurements equivalent to know the modulus $|f(z)|.$ In the second scheme we do not use deep complex analysis, but require some $2$- and $3$-intensity measurements. The third scheme, as an application of AFD, gives sparse representation of $f(z)$ converging quickly in the energy sense, depending on consecutively selected maximal $n$-intensity measurements $|\langle f,E_{a_1\cdots a_n}\rangle|.$ Reference | Related Articles | Metrics

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GLOBAL STRONG SOLUTION AND EXPONENTIAL DECAY OF 3D NONHOMOGENEOUS ASYMMETRIC FLUID EQUATIONS WITH VACUUM Guochun WU, Xin ZHONG Acta mathematica scientia,Series B    2021, 41 (5): 1428-1444.   DOI: 10.1007/s10473-021-0503-8 Abstract （52）      PDF       Save We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time-weighted techniques. Reference | Related Articles | Metrics

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MARTINGALE INEQUALITIES UNDER G-EXPECTATION AND THEIR APPLICATIONS Hanwu LI Acta mathematica scientia,Series B    2021, 41 (2): 349-360.   DOI: 10.1007/s10473-021-0201-6 Abstract （51）      PDF       Save In this paper, we study the martingale inequalities under $G$-expectation and their applications. To this end, we introduce a new kind of random time, called $G$-stopping time, and then investigate the properties of a $G$-martingale (supermartingale) such as the optional sampling theorem and upcrossing inequalities. With the help of these properties, we can show the martingale convergence property under $G$-expectation. Reference | Related Articles | Metrics

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RIGIDITY RESULTS FOR SELF-SHRINKING SURFACES IN $\mathbb{R}^4$ Xuyong JIANG, Hejun SUN, Peibiao ZHAO Acta mathematica scientia,Series B    2021, 41 (5): 1417-1427.   DOI: 10.1007/s10473-021-0502-9 Abstract （48）      PDF       Save In this paper, we give some rigidity results for complete self-shrinking surfaces properly immersed in $\mathbb{R}^4$ under some assumptions regarding their Gauss images. More precisely, we prove that this has to be a plane, provided that the images of either Gauss map projection lies in an open hemisphere or $\mathbb{S}^2(1/\sqrt{2})\backslash \bar{\mathbb{S}}^1_+(1/\sqrt{2})$. We also give the classification of complete self-shrinking surfaces properly immersed in $\mathbb{R}^4$ provided that the images of Gauss map projection lies in some closed hemispheres. As an application of the above results, we give a new proof for the result of Zhou. Moreover, we establish a Bernstein-type theorem. Reference | Related Articles | Metrics

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GLOBAL WEAK SOLUTIONS TO THE α-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS Yabo REN, Boling GUO, Shu WANG Acta mathematica scientia,Series B    2021, 41 (3): 679-702.   DOI: 10.1007/s10473-021-0303-1 Abstract （47）      PDF       Save Global in time weak solutions to the $\alpha$-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to $\alpha$-model regularization for the three dimension compressible Euler-Poisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies $\gamma>\frac{4}{3}$. Reference | Related Articles | Metrics

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CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION Xinyu TU, Chunlai MU, Shuyan QIU Acta mathematica scientia,Series B    2021, 41 (1): 1-18.   DOI: 10.1007/s10473-021-0101-9 Abstract （46）      PDF       Save In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a Finsler-type norm on the tangent space for solutions, we first establish the Lipschitz metric for smooth solutions, then by proving the generic regularity result, we extend this metric to general weak solutions. Reference | Related Articles | Metrics

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A REMARK ON GENERAL COMPLEX (α,β) METRICS Hongchuan XIA, Chunping ZHONG Acta mathematica scientia,Series B    2021, 41 (3): 670-678.   DOI: 10.1007/s10473-021-0302-2 Abstract （43）      PDF       Save In this paper, we give a characterization for the general complex (α,β) metrics to be strongly convex. As an application, we show that the well-known complex Randers metrics are strongly convex complex Finsler metrics, whereas the complex Kropina metrics are only strongly pseudoconvex. Reference | Related Articles | Metrics

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ANALYSIS OF THE GENOMIC DISTANCE BETWEEN BAT CORONAVIRUS RATG13 AND SARS-COV-2 REVEALS MULTIPLE ORIGINS OF COVID-19 Shaojun PEI, Stephen S. -T. YAU Acta mathematica scientia,Series B    2021, 41 (3): 1017-1022.   DOI: 10.1007/s10473-021-0323-x Abstract （37）      PDF       Save The severe acute respiratory syndrome COVID-19 was discovered on December 31, 2019 in China. Subsequently, many COVID-19 cases were reported in many other countries. However, some positive COVID-19 samples had been reported earlier than those officially accepted by health authorities in other countries, such as France and Italy. Thus, it is of great importance to determine the place where SARS-CoV-2 was first transmitted to human. To this end, we analyze genomes of SARS-CoV-2 using k-mer natural vector method and compare the similarities of global SARS-CoV-2 genomes by a new natural metric. Because it is commonly accepted that SARS-CoV-2 is originated from bat coronavirus RaTG13, we only need to determine which SARS-CoV-2 genome sequence has the closest distance to bat coronavirus RaTG13 under our natural metric. From our analysis, SARS-CoV-2 most likely has already existed in other countries such as France, India, Netherland, England and United States before the outbreak at Wuhan, China. Reference | Related Articles | Metrics

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CONTINUOUS TIME MIXED STATE BRANCHING PROCESSES AND STOCHASTIC EQUATIONS Shukai CHEN, Zenghu LI Acta mathematica scientia,Series B    2021, 41 (5): 1445-1473.   DOI: 10.1007/s10473-021-0504-7 Abstract （37）      PDF       Save A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup. Meanwhile, we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration. Reference | Related Articles | Metrics

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LIMIT CYCLE BIFURCATIONS OF A PLANAR NEAR-INTEGRABLE SYSTEM WITH TWO SMALL PARAMETERS Feng LIANG, Maoan HAN, Chaoyuan JIANG Acta mathematica scientia,Series B    2021, 41 (4): 1034-1056.   DOI: 10.1007/s10473-021-0402-z Abstract （36）      PDF       Save In this paper we consider a class of polynomial planar system with two small parameters, $\varepsilon$ and $\lambda$, satisfying $0<\varepsilon\ll\ lambda\ll1$. The corresponding first order Melnikov function $M_1$ with respect to $\varepsilon$ depends on $\lambda$ so that it has an expansion of the form $M_1(h,\lambda)=\sum\limits_{k=0}^\infty M_{1k}(h)\lambda^k.$ Assume that $M_{1k'}(h)$ is the first non-zero coefficient in the expansion. Then by estimating the number of zeros of $M_{1k'}(h)$, we give a lower bound of the maximal number of limit cycles emerging from the period annulus of the unperturbed system for $0<\varepsilon\ll\lambda\ll1$, when $k'=0$ or $1$. In addition, for each $k\in \mathbb{N}$, an upper bound of the maximal number of zeros of $M_{1k}(h)$, taking into account their multiplicities, is presented. Reference | Related Articles | Metrics

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SOME OSCILLATION CRITERIA FOR A CLASS OF HIGHER ORDER NONLINEAR DYNAMIC EQUATIONS WITH A DELAY ARGUMENT ON TIME SCALES Xin WU Acta mathematica scientia,Series B    2021, 41 (5): 1474-1492.   DOI: 10.1007/s10473-021-0505-6 Abstract （32）      PDF       Save In this paper, we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form \begin{align*}[r_n\varphi(\cdots r_2(r_1x^{\Delta})^{\Delta}\cdots)^{\Delta}]^{\Delta}(t)+h(t)f(x(\tau(t)))=0 \end{align*} on an arbitrary time scale $\mathbb{T}$ with $\sup\mathbb{T}=\infty$, where $n\geq 2$, $\varphi(u)=|u|^{\gamma}$sgn$(u)$ for $\gamma>0$, $r_i(1\leq i\leq n)$ are positive rd-continuous functions and $h\in {\mathrm{C}_{\mathrm{rd}}}(\mathbb{T},(0,\infty))$. The function $\tau\in {\mathrm{C}_{\mathrm{rd}}}(\mathbb{T},\mathbb{T})$ satisfies $\tau(t)\leq t$ and $\lim\limits_{t\rightarrow\infty}\tau(t)=\infty$ and $f\in {\mathrm{C}}(\mathbb{R},\mathbb{R})$. By using a generalized Riccati transformation, we give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero. The obtained results are new for the corresponding higher order differential equations and difference equations. In the end, some applications and examples are provided to illustrate the importance of the main results. Reference | Related Articles | Metrics

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DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE Junxian YANG, Leihong WANG Acta mathematica scientia,Series B    2021, 41 (3): 991-1016.   DOI: 10.1007/s10473-021-0322-y Abstract （32）      PDF       Save In this paper, dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated. The model involves the concentrations of uninfected cells, infected cells, free virus, CTL response cells, and antibody antibody response cells. There are three delays in the model: the intracellular delay, virus replication delay and the antibody delay. The basic reproductive number of viral infection, the antibody immune reproductive number, the CTL immune reproductive number, the CTL immune competitive reproductive number and the antibody immune competitive reproductive number are derived. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions for the stability of each equilibrium is established. The results show that the intracellular delay and virus replication delay do not impact upon the stability of each equilibrium, but when the antibody delay is positive, Hopf bifurcation at the antibody response and the interior equilibrium will exist by using the antibody delay as a bifurcation parameter. Numerical simulations are carried out to justify the analytical results. Reference | Related Articles | Metrics

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PREFACE Shaoji FENG, Caiheng OUYANG, Quanhua XU, Lixin YAN, Xiangyu ZHOU Acta mathematica scientia,Series B    2021, 41 (6): 1827-1828.   DOI: 10.1007/s10473-021-0601-7 Abstract （31）            Save Related Articles | Metrics

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REVISITING A NON-DEGENERACY PROPERTY FOR EXTREMAL MAPPINGS Xiaojun HUANG Acta mathematica scientia,Series B    2021, 41 (6): 1829-1838.   DOI: 10.1007/s10473-021-0602-6 Abstract （30）      PDF       Save We extend an earlier result obtained by the author in[7]. Reference | Related Articles | Metrics

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ISOMORPHISMS OF VARIABLE HARDY SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS Junqiang ZHANG, Dachun YANG Acta mathematica scientia,Series B    2021, 41 (1): 39-66.   DOI: 10.1007/s10473-021-0103-7 Abstract （26）      PDF       Save Let $L:=-\Delta+V$ be the Schrödinger operator on $\mathbb{R}^n$ with $n\geq3$, where $V$ is a non-negative potential satisfying $\Delta^{-1}(V)\in L^\infty(\mathbb{R}^n)$. Let $w$ be an $L$-harmonic function, determined by $V$, satisfying that there exists a positive constant $\delta$ such that, for any $x\in\mathbb{R}^n$, $0<\delta\leq w(x)\leq 1$. Assume that $p(\cdot):\ \mathbb{R}^n\to (0,\,1]$ is a variable exponent satisfying the globally $\log$-Hölder continuous condition. In this article, the authors show that the mappings $H_L^{p(\cdot)}(\mathbb{R}^n)\ni f\mapsto wf\in H^{p(\cdot)}(\mathbb{R}^n)$ and $H_L^{p(\cdot)}(\mathbb{R}^n)\ni f\mapsto (-\Delta)^{1/2}L^{-1/2}(f)\in H^{p(\cdot)}(\mathbb{R}^n)$ are isomorphisms between the variable Hardy spaces $H_L^{p(\cdot)}(\mathbb{R}^n)$, associated with $L$, and the variable Hardy spaces $H^{p(\cdot)}(\mathbb{R}^n)$. Reference | Related Articles | Metrics

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MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER-POISSON EQUATION WITH A GENERAL NONLINEARITY Yongsheng JIANG, Na WEI, Yonghong WU Acta mathematica scientia,Series B    2021, 41 (3): 703-711.   DOI: 10.1007/s10473-021-0304-0 Abstract （25）      PDF       Save We are concerned with the nonlinear Schrödinger-Poisson equation \begin{equation} \tag{P} \left\{\begin{array}{ll} -\Delta u +(V(x) -\lambda)u+\phi (x) u =f(u), \\ -\Delta\phi = u^2,\ \lim\limits_{|x|\rightarrow +\infty}\phi(x)=0, \ \ \ x\in \mathbb{R}^3, \end{array}\right. \end{equation} where $\lambda$ is a parameter, $V(x)$ is an unbounded potential and $f(u)$ is a general nonlinearity. We prove the existence of a ground state solution and multiple solutions to problem (P). Reference | Related Articles | Metrics

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HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION Antonella NASTASI, Stepan TERSIAN, Calogero VETRO Acta mathematica scientia,Series B    2021, 41 (3): 712-718.   DOI: 10.1007/s10473-021-0305-z Abstract （25）      PDF       Save The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals. Reference | Related Articles | Metrics