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On a universal inequality for approximate phase isometries Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Duanxu Dai, Haixin Que, Longfa Sun, Bentuo Zheng
Let X and Y be two normed spaces. Let \({\cal U}\) be a non-principal ultrafilter on ℕ. Let g: X → Y be a standard ε-phase isometry for some ε ≥ 0, i.e., g(0) = 0, and for all u, v ϵ X, $$|\,\,|\,||g(u) + g(v)|| \pm ||g(u) - g(v)||\,| - |\,||u + v|| \pm ||u - v||\,|\,\,|\, \le \varepsilon .$$ The mapping g is said to be a phase isometry provided that ε = 0. In this paper, we show the following universal
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The limit cycle bifurcations of a whirling pendulum with piecewise smooth perturbations Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Jihua Yang
This paper deals with the problem of limit cycles for the whirling pendulum equation ẋ = y, ẏ = sin x(cos x − r) under piecewise smooth perturbations of polynomials of cos x, sin x and y of degree n with the switching line x = 0. The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations, which the generating functions
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Big Hankel operators on Hardy spaces of strongly pseudoconvex domains Acta Math. Sci. (IF 1.0) Pub Date : 2024-05-01
Abstract In this article, we investigate the (big) Hankel operator Hf on the Hardy spaces of bounded strongly pseudoconvex domains Ω in ℂn. We observe that Hf is bounded on Hp (Ω) (1 < p < ∞) if f belongs to BMO and we obtain some characterizations for Hf on H2 (Ω) of other pseudoconvex domains. In these arguments, Amar’s Lp-estimations and Berndtsson’s L2-estimations for solutions of the \({{\bar
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The global existence of strong solutions to thermomechanical Cucker-Smale-Stokes equations in the whole domain Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Weiyuan Zou
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale (for short, TCS) model coupled with Stokes equations in the whole space. The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force. In this paper, we present a complete analysis of the existence of global-in-time strong
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The radial symmetry of positive solutions for semilinear problems involving weighted fractional Laplacians Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Ying Wang, Yanjing Qiu, Qingping Yin
This paper deals with the radial symmetry of positive solutions to the nonlocal problem $$( - \Delta )_\gamma ^su = b(x)f(u)\,\,\,\,\,{\rm{in}}\,\,\,{B_1}\backslash \{ 0\} ,\,\,\,\,\,\,u = h\,\,\,\,{\rm{in}}\,\,{\mathbb{R}^N}\backslash {B_1},$$ where b: B1 → ℝ is locally Holder continuous, radially symmetric and decreasing in the ∣x∣ direction, f: ℝ → ℝ is a Lipschitz function, h: B1 → ℝ is radially
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Multiplicity of normalized solutions for the fractional Schrödinger-Poisson system with doubly critical growth Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Yuxi Meng, Xiaoming He
In this paper, we are concerned with solutions to the fractional Schrödinger-Poisson system $$\left\{ {\matrix{{{{( - \Delta )}^s}u - \phi |u{|^{2_s^ * - 3}}u = \lambda u + \mu |u{|^{q - 2}}u + |u{|^{2_s^ * - 2}}u,} \hfill & {x \in {\mathbb{R}^3},} \hfill \cr {{{( - \Delta )}^s}\phi = |u{|^{2_s^ * - 1}},} \hfill & {x \in {\mathbb{R}^3},} \hfill \cr } } \right.$$ with prescribed mass \(\int_{{\mathbb{R}^3}}
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A note on the general stabilization of discrete feedback control for non-autonomous hybrid neutral stochastic systems with a delay Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Lichao Feng, Chunyan Zhang, Jinde Cao, Zhihui Wu
Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system (HNSDDS) under a highly nonlinear constraint in the H∞ and exponential forms. Nevertheless, the existing work just adapted to autonomous cases, and the obtained results were mainly on exponential stabilization. In comparison with autonomous cases, non-autonomous systems are of great interest
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The optimal large time behavior of 3D quasilinear hyperbolic equations with nonlinear damping Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Han Wang, Yinghui Zhang
We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping. The main novelty of this paper is two-fold. First, we prove the optimal decay rates of the second and third order spatial derivatives of the solution, which are the same as those of the heat equation, and in particular, are faster than ones of previous related works. Second, for well-chosen
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The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B p n of ℂn Acta Math. Sci. (IF 1.0) Pub Date : 2024-05-01
Abstract By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B p n of ℂn. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on B p n is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p = 2, and the unit polydisk
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The global existence and analyticity of a mild solution to the 3D regularized MHD equations Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Cuntao Xiao, Hua Qiu, Zheng-an Yao
In this paper, we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms. We establish the global existence of mild solutions to this system with small initial data. In addition, we also obtain the Gevrey class regularity and the temporal decay rate of the solution.
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Sums of dual Toeplitz products on the orthogonal complements of Fock-Sobolev spaces Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Yong Chen, Young Joo Lee
We consider dual Toeplitz operators on the orthogonal complements of the Fock-Sobolev spaces of all nonnegative real orders. First, for symbols in a certain class containing all bounded functions, we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero. Next, for bounded symbols, we construct a symbol map and exhibit a short exact sequence associated
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Global weak solutions for an attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Xiaoshan Wang, Zhongqian Wang, Zhe Jia
This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source $$\left\{ {\matrix{{{u_t} = \nabla \cdot (|\nabla u{|^{p - 2}}\nabla u) - \chi \nabla \cdot (u\nabla v) + \xi \nabla \cdot (u\nabla w) + f(u),} \hfill & {x \in \Omega ,\,\,t > 0,} \hfill \cr {{v_t} = \Delta v - \beta v + \alpha {u^{{k_1}}},} \hfill & {x \in \Omega ,\,\,t
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The nonlinear stability of plane parallel shear flows with respect to tilted perturbations Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Lanxi Xu, Fangfang Guan
The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods. Tilted perturbation refers to the fact that perturbations form an angle \(\theta \in (0,{\pi \over 2})\) with the direction of the basic flows. By defining an energy functional, it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for
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Mathematical modeling and bifurcation analysis for a biological mechanism of cancer drug resistance Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Kangbo Bao, Guizhen Liang, Tianhai Tian, Xinan Zhang
Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases. It has also been demonstrated to be related to cancer heterogeneity, which promotes the emergence of treatment-refractory cancer cell populations. Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system, we propose a mathematical model for studying the
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The persistence of solutions in a nonlocal predator-prey system with a shifting habitat Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Min Zhao, Rong Yuan
In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that Choi et al. [J Differ Equ, 2021, 302: 807–853] studied the persistence or extinction of the prey and of the predator separately in various moving frames. In particular, they achieved a complete picture in the local diffusion case. However, the question of
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The global existence of strong solutions for a non-isothermal ideal gas system Acta Math. Sci. (IF 1.0) Pub Date : 2024-05-01
Abstract We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space H2 (ℝ3) for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space \(\dot{\boldsymbol{B}}_{\boldsymbol{2
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Energy conservation for the weak solutions to the 3D compressible nematic liquid crystal flow Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Zhong Tan, Xinliang Li, Hui Yang
In this paper, we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.
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Minimizers of L2-subcritical variational problems with spatially decaying nonlinearities in bounded domains Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Bin Chen, Yongshuai Gao, Yujin Guo, Yue Wu
This paper is concerned with the minimizers of L2-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Ω of ℝN (N ≥ 1). We prove that the problem admits minimizers for any M > 0. Moreover, the limiting behavior of minimizers as M → ∞ is also analyzed rigorously.
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The asymptotic behavior and oscillation for a class of third-order nonlinear delay dynamic equations Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Xianyong Huang, Xunhuan Deng, Qiru Wang
In this paper, we consider a class of third-order nonlinear delay dynamic equations. First, we establish a Kiguradze-type lemma and some useful estimates. Second, we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero. Third, we obtain new oscillation criteria by employing the Pötzsche chain rule. Then, using the generalized
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The existence and uniqueness of time-periodic solutions to the non-isothermal model for compressible nematic liquid crystals in a periodic domain Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-14 Shuang Chen, Shanshan Guo, Qiuju Xu
In this paper, we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain. Under some smallness and structural assumptions imposed on the time-periodic force, we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory. We also prove a
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Sharp Morrey regularity theory for a fourth order geometrical equation Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract This paper is a continuation of recent work by Guo-Xiang-Zheng [10]. We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation $$\Delta^{2}u=\Delta(V\nabla u)+{\text{div}}(w\nabla u)+(\nabla\omega+F)\cdot\nabla u+f\qquad\text{in}B^{4},$$ under the smallest regularity assumptions of V, ω, ω, F, where f belongs to some Morrey spaces
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Maximal function characterizations of Hardy spaces associated with both non-negative self-adjoint operators satisfying Gaussian estimates and ball quasi-Banach function spaces Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract Assume that L is a non-negative self-adjoint operator on L2(ℝn) with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space on ℝn satisfying some mild assumptions. Let HX, L(ℝn) be the Hardy space associated with both X and L, which is defined by the Lusin area function related to the semigroup generated by L. In this article
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Flocking of a thermodynamic Cucker-Smale model with local velocity interactions Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system
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The smoothing effect in sharp Gevrey space for the spatially homogeneous non-cutoff Boltzmann equations with a hard potential Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive
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The limiting profile of solutions for semilinear elliptic systems with a shrinking self-focusing core Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Ke Jin, Ying Shi, Huafei Xie
In this paper, we consider the semilinear elliptic equation systems $$\left\{ {\matrix{{ - \Delta u + u = \alpha {Q_n}(x)|u{|^{\alpha - 2}}|v{|^\beta }u\,\,{\rm{in}}\,{\mathbb{R}^N},} \hfill \cr { - \Delta v + v = \beta Q(x)|u{|^\alpha }|v{|^{\beta - 2}}v\,\,\,\,{\rm{in}}\,{\mathbb{R}^N},} \hfill \cr } } \right.$$ where \(N\geqslant 3,\,\,\alpha ,\,\,\beta > 1,\,\alpha + \beta < {2^ * },\,{2^ * } =
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A flexible objective-constraint approach and a new algorithm for constructing the Pareto front of multiobjective optimization problems Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 N. Hoseinpoor, M. Ghaznavi
In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal
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The weighted Kato square root problem of elliptic operators having a BMO anti-symmetric part Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Wenxian Ma, Sibei Yang
Let n ≥ 2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝn. In this article, we consider the weighted Kato square root problem for L. More precisely, we prove that the square root L1/2 satisfies the weighted Lp estimates \(||{L^{1/2}}(f)|{|_{L_\omega ^p({\mathbb{R}^n})}} \le C||\nabla
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The absence of singular continuous spectrum for perturbed Jacobi operators Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Zhengqi Fu, Xiong Li
This paper is mainly about the spectral properties of a class of Jacobi operators $$({H_{c,b}}u)(n) = {c_n}u(n + 1) + {c_{n - 1}}u(n - 1) + {b_n}u(n),$$ where ∣cn − 1∣ = O(n−α) and bn = O(n−1). We will show that, for α ≥ 1, the singular continuous spectrum of the operator is empty.
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Strongly convergent inertial forward-backward-forward algorithm without on-line rule for variational inequalities Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Yonghong Yao, Abubakar Adamu, Yekini Shehu
This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces. In our convergence analysis, we do not assume the on-line rule of the inertial parameters and the iterates, which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational
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A generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Zhiyong Si
This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations. In this method, the system is decoupled and linearized to avoid solving the non-linear equation at each step. The theoretical analysis proves that the generalized
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Blow-up conditions for a semilinear parabolic system on locally finite graphs Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our
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An optimal control problem for a Lotka-Volterra competition model with chemo-repulsion Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Diana I. Hernández, Diego A. Rueda-Gómez, Élder J. Villamizar-Roa
In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝℕ, N = 2, 3. This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism. We prove the existence and uniqueness of weak-strong solutions, and then we analyze the existence
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A novel stochastic Hepatitis B virus epidemic model with second-order multiplicative α-stable noise and real data Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus (HBV) propagation in an environment characterized by variability and stochas-ticity. Based on some biological features of the virus and the assumptions, the corresponding deterministic model is formulated, which takes into consideration the effect of vaccination. This deterministic model is extended
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A stability result for translating spacelike graphs in Lorentz manifolds Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ Mn in the Lorentz manifold Mn × ℝ with the metric −ds2 + σ, where Mn is a complete Riemannian n-manifold with the metric σ, Ω has piecewise smooth boundary, and ℝ denotes the Euclidean 1-space. We prove an interesting stability result for translating spacelike graphs in Mn × ℝ under a conformal transformation.
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Three kinds of dentabilities in Banach spaces and their applications Acta Math. Sci. (IF 1.0) Pub Date : 2024-03-01
Abstract In this paper, we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property. We introduce the concepts of the weak*-weak denting point and the weak*-weak* denting point of a set. These are the generalizations of the weak* denting point of a set in a dual Banach space. By use of the weak*-weak denting point, we characterize the very smooth space
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The sparse representation related with fractional heat equations Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Wei Qu, Tao Qian, Ieng Tak Leong, Pengtao Li
This study introduces a pre-orthogonal adaptive Fourier decomposition (POAFD) to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre (generalized Poisson equation). As a first step, the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence, and
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The extremes of dependent chi-processes attracted by the Brown-Resnick process Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Junjie Sun, Zhongquan Tan
Motivated by some recent works on the topic of the Brown-Resnick process, we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes. It is proven that the properly normalized pointwise maxima of those processes are attracted by the Brown-Resnick process.
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The long time behavior of the fractional Ornstein-Uhlenbeck process with linear self-repelling drift Acta Math. Sci. (IF 1.0) Pub Date : 2024-02-06 Xiaoyu Xia, Litan Yan, Qing Yang
Let BH be a fractional Brownian motion with Hurst index \({1 \over 2} \le H < 1\). In this paper, we consider the equation (called the Ornstein-Uhlenbeck process with a linear self-repelling drift) $${\rm{d}}X_t^H = dB_t^H + \sigma X_t^H{\rm{d}}t + \nu {\rm{d}}t - \theta \left( {\int_0^t {(X_{^t}^H - X_s^H){\rm{d}}s} } \right){\rm{d}}t,$$ where θ < 0, σ, v ∈ ℝ. The process is an analogue of self-attracting
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On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries Acta Math. Sci. (IF 1.0) Pub Date : 2023-12-09 Jian Chen
In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type \(\Omega = \tilde \Omega \backslash \overline { \cup _{j = 1}^m{\Omega _j}} \), where \({\tilde \Omega }\) and \(\{ {\Omega _j}\} _{j = 1}^m\Subset \tilde \Omega \) are bounded pseudoconvex domains in ℂn with smooth boundaries, and \({\overline \Omega_1}
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From wave functions to tau-functions for the Volterra lattice hierarchy Acta Math. Sci. (IF 1.0) Pub Date : 2023-12-09 Ang Fu, Mingjin Li, Di Yang
For an arbitrary solution to the Volterra lattice hierarchy, the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method. In this paper, we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent; based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in
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Complete Kähler metrics with positive holomorphic sectional curvatures on certain line bundles (related to a cohomogeneity one point of view on a Yau conjecture) Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Xiaoman Duan, Zhuangdan Guan
In this article, we study Kähler metrics on a certain line bundle over some compact Kähler manifolds to find complete Kähler metrics with positive holomorphic sectional (or bisectional) curvatures. Thus, we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.
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The Riemann problem for isentropic compressible Euler equations with discontinuous flux Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Yinzheng Sun, Aifang Qu, Hairong Yuan
We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux, more specifically, for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x = x(t). We prove that this problem admits global Radon measure solutions for all kinds of initial data. The over-compressing condition on the discontinuity x
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Classifications of Dupin hypersurfaces in Lie sphere geometry Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Thomas E. Cecil
This is a survey of local and global classification results concerning Dupin hypersurfaces in Sn (or Rn) that have been obtained in the context of Lie sphere geometry. The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres. Along with these classification results, many important concepts from Lie sphere geometry, such as curvature spheres, Lie curvatures
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Global classical solutions of semilinear wave equations on $${\mathbb{R}^3} \times \mathbb{T}$$ with cubic nonlinearities Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Fei Tao
In this paper, we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space \({\mathbb{R}^3} \times \mathbb{T}\). The semilinear nonlinearity is assumed to be of the cubic form. The main ingredient here is the establishment of the L2–L∞ decay estimates and the energy estimates for the linear problem, which are adapted to the
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The exact meromorphic solutions of some nonlinear differential equations Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Huifang Liu, Zhiqiang Mao
We find the exact forms of meromorphic solutions of the nonlinear differential equations $${f^n} + q(z){{\rm{e}}^{Q(z)}}{f^{(k)}} = {p_1}{{\rm{e}}^{{\alpha _1}z}} + {p_2}{{\rm{e}}^{{\alpha _2}z}},\,\,\,\,n \ge 3,\,\,\,k \ge 1,$$ where q, Q are nonzero polynomials, Q ≡ Const., and p1, p2, α1, α2 are nonzero constants with α1 ≠ α2. Compared with previous results on the equation p(z)f3 + q(z)f″ = − sin
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The logarithmic Sobolev inequality for a submanifold in manifolds with asymptotically nonnegative sectional curvature Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Yuxin Dong, Hezi Lin, Lingen Lu
In this note, we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature. Like the Michale-Simon Sobolev inequality, this inequality contains a term involving the mean curvature.
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Quasiperiodicity of transcendental meromorphic functions Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Xinling Liu, Kai Liu, Risto Korhonen, Galina Filipuk
This paper is devoted to considering the quasiperiodicity of complex differential polynomials, complex difference polynomials and complex delay-differential polynomials of certain types, and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.
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Convexity of the free boundary for an axisymmetric incompressible impinging jet Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Xiaohui Wang
This paper is devoted to the study of the shape of the free boundary for a three-dimensional axisymmetric incompressible impinging jet. To be more precise, we will show that the free boundary is convex to the fluid, provided that the uneven ground is concave to the fluid.
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Cauchy type integrals and a boundary value problem in a complex Clifford analysis Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Nanbin Cao, Zunfeng Li, Heju Yang, Yuying Qiao
Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its conclusions can be applied to the Maxwell equation, Yang-Mill field theory, quantum mechanics and value problems. In this paper, we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis, and get the Plemelj formula for it. Second
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Estimate on the Bloch constant for certain harmonic mappings under a differential operator Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Jieling Chen, Mingsheng Liu
In this paper, we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form \(L(f) = z{f_z} - \bar z{f_{\bar z}}\), where f represents normalized harmonic mappings with bounded dilation. Then, using these results, we present better estimations for the Bloch constants of certain harmonic mappings L(f), where f is a K-quasiregular harmonic or open
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Some properties of the integration operators on the spaces F(p, q, s) Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Jiale Chen
We study the closed range property and the strict singularity of integration operators acting on the spaces F(p, pα − 2, s). We completely characterize the closed range property of the Volterra companion operator Ig on F(p, pα − 2, s), which generalizes the existing results and answers a question raised in [A. Anderson, Integral Equations Operator Theory, 69 (2011), no. 1, 87–99]. For the Volterra
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Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Shijin Ding, Yinghua Li, Yu Wang
This paper is concerned with the Navier-Stokes/Allen-Cahn system, which is used to model the dynamics of immiscible two-phase flows. We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form of η(ρ) = ρα. The existence of unique global H2m-solutions (m ∈ ℕ) to the free boundary problem is proven for when \(0 < \alpha < {1 \over 4}\). Furthermore
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Interface behavior and decay rates of compressible Navier-Stokes system with density-dependent viscosity and a vacuum Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Zhenhua Guo, Xueyao Zhang
In this paper, we study the one-dimensional motion of viscous gas near a vacuum, with the gas connecting to a vacuum state with a jump in density. The interface behavior, the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficient μ(ρ) = ρα for any 0 < α < 1; this includes the time-weighted boundedness from below and above.
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Entire solutions of higher order differential equations with entire coefficients having the same order Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Ziheng Feng, Zhibo Huang, Yezhou Li
In this paper, we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order, and prove that the entire solutions are of infinite lower order. The properties on the radial distribution, the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
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The boundedness of operators on weighted multi-parameter local Hardy spaces Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-29 Wei Ding, Yan Tang, Yueping Zhu
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators, untill now, the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates. In this paper, we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition
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A Derivative-Hilbert operator acting on Hardy spaces Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-06 Shanli Ye, Guanghao Feng
Let μ be a positive Borel measure on the interval [0, 1). The Hankel matrix \({{\cal H}_\mu} = {({\mu _{n,k}})_{n,k \ge 0}}\) with entries μn,k = μn+k, where μn = ∫[0,1)tndμ(t), induces formally the operator as ${\cal D}{{\cal H}_\mu}(f)(z) = \sum\limits_{n = 0}^\infty {\left({\sum\limits_{k = 0}^\infty {{\mu _{n,k}}{a_k}}} \right)(n + 1){z^n},z \in \mathbb{D}} $ where \(f(z) = \sum\limits_{n = 0}^\infty
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The regularity criteria of weak solutions to 3D axisymmetric incompressible Boussinesq equations Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-06 Yu Dong, Yaofang Huang, Li Li, Qing Lu
In this paper, we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations. To be more precise, under some conditions on the swirling component of vorticity, we can conclude that the weak solutions are regular.
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Isometry and phase-isometry of non-Archimedean normed spaces Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-06 Ruidong Wang, Wenting Yao
In this paper, we study isometries and phase-isometries of non-Archimedean normed spaces. We show that every isometry f : Sr (X) → Sr (X), where X is a finite-dimensional non-Archimedean normed space and Sr(X) is a sphere with radius r ∈ ∥X∥, is surjective if and only if \(\mathbb{K}\) is spherically complete and k is finite. Moreover, we prove that if X and Y are non-Archimedean normed spaces over
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Entire solutions of Lotka-Volterra competition systems with nonlocal dispersal Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-06 Yuxia Hao, Wantong Li, Jiabing Wang, Wenbing Xu
This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal (convolution) dispersals: $\left\{{\matrix{{{u_t} = k * u - u + u(1 - u - av),} \hfill & {x \in \mathbb{R},\,\,t \in \mathbb{R},} \hfill \cr {{v_t} = d(k * v - v) + rv(1 - v - bu),} \hfill & {x \in \mathbb{R},\,\,t \in \mathbb{R}.} \hfill \cr}} \right.$((0.1)) Here a ≠ 1
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Notes on the log-Brunn-Minkowski inequality Acta Math. Sci. (IF 1.0) Pub Date : 2023-11-06 Yunlong Yang, Nan Jiang, Deyan Zhang
Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality. In this paper, we investigate the relative positive center set of planar convex bodies. As an application of the relative positive center, we prove the log-Minkowski inequality and the log-Brunn-Minkowski