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On the Cauchy problem for Aw-Rascle system with linear damping Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Juan C. Juajibioy
The existence of global BV solutions for the Aw-Rascle system with linear damping is considered. In order to get approximate solutions we consider the system in Lagrangian coordinates, then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of [1] we get a sequence of approximate solutions. Finally we show the convergence of this approximate sequence
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The local well-posedness of a chemotaxis-shallow water system with vacuum Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Jishan Fan, Fucai Li, Gen Nakamura
In this paper we prove the local well-posedness of strong solutions to a chemotaxis-shallow water system with initial vacuum in a bounded domain Ω ų ℝ2 without the standard compatibility condition for the initial data. This improves some results obtained in [J. Differential Equations 261(2016), 6758–6789].
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Gleason’s problem on Fock-Sobolev spaces Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Jineng Dai, Jingyun Zhou
In this article, we solve completely Gleason’s problem on Fock-Sobolev spaces Fp,m for any non-negative integer m and 0 < p ≤ ∞.
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Weighted Lasso estimates for sparse logistic regression: non-asymptotic properties with measurement errors Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Huamei Huang, Yujing Gao, Huiming Zhang, Bo Li
For high-dimensional models with a focus on classification performance, the ℓ1-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We propose two types of weighted Lasso estimates, depending upon covariates determined by the McDiarmid inequality. Given
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The average abundance function with mutation of the multi-player snowdrift evolutionary game model Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Ke Xia, Xianjia Wang
This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation. The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of
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On the existence with exponential decay and the blow-up of solutions for coupled systems of semi-linear corner-degenerate parabolic equations with singular potentials Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Hua Chen, Nian Liu
In this article, we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities. Firstly, we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality, the Poincaré inequality, and the Hardy inequality. Then, by using the potential well method and the inequality
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Isomorphisms of variable Hardy spaces associated with Schrödinger operators Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Junqiang Zhang, Dachun Yang
Let L:= −Δ + V be the Schrödinger operator on ℝn with n ≥ 3, where V is a non-negative potential satisfying Δ−1 (V) ∈ L∞(ℝn). Let w be an L-harmonic function, determined by V, satisfying that there exists a positive constant ö such that, for any x ∈ ℝn, 0 < δ ≤ w(x) ≤ 1. Assume that p(·): ℝn → (0, 1] is a variable exponent satisfying the globally log-Hölder continuous condition. In this article, the
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A generalized result on the polynomial-like iterative equation Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Pingping Zhang, Yingying Zeng
Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone, while a work by L. Liu and X. Gong gets non-monotone PM solutions with height 1 when the given function is of the same case. Removing the condition on height for the given function, we first give a method to assert the nonexistence of C0 solutions, then present equivalent conditions
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Understanding Schubert’s book (I) Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Banghe Li
Hilbert Problem 15 required an understanding of Schubert’s book [1], both its methods and its results. In this paper, following his idea, we prove that the formulas in §6, §7, §10, about the incidence of points, lines and planes, are all correct. As an application, we prove formulas 8 and 9 in §12, which are frequently used in his book.
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Continuous dependence on data under the Lipschitz metric for the rotation-Camassa-Holm equation Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Xinyu Tu, Chunlai Mu, Shuyan Qiu
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.
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Global well-posedness for fractional Navier-Stokes equations in variable exponent Fourier-Besov-Morrey spaces Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Muhammad Zainul Abidin, Jiecheng Chen
In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space \({\cal F}\dot {\cal N}_{p\left( \cdot \right),h\left( \cdot \right),q}^{s\left( \cdot \right)}\left( {{\mathbb{R}^3}} \right)\) with \(s\left( \cdot \right) = 4 - 2\alpha - {3 \over {p\left( \cdot \right)}}\). We prove global well-posedness result
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Doob’s maximal inequalities for martingales in variable Lebesgue space Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Peide Liu
In this paper we deal with the martingales in variable Lebesgue space over a probability space. We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space. The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue
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Hitting probabilities of weighted Poisson processes with different intensities and their subordinations Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Heng Zuo, Zhaohui Shen, Guanglin Rang
In this article, we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities. Furthermore, we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.
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A fractional nonlinear evolutionary delay system driven by a hemi-variational inequality in Banach spaces Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Yunhua Weng, Xuesong Li, Nanjing Huang
This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space. Utilizing the KKM theorem, a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established. By using a fixed point theorem for a condensing set-valued map, the nonemptiness and compactness of the set
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Some special self-similar solutions for a model of inviscid liquid-gas two-phase flow Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Jianwei Dong, Manwai Yuen
In this article, we are concerned with analytical solutions for a model of inviscid liquid-gas two-phase flow. On the basis of Yuen’s works [25, 27–29] on self-similar solutions for compressible Euler equations, we present some special self-similar solutions for a model of inviscid liquid-gas two-phase flow in radial symmetry with and without rotation, and in elliptic symmetry without rotation. Some
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On the mixed radial-angular integrability of Marcinkiewicz integrals with rough kernels Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Ronghui Liu, Feng Liu, Huoxiong Wu
This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along “polynomial curves”. Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.
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The existence and stability of stationary solutions of the inflow problem for full compressible Navier-Stokes-Poisson system Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Hakho Hong
In this paper, we consider an inflow problem for the non-isentropic Navier-Stokes-Poisson system in a half line (0, ∞). For the general gas including ideal polytropic gas, we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4 × 4 system of autonomous ordinary differential equations. We also show the time asymptotic stability of the stationary
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Weak solution to the incompressible viscous fluid and a thermoelastic plate interaction problem in 3D Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Srđan Trifunović, Yaguang Wang
In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate. The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models. We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that, via
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Precise values of the Bloch constants of certain log- p -harmonic mappings Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Mingsheng Liu, Lifang Luo
The aim of this article is twofold. One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method. The other is to obtain the precise values of Bloch constants for certain log-p-harmonic mappings. These results improve upon the corresponding results given in Bai et al. (Complex Anal. Oper. Theory, 13(2): 321–340
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Inheritance of divisibility forms a large subalgebra Acta Math. Sci. (IF 0.919) Pub Date : 2020-12-24 Qingzhai Fan, Xiaochun Fang, Xia Zhao
Let A be an infinite dimensional stably finite unital simple separable C*-algebra. Let B ⊂ A be a stably (centrally) large subalgebra in A such that B is m-almost divisible (m-almost divisible, weakly (m, n)-divisible). Then A is 2(m + 1)-almost divisible (weakly m-almost divisible, secondly weakly (m, n)-divisible).
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On the Nuclearity of Completely 1-Summing Mapping Spaces Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Zhe Dong, Yafei Zhao
In this paper, we investigate the λ-nuclearity in the system of completely 1-summing mapping spaces (Π1(·, ·), π1). In Section 2, we obtain that ℂ is the unique operator space that is nuclear in the system (Π1(·, ·), π1). We generalize some results in Section 2 to λ-nuclearity in Section 3.
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The Cauchy Problem for the Two Layer Viscous Shallow Water Equations Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Pengcheng Mu, Qiangchang Ju
In this paper, the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data. The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs’ regularization method.
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Strong Equivalences of Approximation Numbers and Tractability of Weighted Anisotropic Sobolev Embeddings Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Jidong Hao, Heping Wang
In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a = {aj}j≥1 and b = {bj}j≥1 of positive numbers. We obtain strong equivalences of the approximation numbers, and necessary and sufficient conditions on a, b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.
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A Globally Convergent QP-Free Algorithm for Inequality Constrained Minimax Optimization Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Jinbao Jian, Guodong Ma
Although QP-free algorithms have good theoretical convergence and are effective in practice, their applications to minimax optimization have not yet been investigated. In this article, on the basis of the stationary conditions, without the exponential smooth function or constrained smooth transformation, we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints
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Global Optimization of the Difference of two Increasing Plus-Convex-Along-Rays Functions Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 H. Shahriaripour, H. Mohebi
The theory of increasing and convex-along-rays (ICAR) functions defined on a convex cone in a real locally convex topological vector space X was already well developed. In this paper, we first examine abstract convexity of increasing plus-convex-along-rays (IPCAR) functions defined on a real normed linear space X. We also study, for this class of functions, some concepts of abstract convexity, such
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Asymptotic Stability of a Boundary Layer and Rarefaction Wave for the Outflow Problem of the Heat-Conductive Ideal Gas without Viscosity Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Lili Fan, Meichen Hou
This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and give a rigorous proof of the asymptotic stability of both the degenerate boundary layer and its superposition with the 3-rarefaction wave under some smallness conditions
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Existence and Uniqueness of the Positive Steady State Solution for a Lotka-Volterra Predator-Prey Model with a Crowding Term Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Xianzhong Zeng, Lingyu Liu, Weiyuan Xie
This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation. We obtain a critical value λ D1 (Ω0), and demonstrate that the existence of the predator in \({\overline \Omega _0}\) only depends on the relationship of the growth rate μ of the predator and λ D1 (Ω0), not on the prey. Furthermore, when μ < λ D1 (Ω0), we obtain the existence and uniqueness of
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On the Complete 2-Dimensional λ -Translators with a Second Fundamental form of Constant Length Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Xingxiao Li, Ruina Qiao, Yangyang Liu
In this article we study the two-dimensional complete λ-translators immersed in the Euclidean space ℝ3 and Minkovski space ℝ31 . We obtain two classification theorems: one for two-dimensional complete λ-translators x: M2 → ℝ3 and one for two-dimensional complete space-like λ-translators x: M2 → ℝ31 , with a second fundamental form of constant length.
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On Vortex Alignment and the Boundedness of the L q -Norm of Vorticity in Incompressible Viscous Fluids Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Siran Li
We show that the spatial Lq-norm (q > 5/3) of the vorticity of an incompressible viscous fluid in ℝ3 remains bounded uniformly in time, provided that the direction of vorticity is Hölder continuous in space, and that the space-time Lq-norm of vorticity is finite. The Hölder index depends only on q. This serves as a variant of the classical result by Constantin-Fefferman (Direction of vorticity and
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The Existence of a Nontrivial Weak Solution to a Double Critical Problem Involving a Fractional Laplacian in ℝ N with a Hardy Term Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Gongbao Li, Tao Yang
In this paper, we consider the existence of nontrivial weak solutions to a double critical problem involving a fractional Laplacian with a Hardy term: $${( - \Delta )^s}u - \gamma {u \over {{{\left| x \right|}^{2s}}}} = {{{{\left| u \right|}^{2_s^ * (\beta ) - 2}}u} \over {{{\left| x \right|}^\beta }}} + \left[ {{I_\mu } * {F_\alpha }( \cdot ,u)} \right](x){f_\alpha }(x,u),\;\;\;\;u \in {\dot H^{^s}}({\mathbb{R}^n})
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Spectra of Composition Groups on the Weighted Dirichlet Space of the Upper Half-Plane Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 M. O. Agwang, J. O. Bonyo
We prove that the group of weighted composition operators induced by continuous automorphism groups of the upper half plane \(\mathbb{U}\) is strongly continuous on the weighted Dirichlet space of \(\mathbb{U}\), \({{\cal D}_\alpha }(\mathbb{U})\). Further, we investigate when they are isometries on \({{\cal D}_\alpha }(\mathbb{U})\). In each case, we determine the semigroup properties while in the
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The Decay Estimates for Magnetohydrodynamic Equations with Coulomb Force Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Wenxuan Zheng, Zhong Tan
In this article we consider the compressible viscous magnetohydrodynamic equations with Coulomb force. By spectral analysis and energy methods, we obtain the optimal time decay estimate of the solution. We show that the global classical solution converges to its equilibrium state at the same decay rate as the solution of the linearized equations.
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Parametric Representations of Quasiconformal Mappings Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Zhenlian Lin, Qingtian Shi
In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of Σ0K have some gaps. Then we also find that the area derivative formula (1.6), which is used to estimate the area distortion of Σ0K , cannot be derived from [6], but that formula still holds for Σ0K through our amendatory parametric representation for the one obtained by Eremenko
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Existence of Solutions for the Fractional ( p, q )-Laplacian Problems Involving a Critical Sobolev Exponent Acta Math. Sci. (IF 0.919) Pub Date : 2020-11-20 Fanfan Chen, Yang Yang
In this article, we study the following fractional (p, q)-Laplacian equations involving the critical Sobolev exponent: $$({P_{\mu ,\lambda }})\left\{ {\begin{array}{*{20}{l}} {( - \Delta )_p^{{s_1}}u + ( - \Delta )_q^{{s_2}}u = \mu |u{|^{q - 2}}u + \lambda |u{|^{p - 2}}u + |u{|^{p_{{s_1}}^* - 2}}u,}&{\text{in}\;\Omega ,} \\ {u = 0,}&{\text{in}\;{\mathbb{R}^N}\backslash \Omega ,} \end{array}} \right
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On Refinement of the Coefficient Inequalities for a Subclass of Quasi-Convex Mappings in Several Complex Variables Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Qinghua Xu, Yuanping Lai
Let K be the familiar class of normalized convex functions in the unit disk. In [14], Keogh and Merkes proved that for a function \(f(z) = z + \sum\limits_{k = 2}^\infty {{a_k}} {z^k}\) in the class K, $$\left| {{a_3} - \lambda a_2^2} \right| \le \max \left\{ {{1 \over 3},\left| {\lambda - 1} \right|} \right\},\;\;\;\;\lambda \in \mathbb{C}.$$ The above estimate is sharp for each λ. In this article
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VaR and CTE Based Optimal Reinsurance from a Reinsurer’s Perspective Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Tao Tan, Tao Chen, Lijun Wu, Yuhong Sheng, Yijun Hu
In this article, we study optimal reinsurance design. By employing the increasing convex functions as the admissible ceded loss functions and the distortion premium principle, we study and obtain the optimal reinsurance treaty by minimizing the VaR (value at risk) of the reinsurer’s total risk exposure. When the distortion premium principle is specified to be the expectation premium principle, we also
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Generalized Roper-Suffridge Operator for ϵ Starlike and Boundary Starlike Mappings Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Jie Wang, Jianfei Wang
This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties. First, we prove that the Roper-Suffridge extension operator preserves ϵ starlikeness on the open unit ball of a complex Banach space ℂ × X, where X is a complex Banach space. This result includes many known results. Secondly, by introducing a new class of almost boundary starlike mappings
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A Subclass of Quasi-Convex Mappings on a Reinhardt Domain in ℂ n Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Xiaosong Liu
Let \({D_{{p_1},{p_2}, \cdots ,{p_n}}} = {\rm{\{ }}z \in {\mathbb{C}^n}{\rm{:}}\sum\limits_{l = 1}^n {{{\left| {{z_l}} \right|}^{{p_l}}} < 1{\rm{\} }},{p_l} > 1,l = 1,2, \cdots \;,n}.\). In this article, we first establish the sharp estimates of the main coefficients for a subclass of quasi-convex mappings (including quasi-convex mappings of type \(\mathbb{A}\) and quasi-convex mappings of type \(\mathbb{B}\))
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Existence and Multiplicity of Solutions for a Coupled System of Kirchhoff Type Equations Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Yaghoub Jalilian
In this paper, we study the coupled system of Kirchhoff type equations $$\left\{ {\matrix{ { - \left( {a + b\int_{{\mathbb{R}^3}} {{{\left| {\nabla u} \right|}^2}{\rm{d}}x} } \right)\Delta u + u = {{2\alpha } \over {\alpha + \beta }}{{\left| u \right|}^{\alpha - 2}}u{{\left| v \right|}^\beta },\;x \in {\mathbb{R}^3},} \hfill \cr { - \left( {a + b\int_{{\mathbb{R}^3}} {{{\left| {\nabla v} \right|}^2}{\rm{d}}x}
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Continuity Properties for Born-Jordan Operators with Symbols in Hörmander Classes and Modulation Spaces Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Maurice de Gosson, Joachim Toft
We show that the Weyl symbol of a Born-Jordan operator is in the same class as the Born-Jordan symbol, when Hörmander symbols and certain types of modulation spaces are used as symbol classes. We use these properties to carry over continuity, nuclearity and Schatten-von Neumann properties to the Born-Jordan calculus.
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Itô Differential Representation of Singular Stochastic Volterra Integral Equations Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Nguyen Tien Dung
In this paper we obtain an Itô differential representation for a class of singular stochastic Volterra integral equations. As an application, we investigate the rate of convergence in the small time central limit theorem for the solution.
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Asymptotics of the Cross-Variation of Young Integrals with Respect to a General Self-Similar Gaussian Process Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Soukaina Douissi,Khalifa Es-Sebaiy,Soufiane Moussaten
We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of order β ∈ (1/2, 3/4] is normal according to the values of β . We apply our results to two self-similar Gaussian processes: the subfractional Brownian motion and the bifractional Brownian motion.
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Dynamic for a Stochastic Multi-Group AIDS Model with Saturated Incidence Rate Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Qixing Han,Daqing Jiang
In this paper, a stochastic multi-group AIDS model with saturated incidence rate is studied. We prove that the system is persistent in the mean under some parametric restrictions. We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function. Our results indicate that the existence of ergodic stationary distribution
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Radially Symmetric Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators in an Orlicz-Sobolev Space Setting Acta Math. Sci. (IF 0.919) Pub Date : 2020-10-10 Jae-Myoung Kim,Yun-Ho Kim,Jongrak Lee
We investigate the following elliptic equations: $$\left\{ {\matrix{ { - M\left( {\int_{{\mathbb{R}^N}} {\phi ({{\left| {\nabla u} \right|}^2}){\rm{d}}x} } \right){\rm{div(}}\phi \prime ({{\left| {\nabla u} \right|}^2})\nabla u{\rm{) + }}{{\left| u \right|}^{\alpha - 2}}u = \lambda h(x,u),} \hfill \cr {u(x) \to 0,\;\;\;\;\;{\rm{as}}\left| x \right| \to \infty ,} \hfill \cr } } \right.\;\;\;\;\;\;\
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Boundedness of Variation Operators Associated with the Heat Semigroup Generated by High Order Schrödinger Type Operators Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-20 Suying Liu; Chao Zhang
In this article, we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrödinger type operator (−Δ)2 + V2 in ℝn(n ≥ 5) with V being a nonnegative potential satisfying the reverse Hölder inequality. Furthermore, we prove the boundedness of the variation operators on associated Morrey spaces. In the proof of the main results
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Retraction Note: “Minimal Period Symmetric Solutions for Some Hamiltonian Systems via the Nehari Manifold Method” Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01
The Editor-in-Chief has retracted this article [1], because one of the Editorial Board Mem- bers pointed out that Lemma 3.5 in [1] has an uncorrectable gap which can only be true when n = 1, 2, 3, indicating that the major theorem 1.1 in [1] is only a special case of Theorem 1 in [2], and Theorem 1.2 in [1] is only a trivial result in [3]. The author refused to retract the article [1] in his first
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The Existence of a Bounded Invariant Region for Compressible Euler Equations in Different Gas States Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Weifeng Jiang; Zhen Wang
In this article, by the mean-integral of the conserved quantity, we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region. Moreover, we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process. Finally, we provide a mathematical example showing that with a special
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A Block-Centered Upwind Approximation of the Semiconductor Device Problem on a Dynamically Changing Mesh Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Yirang Yuan; Changfeng Li; Huailing Song
The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initial-boundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature
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Central Limit Theorem and Moderate Deviations for a Class of Semilinear Stochastic Partial Differential Equations Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Shulan Hu; Ruinan Li; Xinyu Wang
In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.
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A Least Square Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence Form Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Peng Zhu; Xiaoshen Wang
This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator. Naturally, the resulting linear system is symmetric and positive definite, and thus the algorithm is easy to implement and analyze. Convergence analysis in the H2 equivalent norm is established on an arbitrary shape regular
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Nonlinear Stability of Rarefaction Waves for a Compressible Micropolar Fluid Model with Zero Heat Conductivity Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Jing Jin; Noor Rehman; Qin Jiang
In 2018, Duan [1] studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model. Due to the absence of heat conductivity, it is quite difficult to close the energy estimates. He considered the far-field states of the initial data to be constants; that is, \(\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = (1,0,0,1)\). He proved
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Asymptotic Stability of a Viscous Contact Wave for the One-Dimensional Compressible Navier-Stokes Equations for a Reacting Mixture Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Lishuang Peng
We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable, provided the strength of contact
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On Singular Equations Involving Fractional Laplacian Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Ahmed Youssfi; Ghoulam Ould Mohamed Mahmoud
We study the existence and the regularity of solutions for a class of nonlocal equations involving the fractional Laplacian operator with singular nonlinearity and Radon measure data.
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Local Existence and Uniqueness of Strong Solutions to the Two Dimensional Nonhomogeneous Incompressible Primitive Equations Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Quansen Jiu; Fengchao Wang
In this article, we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions. The initial vacuum is allowed.
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Lipschitz Type Characterizations for Bergman-Orlicz Spaces and Their Applications Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Rumeng Ma; Jingshi Xu
We give characterizations for Bergman-Orlicz spaces with standard weights via a Lipschitz type condition in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As an application, we obtain the boundeness of the symmetric lifting operator from Bergman-Orlicz spaces on the unit disk into Bergman-Orlicz spaces on the bidisk.
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Positive Solutions and Infinitely Many Solutions for a Weakly Coupled System Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Xueliang Duan; Gongming Wei; Haitao Yang
We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we prove the existence and nonexistence of ground state solutions for the system with close-to-periodic potentials.
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Parameters Identification in a Saltwater Intrusion Problem Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Ji Li; Carole Rosier
This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic
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Existence and Concentration Behavior of Ground State Solutions for a Class of Generalized Quasilinear Schrödinger Equations in ℝ N Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Jianhua Chen; Xianjiu Huang; Bitao Cheng; Xianhua Tang
In this article, we study the generalized quasilinear Schrödinger equation$$ - \text{div}({\varepsilon ^2}{g^2}(u)\nabla u) + {\varepsilon ^2}g(u)g'(u){\left| {\nabla u} \right|^2} + V(x)u = K(x){\left| u \right|^{p - 2}}u,\;\;\;\;x \in {\mathbb{R}^N},$$where N ≥ 3, ε> 0, 4
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On Boundedness Property of Singular Integral Operators Associated to a Schrödinger Operator in a Generalized Morrey Space and Applications Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 Xuan Truong Le; Thanh Nhan Nguyen; Ngoc Trong Nguyen
In this paper, we provide the boundedness property of the Riesz transforms associated to the Schrödinger operator \({\cal L} = \Delta + {\bf{V}}\) in a new weighted Morrey space which is the generalized version of many previous Morrey type spaces. The additional potential V considered in this paper is a non-negative function satisfying the suitable reverse Hölder’s inequality. Our results are new and
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Dynamics on Noncommutative Orlicz Spaces Acta Math. Sci. (IF 0.919) Pub Date : 2020-09-01 L. E. Labuschagne; W. A. Majewski
Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. This complements earlier work [26] where we made a strong case for the assertion that statistical physics of regular systems should properly be based on the pair of Orlicz spaces 〈Lcosh−1, L log(L + 1)〉, since this framework gives a better description of regular observables, and also allows for a
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