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Clustering for Bivariate Functional Data Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Shi-yun Cao, Yan-qiu Zhou, Yan-ling Wan, Tao Zhang
In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The k-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative
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Geometric Constraints for Global Regularity of 3D Shear Thickening Fluids Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Jia-qi Yang
We consider the relation between the direction of the vorticity and the global regularity of 3D shear thickening fluids. It is showed that a weak solution to the non-Newtonian incompressible fluid in the whole space is strong if the direction of the vorticity is \({{11 - 5p} \over 2}\)-Hölder continuous with respect to the space variables when \(2 < p < {{11} \over 5}\).
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Global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Ming-hua Yang, Si-ming Huang, Jin-yi Sun
In this paper, we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations. That is, the paper deals with a singular limit problem of $$\left\{ \begin{gathered} \begin{array}{*{20}{c}} {u_t^\varepsilon+ {u^\varepsilon } \cdot \nabla {u^\varepsilon } - \Delta {u^\varepsilon } +
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Neighbor Sum Distinguishing Total Choosability of Planar Graphs with Maximum Degree at Least 10 Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Dong-han Zhang, You Lu, Sheng-gui Zhang, Li Zhang
A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that \(\sum\limits_{z \in {E_G}(u) \cup \{u\}} {\phi (z) \ne} \sum\limits_{z \in {E_G}(v) \cup \{v\}} {\phi (z)} \) for each edge uv ∈ E(G), where EG(u) is the set of edges incident with a vertex u. In 2015, Pilśniak and Woźniak conjectured that every graph with maximum degree Δ has an NSD total (Δ + 3)-coloring
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Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Qiang Wen, Guo-qiang Ren, Bin Liu
In this paper, we consider a susceptible-infective-susceptible (SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique, the uniform boundedness of solution is established. In addition, the spatial-temporal risk index \({{\cal R}_0}(\rho)\) depending on the domain evolution rate ρ(t) as well as its analytical
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Acyclic Edge Coloring of 1-planar Graphs without 4-cycles Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-01
Abstract An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in G. The acyclic chromatic index \(\cal{X}_{\alpha}^{\prime}(G)\) of G is the smallest k such that G has an acyclic edge coloring using k colors. It was conjectured that every simple graph G with maximum degree Δ has \(\cal{X}_{\alpha}^{\prime}(G)\le\Delta+2\) . A 1-planar graph is a
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On the Pathwise Uniqueness of Solutions of One-dimensional Reflected Stochastic Differential Equations with Jumps Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Hua Zhang
In this paper, we are concerned with the problem of the pathwise uniqueness of one-dimensional reflected stochastic differential equations with jumps under the assumption of non-Lipschitz continuous coefficients whose proof are based on the technique of local time.
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Existence of Positive Solutions to a Fractional-Kirchhoff System Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Peng-fei Li, Jun-hui Xie, Dan Mu
Let Ω be a bounded smooth domain in ℝN (N ≥ 3). Assuming that 0 < s < 1, \(1 < p,q \le {{N + 2s} \over {N - 2s}}\) with \((p,q) \ne ({{N + 2s} \over {N - 2s}},{{N + 2s} \over {N - 2s}})\), and a, b > 0 are constants, we consider the existence results for positive solutions of a class of fractional elliptic system below,$$\left\{{\matrix{{(a + b[u]_s^2){{(- \Delta)}^s}u = {v^p} + {h_1}(x,u,v,\nabla
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Pseudomonotonicity of Nonlinear Transformations on Euclidean Jordan Algebras Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Yuan-Min Li
In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.
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Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Yong Liu, Zi-yu Liu
We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous Markov-Feller semigroup in continuous time, if there exists an ergodic measure whose support
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Nonlinear Extrapolation Estimates of π Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Wen-qing Xu, Sha-sha Wang, Da-chuan Xu
The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in ℝ2 and it is well-known that by using linear combinations of these basic estimates, modern extrapolation techniques can greatly speed up the approximation process. Similarly, when n vertices are randomly selected on the circle, the semiperimeter and area
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The Perturbed Compound Poisson Risk Model with Proportional Investment Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Nai-dan Deng, Chun-wei Wang, Jia-en Xu
In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc
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Double Moving Extremes Ranked Set Sampling Design Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Meng Chen, Wang-xue Chen, Rui Yang
The traditional simple random sampling (SRS) design method is ine cient in many cases. Statisticians proposed some new designs to increase e ciency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS
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On the Difference Between the Skew-rank of an Oriented Graph and the Rank of Its Underlying Graph Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2024-01-03 Jia-min Zhu, Bo-jun Yuan, Yi Wang
Let G be a simple graph and Gσ be the oriented graph with G as its underlying graph and orientation σ. The rank of the adjacency matrix of G is called the rank of G and is denoted by r(G). The rank of the skew-adjacency matrix of Gσ is called the skew-rank of Gσ and is denoted by sr(Gσ). Let V(G) be the vertex set and E(G) be the edge set of G. The cyclomatic number of G, denoted by c(G), is equal
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Ramsey Numbers of Trees Versus Multiple Copies of Books Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-12-29
Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that \(R(G
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Multicolored Bipartite Ramsey Numbers of Large Cycles Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-12-29 Shao-qiang Liu, Yue-jian Peng
For an integer r ≥ 2 and bipartite graphs Hi, where 1≤ i ≤ r the bipartite Ramsey number br(H1, H2, …, Hr) is the minimum integer N such that any r-edge coloring of the complete bipartite graph KN,N contains a monochromatic subgraph isomorphic to Hi in color i for some 1 ≤ i ≤ r. We show that if \(r \ge 3,{\alpha _1},{\alpha _2} > 0,{\alpha _{j + 2}} \ge [(j + 2)! - 1]\sum\limits_{i = 1}^{j + 1} {{\alpha
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A Minimum Residual Based Gradient Iterative Method for a Class of Matrix Equations Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-30 Qing-qing Zheng
In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally
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An Upwind Mixed Finite Volume Element-fractional Step Method and Convergence Analysis for Three-dimensional Compressible Contamination Treatment from Nuclear Waste Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Chang-feng Li, Yi-rang Yuan, Huai-ling Song
In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume
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Stochastic Volatility Modeling based on Doubly Truncated Cauchy Distribution and Bayesian Estimation for Chinese Stock Market Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Cai-feng Wang, Cong Xie, Zi-yu Ma, Hui-min Zhao
In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dtC model, a stochastic volatility (SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis
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Non-existence of Multi-peak Solutions to the Schrödinger-Newton System with L2-constraint Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Qing Guo, Li-xiu Duan
In this paper, we are concerned with the the Schrödinger-Newton system with L2-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V(x) under certain assumptions on asymptotic behavior of V(x) and its first derivatives near these points. Especially, the critical points of V(x) in this paper must be degenerate. The main
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On Real-rootedness of Independence Polynomials of Rooted Products of Graphs Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Aria Ming-yue Zhu, Bao-xuan Zhu
An independent set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial \(\sum\limits_A {{x^{|A|}}} \), where the sum is over all independent sets A of G. In 1987, Alavi, Malde, Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal. Although this unimodality conjecture has attracted many researchers’ attention
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Global Solutions and Interactions of Non-selfsimilar Elementary Waves for n-D Non-homogeneous Burgers Equation Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Yuan-an Zhao, Gao-wei Cao, Xiao-zhou Yang
We investigate the global structures of the non-selfsimilar solutions for n-dimensional (n-D) non-homogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a (n − 1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions
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Global Strong Solutions and Large-time Behavior of 2D Tropical Climate Model Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Dong-juan Niu, Ying Wang
In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of
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Contact Extension and Symplectification Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Qi-huai Liu, An Xie, Chao Wang
This paper mainly studies the contact extension of conservative or dissipative systems, including some old and new results for wholeness. Then extension of contact system is corresponding to the symplectification of contact Hamiltonian system. This is a reciprocal process and the relation between symplectic system and contact system has been discussed. We have an interesting discovery that by adding
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A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Bo Tang, Yan-ping Chen, Bin Xie, Xiu-xiu Lin
This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions for temporal discretization and the Lagrangian polynomials are used for spatial discretization. An efficient spectral approximation of the weak solution is established. The main work
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Bayesian Estimation and Model Selection for the Spatiotemporal Autoregressive Model with Autoregressive Conditional Heteroscedasticity Errors Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Bing Su, Fu-kang Zhu, Ju Huang
The spatial and spatiotemporal autoregressive conditional heteroscedasticity (STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive (STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations
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Parametric Anisotropic (p, q)-Neumann Problems Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Zhen-hai Liu, Nikolaos S. Papageorgiou
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Formation of Singularity for Full Compressible Magnetohydrodynamic Equations with Zero Resistivity in Two Dimensional Bounded Domains Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Xin Zhong
We are concerned with singularity formation of strong solutions to the two-dimensional (2D) full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain. By energy method and critical Sobolev inequalities of logarithmic type, we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded. Our result is
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Large Time Behavior of Solutions to a 3D Keller-Segel-Stokes System Involving a Tensor-valued Sensitivity with Saturation Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Yuan-yuan Ke, Jia-Shan Zheng
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Injective Δ+2 Coloring of Planar Graph Without Short Cycles Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-11-08 Ying Chen, Lan Tao, Li Zhang
A coloring of graph G is an injective coloring if its restriction to the neighborhood of any vertex is injective, which means that any two vertices get different colors if they have a common neighbor. The injective chromatic number χi(G) of G is the least integer k such that G has an injective k-coloring. In this paper, we prove that (1) if G is a planar graph with girth g ≥ 6 and maximum degree Δ
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Dynamic Analysis of the Multi-state Reliability System with Priority Repair Discipline Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-07-19 Aihemaitijiang Yumaier, Ehmet Kasim
This paper considers a multi-state repairable system that is composed of two classes of components, one of which has a priority for repair. First, we investigate the well-posedenss of the system by applying the operator semigroup theory. Then, using Greiner’s idea and the spectral properties of the corresponding operator, we obtain that the time-dependent solution of the system converges strongly to
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Existence of Optical Vortex Solitons in Pair Plasmas Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Rui-feng Zhang
Optical vortices arise as phase dislocations of light fields and they are of importance in modern optical physics. In this study, we employ the calculus of variations method to develop an existence theory for the steady state vortex solutions of a nonlinear Schrödinger type equation to model light waves that propagate in a medium with a new focusing-defocusing nonlinearity. First, we demonstrate the
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Dynamical Analysis of Nonautonomous Trophic Cascade Chemostat Model with Regime Switching and Nonlinear Perturbations in a Polluted Environment Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Ya-jie Li, Hao-kun Qi, Zheng-bo Chang, Xin-zhu Meng
This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, sufficient conditions for stochastically ultimate boundedness and stochastically permanence are obtained, and we demonstrate that the stochastic system has at least one nontrivial positive
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Large Deviation Principle for the Two-dimensional Stochastic Navier-Stokes Equations with Anisotropic Viscosity Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Bing-guang Chen, Xiang-chan Zhu
In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time. The proof for large deviation principle is based on the weak convergence approach. For small time asymptotics we use the exponential equivalence to prove the result.
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Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman’s ρ and Kendall’s τ Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Ling-yue Zhang, Heng-jian Cui
This paper introduces two local conditional dependence matrices based on Spearman’s ρ and Kendall’s τ given the condition that the underlying random variables belong to the intervals determined by their quantiles. The robustness is studied by means of the influence functions of conditional Spearman’s ρ and Kendall’s τ. Using the two matrices, we construct the corresponding test statistics of local
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Structures of Interaction of Non-selfsimilar Elementary Waves for 2D Scalar Conservation Law with Two Initial Discontinuities Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Gui-qin Qiu, Gao-wei Cao, Xiao-zhou Yang
In this paper, we investigate the global solution and the structures of interaction between two dimensional non-selfsimilar shock wave and rarefaction wave of general two-dimensional scalar conservation law in which flux functions f(u) and g(u) do not need to be convex, and the initial value contains three constant states which are respectively separated by two general initial discontinuities. When
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Characterizations of the BMO and Lipschitz Spaces via Commutators on Weak Lebesgue and Morrey Spaces Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Ding-huai Wang, Jiang Zhou
We prove that the weak Morrey space WM pq is contained in the Morrey space \(M_{{q_1}}^p\) for 1 ≤ q1 < q ≤ p < ∞. As applications, we show that if the commutator [b, T] is bounded from Lp to Lp,∞ for some p ∈ (1, ∞), then b ∈ BMO, where T is a Calderón-Zygmund operator. Also, for 1 < p ≤ q < ∞, b ∈ BMO if and only if [6, T] is bounded from M pq to WM pq . For b belonging to Lipschitz class, we obtain
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Existence of Solutions for a Quasilinear Schrödinger Equation with Potential Vanishing Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Yan-fang Xue, Jian-xin Han, Xin-cai Zhu
We study the following quasilinear Schrödinger equation $$ - \Delta u + V(x)u - \Delta ({u^2})u = K(x)g(u),\,\,\,\,\,\,\,\,x \in {\mathbb{R}^3},$$ where the nonlinearity g(u) is asymptotically cubic at infinity, the potential V(x) may vanish at infinity. Under appropriate assumptions on K(x), we establish the existence of a nontrivial solution by using the mountain pass theorem.
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Sequential Experiment Design Method Based on Uniformity and Distortion of Responses Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Qian-yi Huang, Liang-wei Qi, Jing-ke Zhang, Yu Tang
With the development of modern electronic countermeasure technology, the fight between radar jamming and anti-jamming in aviation military has become increasingly fierce. There are some special requirements for radar countermeasure experiments. For example, such experiments are often divided into several stages, and responses of the previous stages will become factors of the next stages. Moreover,
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Stability and Turing Patterns of a Predator-prey Model with Holling Type II Functional Response and Allee Effect in Predator Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Lu Chen, Feng Yang, Yong-li Song
In this paper, we are concerned with a predator-prey model with Holling type II functional response and Allee effect in predator. We first mathematically explore how the Allee effect affects the existence and stability of the positive equilibrium for the system without diffusion. The explicit dependent condition of the existence of the positive equilibrium on the strength of Allee effect is determined
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Mesh Conditions of the Preserving-Maximum-Principle Linear Finite Volume Element Method for Anisotropic Diffusion-Convection-Reaction Equations Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Lei Lin, Jun-liang Lv, Jing-yan Yue, Guang-wei Yuan
We develop mesh conditions for linear finite volume element approximations of anisotropic diffusionconvectionreaction problems to satisfy the discrete maximum principle. We obtain the sufficient conditions to gurantee the both upper and lower bounds of the numerical solution when each angle of arbitrary triangle is \(\cal{O}(\Vert q\Vert_{\infty}h+\Vert g\Vert_{\infty}h^{2})\)-acute and h is small
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The Global Well-posedness of Strong Solutions to 2D MHD Equations in Lei-Lin Space Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Bao-quan Yuan, Ya-min Xiao
In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space χ−1(ℝ2) with any initial data in χ−1(ℝ2) ∩ L2(ℝ2) is established. Furthermore, the uniqueness of the strong solution in χ−1(ℝ2) and the Leray-Hopf weak solution in L2(ℝ2) is proved.
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A Bond Pricing Model with Credit Migration Risk: Different Upgrade and Downgrade Thresholds Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Jin Liang, Yang Lin
In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising or falling of credit ratings, which forms a buffer zone that could reduce the frequency of credit rating changes. Mathematically, this model is a system of partial differential equations with overlapping area. The existence, uniqueness, regularity and asymptotic
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The Generalized Riemann Problem for a Chromatography System Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Wan-cheng Sheng, Ting Zhang
The generalized Riemann problem for a model of chromatography system in a conservative form is considered. The unique local solution in the class of piecewise C1 functions in a neighborhood of the origin is obtained. The structures of the solutions are similar to the corresponding Riemann problem, which means the Riemann solutions are stable.
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Analysis of a Linearized Energy Stable Numerical Scheme for a Modified Incompressible Cahn-Hilliard-Navier-Stokes System Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Xue Wang, Hong-en Jia, Ming Li, Kai-tai Li
In this paper, a linearized energy stable numerical scheme is used to solve the modified Cahn-Hilliard-Navier-Stokes model, which is a phase-field model for two-phase incompressible flows. The time discretization is based on the convex splitting of the energy functional, which leads to a linearized system. In order to maintain the energy stability, the definition domain of energy function is extended
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Comparison of Riemann Solutions for Non-isentropic Modified and Pure Chaplygin Gas Dynamics Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Wen-jia Wu, Li Wang
In this paper, we investigate the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas and the pure Chaplygin gas, which are the set of all rarefaction waves, shock waves, contact discontinuity and δ-shock waves. Under some appropriate conditions, by studing the limiting behavior, we find that the Riemann solutions of modified Chaplygin gas is the same as pure Chaplygin
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On the Inertia Index of a Mixed Graph in Terms of the Matching Number Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-06-17 Sheng-jie He, Rong-Xia Hao, Ai-mei Yu
A mixed graph \({\tilde G}\) is obtained by orienting some edges of G, where G is the underlying graph of \({\tilde G}\). The positive inertia index, denoted by \({p^ +}(\tilde G)\), and the negative inertia index, denoted by \({n^ -}(\tilde G)\), of a mixed graph \({\tilde G}\) are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of \({\tilde
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Existence and Instability of Some Nontrivial Positive Steady States for the SKT Model with Double Cross Diffusion Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-05-12 Zhi-bao Tang
This paper is concerned with the nonconstant positive steady states of the Shigesada-Kawasaki-Teramoto model for two competing species with double cross-diffusion terms. By applying the Lyapunov-Schmidt decomposition method, the higher order expansion and some detailed spectral analysis, we prove the existence, asymptotic behavior and spectral instability of non-trivial steady states in high-dimensional
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Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-05-12 Ya-zhou Chen, Hakho Hong, Xiao-ding Shi
This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial
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Energy Decay for von Kármán-Gurtin-Pipkin System Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Hanni Dridi
This paper aims to prove the asymptotic behavior of the solution for the thermo-elastic von Karman system where the thermal conduction is given by Gurtin-Pipkins law. Existence and uniqueness of the solution are proved within the semigroup framework and stability is achieved thanks to a suitable Lyapunov functional. Therefore, the stability result clarified that the solutions energy functional decays
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A.S. Convergence Rate and Lp-Convergence of Bisexual Branching Processes in a Random Environment and Varying Environment Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Sheng Xiao, Xiang-dong Liu, Ying-qiu Li
Let (Zn) be a supercritical bisexual branching process in a random environment ξ. We study the almost sure (a.s.) convergence rate of the submartingale \(\overline{W}_{n}=Z_{n}/I_{n}\) to its limit \(\overline{W}\), where (In) is an usually used norming sequence. We prove that under a moment condition of order p ∈ (1, 2), \(\overline{W}-\overline{W}_{n}=o(e^{-na})\) a.s. for some a > 0 that we find
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Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Yu-ling Li, Jun Wang
Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies. The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding. The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored. In this article, we propose the pseudo maximum
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A Bregman-style Partially Symmetric Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Peng-jie Liu, Jin-bao Jian, Guo-dong Ma
The alternating direction method of multipliers (ADMM) is one of the most successful and powerful methods for separable minimization optimization. Based on the idea of symmetric ADMM in two-block optimization, we add an updating formula for the Lagrange multiplier without restricting its position for multi-block one. Then, combining with the Bregman distance, in this work, a Bregman-style partially
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The Spread Speed of Multiple Catalytic Branching Random Walks Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Rong-li Liu
In this paper we study the asymptotic behavior of the maximal position of a supercritical multiple catalytic branching random walk (Xn) on ℤ. If Mn is its maximal position at time n, we prove that there is a constant α > 0 such that Mn/n converges to α almost surely on the set of infinite number of visits to the set of catalysts. We also derive the asymptotic law of the centered process Mn — αn as
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On the Existence of Ground State Solutions to a Quasilinear Schrödinger Equation involving p-Laplacian Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Ji-xiu Wang, Qi Gao
We consider the following quasilinear Schrödinger equation involving p-Laplacian $$ - {\Delta _p}u + V(x)|u{|^{p - 2}}u - {\Delta _p}(|u{|^{2\eta }})|u{|^{2\eta - 2}}u = \lambda {{|u{|^{q - 2}}u} \over {|x{|^\mu }}} + {{|u{|^{2\eta {p^ * }(\nu ) - 2}}u} \over {|x{|^\nu }}}\,\,\,\,{\rm{in}}\,\,{\mathbb{R}^N},$$ where \(N > p > 1,\,\,\eta \ge {p \over {2(p - 1)}},\,\,p < q < 2\eta {p^ * }(\mu ),\,\,{p^
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Solutions of the Camassa-Holm Equation Near the Soliton Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Dan-ping Ding, Wei Lu
In this paper, solutions of the Camassa-Holm equation near the soliton Q is decomposed by pseudo-conformal transformation as follows: λ1/2(t)u(t, λ(t)y + x(t)) = Q(y) +ε(t, y), and the estimation formula with respect to ε(t, y) is obtained: ∣ε(t, y)∣ ≤ Ca3Te−θ∣y∣ + ∣λ1/2(t)ε0∣. For the CH equation, we prove that the solution of the Cauchy problem and the soliton Q is sufficiently close as y → ∞, and
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Star-factorization of the Complete Bipartite Multigraphs Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Jing Shi, Jian Wang, Bei-liang Du
Let λKm,n be a complete bipartite multigraph with two partite sets having m and n vertices, respectively. A Kp,q-factorization of λKm,n is a set of Kp,q-factors of λKm,n which partition the set of edges of λKm,n. When λ = 1, Martin, in [Complete bipartite factorizations by complete bipartite graphs, Discrete Math., 167/168 (1997), 461–480], gave simple necessary conditions for such a factorization
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Best Linear Unbiased Estimators of Location and Scale Ranked Set Parameters under Moving Extremes Sampling Design Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Yan-fei Dong, Wang-xue Chen, Min-yu Xie
In the current paper, the best linear unbiased estimators (BLUEs) of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling (MERSS). Explicit mathematical expressions of these estimators and their variances are derived. Their relative efficiencies with respect to
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Path Factors and Neighborhoods of Independent Sets in Graphs Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Si-zhong Zhou
A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with \({{1 \over 3}}\leq\beta\leq 1\) and k be a
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Defined Contribution Pension Planning with the Return of Premiums Clauses and HARA Preference in Stochastic Environments Acta Math. Appl. Sin. Engl. Ser. (IF 0.8) Pub Date : 2023-04-19 Hao Chang, Xing-jiang Chen
This paper studies a defined contribution (DC) pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment. In practice, most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement. In the mathematical modeling, we assume that a part of pension members