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| 1 | THE TRACE IDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS (Ⅱ)显示文摘An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinearevolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new oneare reductions of the above hierarchy. In each case the relevant Hamiltonian form is established bymaking use of the trase identity. | 屠规彰 孟大志 | 1989 | Acta Mathematicae Applicatae Sinica1989，5，1： | 115 |
| 2 | THE SINGULARLY PERTURBED PROBLEM FOR COMBUSTION REACTION DIFFUSION显示文摘A singularly perturbed combustion reaction diffusion Robin boundary value problem is considered. Using the theory of differential ineaqality, the existence of solution to the problem is proved and the asymptotic estimation of the solution is obtained. | 莫嘉琪 | 2001 | Acta Mathematicae Applicatae Sinica2001，17，2： | 68 |
| 3 | The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem显示文摘The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated,where n is an arbitrary natural number,The main tool is Krasnosel'skii fixed point theorem on the cone. | Qing-liu YaoDepartment of Applied Mthematics, Nanjing University of Economics, Nanjing 210003, China | 2003 | Acta Mathematicae Applicatae Sinica2003，19，1： | 57 |
| 4 | A Nonlinear Singularly Perturbed Problem for Reaction Diffusion Equations with Boundary Perturbation显示文摘A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities. | Jia-qiMo Wan-taoLin | 2005 | Acta Mathematicae Applicatae Sinica2005，21，1： | 50 |
| 5 | A CLASS OF NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION显示文摘The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered. Under suitable conditions, using the fixed point theorem, the asymptotic behavior of solution for the initial boundary value problems is studied. | 莫嘉琪 | 2001 | Acta Mathematicae Applicatae Sinica2001，17，4： | 41 |
| 6 | On the Existence of Positive Periodic Solutions for Neutral Functional Differential Equation with Multiple Deviating Arguments显示文摘By means of an abstract continuation theory for κ-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation dN/dt=N(t)[α(t)-β(t)N(t)-∑j=1^n bj(t)N(t-σj(t))-∑i=1^mci(t)N'(t-γi(t)0]. | Shi-pingLu Wei-gaoGe | 2003 | Acta Mathematicae Applicatae Sinica2003，19，4： | 36 |
| 7 | A CLASS OF SINGULARLY PERTURBED REACTION DIFFUSION INTEGRAL DIFFERENTIAL SYSTEM显示文摘In this paper a class of singularly perturbed initial boundary value problems for the reaction diffusion integral differential system are considered. Using the iteration method and the differential inequalities, the existence, uniqueness and its asymptotic behavior of solution for the initial boundary value problems are studied. | 莫嘉琪 | 1999 | Acta Mathematicae Applicatae Sinica1999，15，1： | 31 |
| 8 | A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation显示文摘A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundaryperturbation are considered.Under suitable conditions,the asymptotic behavior of solution for the initialboundary value problems is studied using the theory of differential inequalities. | Jia-qi Mo Wan-tao Lin | 2006 | Acta Mathematicae Applicatae Sinica2006，22，1： | 33 |
| 9 | Bisexual Galton-Watson Branching Processes in Random Environments显示文摘 | Shi-xia Ma | 2006 | Acta Mathematicae Applicatae Sinica2006，22，3： | 29 |
| 10 | SHAPE PRESERVING PROPERTIES AND CONVERGENCE OF UNIVARIATE MULTIQUADRIC QUASI-INTERPOLATION显示文摘SHAPEPRESERVINGPROPERTIESANDCONVERGENCEOFUNIVARIATEMULTIQUADRICQUASI-INTERPOLATIONWuZONGMIN(吴宗敏)(DepertmentofMathematics,Fuda... | 吴宗敏 | 1994 | Acta Mathematicae Applicatae Sinica1994，10，4： | 26 |
| 11 | Nonconforming H^1-Galerkin Mixed FEM for Sobolev Equations on Anisotropic Meshes显示文摘非一致的 H 1-Galerkin 混合了有限元素方法在各向异性的网孔上为 Sobolev 方程被分析。没有使用 Ritz-Volterra 设计,错误估计被获得。 | Dong-yang Shi Hai-hong Wang | 2009 | Acta Mathematicae Applicatae Sinica2009，25，2： | 26 |
| 12 | Existence of Positive Solutions for Singular Second-order m-Point Boundary Value Problems显示文摘The singular second-order m-point boundary value problem -(Lφ)(x)=h(x)f(φ)(x)),0 | Guo-weiZhang Jing-xianSun | 2004 | Acta Mathematicae Applicatae Sinica2004，20，4： | 23 |
| 13 | Existence of at Least Two Periodic Solutions of a Ratio-dependent Predator-prey Model with Exploited Term显示文摘在这篇论文,我们与利用术语学习一个非自治的比率依赖者食肉动物猎物模型。借助于巧合度理论,我们为这个模型的至少二个积极周期的答案的存在建立一个足够的条件。 | De-sheng Tian Xian-wu Zeng | 2005 | Acta Mathematicae Applicatae Sinica2005，21，3： | 23 |
| 14 | Superconvergence Analysis and Extrapolation of Quasi-Wilson Nonconforming Finite Element Method for Nonlinear Sobolev Equations显示文摘Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa-tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that (▽h ( u-Ihu )1, ▽hvh) h may be estimated as order O ( h2 ) when u ∈ H3 (Ω), where Ihu denotes the bilinear interpolation of u , vh is a polynomial belongs to quasi-Wilson finite element space and ▽h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O ( h2 ) /O ( h3 ) in broken H 1-norm, which is one/two order higher than its interpolation error when u ∈ H3 (Ω) /H4 (Ω). Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapola- tion result of order O ( h3 ), two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme. | Dong-yang SHI Fen-ling WANG Yan-min ZHAO | 2013 | Acta Mathematicae Applicatae Sinica2013，29，2： | 20 |
| 15 | Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems显示文摘This paper deals with eigenvalue problems for linear Fredholm integral equations of the second kind with weakly singular kernels. A new discrete method is proposed for the approximation of eigenvalues.Compactness of the integral operator in L^1[0, 1] space is obtained. This method is based on the approximation of the integral operator by modified interpolatory projection. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Further, convergence of eigenvalue approximation is obtained by analytical tools. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method. | Xin ZHANG Yun-hui HE | 2019 | Acta Mathematicae Applicatae Sinica2019，35，2： | 18 |
| 16 | On the Controllability of an Advection-diffusion Equation with Respect to the Diffusion Parameter:Asymptotic Analysis and Numerical Simulations显示文摘The advection-diffusion equation y_t~ε-εy_(xx)~ε+ M y_x~ε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time T_M, with T_M in the interval [1, 2×3^(1/2)]/M for M > 0 and in the interval [2×2^(1/2), 2(1 +3^(1/2))]/|M | for M < 0. The exact value of TM is however unknown.We investigate in this work the determination of the minimal time T_M employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L^2-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers. | Youcef AMIRAT Arnaud MNCH | 2019 | Acta Mathematicae Applicatae Sinica2019，35，1： | 18 |
| 17 | Characterizations on Heavy-tailed Distributions by Means of Hazard Rate显示文摘Let F(x) be a distribution function supp0orted on[0,∞),with an equilibrium distribution function Fe(x).In this paper we shall study the function re(x)=(-in -↑Fe(x))′=-↑Fe(x)/∫x^∞-↑Fe(u)du,which is called the equilibrium hazard rate of F.By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed.Two broad classes of heavy-tailed distributions are also introduced and strdied. | ChunSu Qi-heTang | 2003 | Acta Mathematicae Applicatae Sinica2003，19，1： | 18 |
| 18 | The Well-Posedness of Solution to Semilinear Pseudo-parabolic Equation显示文摘In this paper, we use the Green's function method to get the pointwise convergence rate of the semilinear pseudo-parabolic equations. By using this precise pointwise structure and introducing negative index Sobolev space condition on the initial data, we release the critical index of the nonlinearity for blowing up. Our result shows that the global existence does not only depend on the nonlinearity but also the initial condition. | Wei-ke WANG Yu-tong WANG | 2019 | Acta Mathematicae Applicatae Sinica2019，35，2： | 17 |
| 19 | Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims显示文摘We will study the following problem. Let Xt, t ∈ [0, T], be an R^d-valued process defined on a time interval t ∈ [0,T]. Let Y be a random value depending on the trajectory of X. Assume that, at each fixed time t ≤ T, the information available to an agent (an individual, a firm, or even a market) is the trajectory of X before t. Thus at time T , the random value of Y(ω) will become known to this agent. The question is: how will this agent evaluate Y at the time t? We will introduce an evaluation operator εt[Y] to define the value of Y given by this agent at time t. This operator εt[·] assigns an (Xs)0≤s≤т-dependent random variable Y to an (Xs)0≤s≤t-dependent random variable εt[Y]. We will mainly treat the situation in which the process X is a solution of a SDE (see equation (3.1)) with the drift coefficient b and diffusion coefficient a containing an unknown parameter θ = θt. We then consider the so called super evaluation when the agent is a seller of the asset Y. We will prove that such super evaluation is a filtration consistent nonlinear expectation. In some typical situations, we will prove that a filtration consistent nonlinear evaluation dominated by this super evaluation is a g-evaluation. We also consider the corresponding nonlinear Markovian situation. | ShigePeng | 2004 | Acta Mathematicae Applicatae Sinica2004，20，2： | 15 |
| 20 | An Upper Bound for the Adjacent Vertex Distinguishing Acyclic Edge Chromatic Number of a Graph显示文摘如果在 G 和颜色没有 2-colored 周期,图 G 的合适的小锚着色被称为区分非循环的边着色的邻近的顶点的 A 边设定到 u 的事件不等于到 υ
的边事件的颜色集合,在的地方 uυ∈
E (G) 。区分非循环的边的邻近的顶点 G 的色彩的数字,由 χ′ 表示了一 (G), 是在区分 G 的非循环的边着色的一个邻近的顶点的颜色的最小的数字。如果,在这篇论文,我们证明那 G (V, E ) 是没有孤立的边的一张图,那么 χ′ 一 (G)≤
32 Δ
。 | Xin-sheng Liu Ming-qiang An Yang Gao | 2009 | Acta Mathematicae Applicatae Sinica2009，25，1： | 15 |
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