深海富钴结核微区X射线荧光光谱分析和数据挖掘

西太平洋富钴结核是近年来新发现的海底固体矿产资源,富含M n,Fe,Co,Ni和Cu等多种关键金属元素.富钴结核是一种非均质的地球化学和矿物学集合体,粒径约6 cm的结核在生长过程中记录了数千万年的海洋沉积历史,亟需高分辨率的分析技术揭示古海洋环境信息.采用微区X射线荧光光谱仪(μ-XRF),对C3BC1704富钴结核...     

高阶非线性差分方程的全局吸引性

研究了一类高阶非线性差分方程所有正解的周期性,不变区间及全局吸引性.证明了方程的正平衡点是在一个依赖于参数的盆里的全局吸引子.     

Asymptotic Behavior of Solutions of a Strongly Nonlinear Model of a Crystal Lattice

We consider a system of hyperbolic nonlinear equations describing the dynamics of interaction between optical and acoustic modes of a complex crystal lattice (without a symmetry center) consisting of two sublattices. This system can be considered a nonlinear generalization of the well-known Born-Huang Kun model to the case of arbitrarily large sublattice displacements. For a suitable choice of parameters, the system reduces to the sine-Gordon equation or to the classical equations of elasticity theory. If we introduce physically natural dissipative forces into the system, then we can prove that a compact attractor exists and that trajectories converge to equilibrium solutions. In the one-dimensional case, we describe the structure of equilibrium solutions completely and obtain asymptotic solutions for the wave propagation. In the presence of inhomogeneous perturbations, this system is reducible to the well-known Hopfield model describing the attractor neural network and having complex behavior regimes.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 3, pp. 357–367, June, 2005.     

一类l-半群的l-自同构

设R有1的全序环。记Mn(R)为R上n×n矩阵乘法半群,则Mn(R)在通常格序下成为l-半群。本文对l-半群Mn(R)的∨-自同构,∧-自同构以及l-自同构给出了详细的刻画。     

广义KdV-Burgers方程长时间性态的谱方法

1．引言随着无限维动力系统研究的发展和深入,人们对非线性发展方程长时间性态的研究越来越重视[1－6］,而这种研究在很大程度上依赖于数值计算的结果,因此,计算结果是否可靠,计算格式先得是否合适都是值得探讨和深入研究的问题17－10．广义KdV－Burg6rs方程是一类重要的非线性发展方程,在实际问题中也有着广泛的应用,因此,对它的研究即有理论价值也有实际意义．本文讨论如下的广义KdV－Burgers方程的周期初值问题其中a,q是已知实常数,且a＞0八。）,g（。）,h00是已知实函数．文［10］对上述问题构造了半离散的Fourier谱逼近…     

二维广义Ginzburg-Landau方程的指数吸引子

在文[1]的基础上，得到了二维广义的Ginzburg－Landau方程的指数吸引子的存在性．     

Regularity and asymptotic behavior of solutions of nonautonomous differential equations

The existence of a nonautonomous approximate inertial manifold is shown for problems of the formu + Au + N(t,u)=0, in whichA is a self-adjoint operator with compact resolvent in a Hilbert spaceH. The operatorN(t, u) = G(u) + F(t, u) is nonlinear withG a monotone gradient that is locally Lipschitz fromD(A ^1/2) intoH, andF:⁺×HH a Lipschitz perturbation that is Hölder continuous int. Weak solutions are shown to be uniformly locally Hölder continuous intoD(A) with equicontinuity in families of solutions with ¦u(0)¦ r.A priori estimates of ¦Au(t)¦ are also verified and used in a skew-product flow to show there is a global attractor whose component elements form a equicontinuous family of solutions.     

An example of PDE with two attractors

ＡＮＥＸＡＭＰＬＥＯＦＰＤＥＷＩＴＨＴＷＯＡＴＴＲＡＣＴＯＲＳＷａｎｇＧｕａｎｘｉａｎｇ（王冠香）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ,Ｓｕｚｈｏｕ２１５００６Ｐ．Ｒ．Ｃｈｉｎａ）ＸｕＺｈｅｎｙｕａｎ（徐...     

Random attractors for stochastic reaction‐diffusion equations with multiplicative noise in

In this paper, we study the random dynamical system generated by a stochastic reaction‐diffusion equation with multiplicative noise and prove the existence of an ‐random attractor for such a random dynamical system. The nonlinearity f is supposed to satisfy some growth of arbitrary order .