ON GLOBAL ASYMPTOTIC STABILITY OF THE ZERO SOLUTION OF A GENERALIZED LIENARD′S SYSTEM

ＯＮＧＬＯＢＡＬＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＯＦＴＨＥＺＥＲＯＳＯＬＵＴＩＯＮＯＦＡＧＥＮＥＲＡＬＩＺＥＤＬＩＥＮＡＲＤ′ＳＳＹＳＴＥＭＰＥＮＧＬＥＱＵＮＡＮＤＨＵＡＮＧＬＩＨＯＮＧＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｓｔｕｄｙｔ...     

STABILITY OF GLOBAL GEVREY SOLUTION TO WEAKLY HYPERBOLIC EQUATIONS

ＳＴＡＢＩＬＩＴＹＯＦＧＬＯＢＡＬＧＥＶＲＥＹＳＯＬＵＴＩＯＮＴＯＷＥＡＫＬＹＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＳＭ．ＲＥＩＳＳＩＧＫ．ＹＡＧＤＪＩＡＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＮｏｖｅｍｂｅｒ１４，１９９４．ＦａｃｕｌｔｙｏｆＭ...     

用Maxwell方程组反演层状地球模型中的ε,μ

用Ｍａｘｗｅｌｌ方程组反演层状地球模型中的ε，μ郑家茂，王元明（东南大学数学系，南京２１００１８）ＳＯＬＶＩＮＧε，μＩＮＬＡＹＥＲＥＤＥＡＲＴＨＭＯＤＥＬＢＹＭＡＸＷＥＬＬＳＹＳＴＥＭ￥ＺＨＥＮＧＪＩＡＭＡＯ；ＷＡＮＧＹＵＡＮＭＩＮＧ（Ｄｅｐａｒｔ...     

SIGN MATRIX，REGULAR SPLITTINGS AND MONOTONIC ENCLOSURE OF SOLUTIONS FOR NONLINEAR SYSTEM OF EQUATIONS，PART Ⅱ

ＳＩＧＮＭＡＴＲＩＸ，ＲＥＧＵＬＡＲＳＰＬＩＴＴＩＮＧＳＡＮＤＭＯＮＯＴＯＮＩＣＥＮＣＬＯＳＵＲＥＯＦＳＯＬＵＴＩＯＮＳＦＯＲＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＯＦＥＱＵＡＴＩＯＮＳ，ＰＡＲＴⅡＸＵＺＯＮＧＢＥＮＡＮＤＹＯＵＺＨＡＯＹＯＮＧＡｂｓｔｒａｃ...     

VIRTUAL SYSTEM METHOD FOR SYSTEM TREE

ＶＩＲＴＵＡＬＳＹＳＴＥＭＭＥＴＨＯＤＦＯＲＳＹＳＴＥＭＴＲＥＥ￥ＺＨＥＮＧＺＨＯＮＧＧＵＯ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙ）Ｂｅ１Ｊｉｎｇ１００８７１，Ｃｈｉｎａ．）（Ｐ...     

BAYESIAN ANALYSIS, LIKELIHOOD RATIO AND INFORMATION

ＢＡＹＥＳＩＡＮＡＮＡＬＹＳＩＳ，ＬＩＫＥＬＩＨＯＯＤＲＡＴＩＯＡＮＤＩＮＦＯＲＭＡＴＩＯＮ￥ＺＨＡＮＧＹＡＯＴＩＮＧＡＮＤＤＵＪＩＮＧＳＯＮＧＡｂｓｔｒａｃｔ：Ｗｅｐｒｅｓｅｎｔａｎｅｗｓｃｈｅｍｅｆｏｒｕｎｃｅｒｔａｉｎｒｅａｓｏｎｉｎｇｂａｓｅ...     

ON INTERIOR POINTS OF THE JULIA SET J（R） FOR RANDOM DYNAMICAL SYSTEM R

ＯＮＩＮＴＥＲＩＯＲＰＯＩＮＴＳＯＦＴＨＥＪＵＬＩＡＳＥＴＪ（Ｒ）ＦＯＲＲＡＮＤＯＭＤＹＮＡＭＩＣＡＬＳＹＳＴＥＭＲ＊＊ＧＯＮＧＺＨＩＭＩＮ＊ＲＥＮＧＵＹＡＯ＊ＡｂｓｔｒａｃｔＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＮｏｖｅｍｂｅｒ２９，１９９４．＊Ｉｎ...     

THE COMPUTATION OF SYMMETRY－BREAKING BIFURCATION POINTS IN Z_2×Z_2－SYMMETRIC NONLINEAR PROBLEMS

ＴＨＥＣＯＭＰＵＴＡＴＩＯＮＯＦＳＹＭＭＥＴＲＹ－ＢＲＥＡＫＩＮＧＢＩＦＵＲＣＡＴＩＯＮＰＯＩＮＴＳＩＮＺ_２×Ｚ_２－ＳＹＭＭＥＴＲＩＣＮＯＮＬＩＮＥＡＲＰＲＯＢＬＥＭＳ￥ＹＥＲＵＩＳＯＮＧＡＮＤＹＡＮＧＺＨＯＮＧＨＵＡＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａ...     

EXPONENTIAL TRICHOTOMY,ORTHOGONALITY CONDITION AND THEIR APPLICATION

ＥＸＰＯＮＥＮＴＩＡＬＴＲＩＣＨＯＴＯＭＹ，ＯＲＴＨＯＧＯＮＡＬＩＴＹＣＯＮＤＩＴＩＯＮＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＺＨＵＤＥＭＩＮＧＸｕＭＩＮＡｂｓｔｒａｃｔＥｘｐｏｎｅｎｔｉａｌｔｒｉｃｈｏｔｏｍｙｔｈｅｏｒｙｉｓｄｅｖｅｌ...     

ON THE DIFFERENTIABILITY OF THE PARITY PROGRESSIVE POPULATION SEMIGROUP

ＯＮＴＨＥＤＩＦＦＥＲＥＮＴＩＡＢＩＬＩＴＹＯＦＴＨＥＰＡＲＩＴＹＰＲＯＧＲＥＳＳＩＶＥＰＯＰＵＬＡＴＩＯＮＳＥＭＩＧＲＯＵＰ￥ＳＨＩＤＥＭＩＮＧＡＮＤＹＡＮＧＬＵＳＨＡＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅ...     

三维保测度映射系统不变流形及其稳定性

本文通过构造形式级数的方式，给出了一种三维保测度映射系统中一维不变流形和二维不变流形的计算方法。利用不变流形的解析表达式我们估计了导致共振带完全失稳的临界参数。     

WAVE COMPUTATION ON THE HYPERBOLIC DOUBLE DOUGHNUT

We compute the waves propagating on the compact surface of constant negative curvature and genus 2 that is a toy model in quantum chaos theory and cosmic topology. We adopt a variational approach using finite elements. We have to implement the action of the fuchsian group by suitable boundary conditions of periodic type. Despite the ergodicity of the dynamics that is quantum weak mixing, the computation is very accurate. A spectral analysis of the transient waves allows to compute the spectrum and the eigenfunctions of the Laplace-Beltrami operator. We test the exponential decay due to a localized dumping satisfying the assumption of geometric control.     

一类总人口变化的传染病模型的极限环及混沌

研究了一类具被动免疫的流行病模型,考虑到了各仓室人口的增长,结合中心流形理论和参数扰动得到了系统极限环和混沌的存在性,并作了数值模拟和仿真.     

Transverse homoclinic orbit bifurcated from a homoclinic manifold by the higher order melnikov integrals

Consider an autonomous ordinary differential equation in $\mathbb{R}^n$ that has a $d$ dimensional homoclinic solution manifold $W^H$. Suppose the homoclinic manifold can be locally parametrized by $(\alpha,\theta) \in \mathbb{R}^{d-1}\times \mathbb{R}$. We study the bifurcation of the homoclinic solution manifold $W^H$ under periodic perturbations. Using exponential dichotomies and Lyapunov-Schmidt reduction, we obtain the higher order Melnikov function. For a fixed $(\alpha_0,\theta_0)$ on $W^H$, if the Melnikov function have a simple zeros, then the perturbed system can have transverse homoclinic solutions near $W^H$.     

Partial synchronization in coupled chemical chaotic oscillators

In this paper we investigate the problem of partial synchronization in diffusively coupled chemical chaotic oscillators with zero-flux boundary conditions. The dynamical properties of the chemical system which oscillates with Uniform Phase evolution, yet has Chaotic Amplitudes (UPCA) are first discussed. By combining numerical and analytical methods, the impossibility of full global synchronization in a network of two or three coupled chemical oscillators is discovered. Mathematically, stable partial synchronization corresponds to convergence to a linear invariant manifold of the global state space. The sufficient conditions for exponential stability of the invariant manifold in a network of three coupled chemical oscillators are obtained via the nonlinear contraction principle.     

A Note on P—Sasakian Manifold

s51.IntroductionLetMbeadifferentiablemanifo1dofdimensionn,ifMadmitsa(l,l)-tensorfieldgl,aPoSitivedefiniteRiemannianmetricg,avectorfieldeandal-formVwhichsatisfythefollow-ingconditions.thensuchamanifoldMiscalledaPara-SasakianmanifoldorbrieflyaP-Sasakianmanifoldby7'.AdatiandK.Matsumoto[ljwhichareconsideredasspecialcaseofanalmostparacontactmanifoldintroducedbyI.Sato[2].WhereVdenotestheoperatorofcovariantdifferentiationwithrespecttothemetrictensorg'X(M)denotesthesetofdifferentiablevectorfiel…     

Stein fillability and the realization of contact manifolds

There is an intrinsic notion of what it means for a contact manifold to be the smooth boundary of a Stein manifold. The same concept has another more extrinsic formulation, which is often used as a convenient working hypothesis. We give a simple proof that the two are equivalent. Moreover it is shown that, even though a border always exists, its germ is not unique; nevertheless the germ of the Dolbeault cohomology of any border is unique. We also point out that any Stein fillable compact contact -manifold has a geometric realization in via an embedding, or in via an immersion.

     

On Flat Complete Causal Lorentzian Manifolds

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental groups are virtually abelian. In dimension 4, there is only one, up to a scaling factor, strictly causal manifold which is not globally hyperbolic. For a generic point of this manifold, either the past or the future is not closed and contains a lightlike straight line     

ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES I

In this paper the authors investigate hypersurfaces M of a semi-Euclidean space Esn+1, n > 4, satisfying (aC + BR) ?H = LkQ(g, Hk), k = 1,2, 3. Using obtained results they show additional curvature properties of investigated hypersurfaces.     

Some remarks about 1-convex manifolds on which all holomorphic line bundles are trivial

We give an abridged proof of an example already considered in [M. Col?oiu, On 1-convex manifolds with 1-dimensional exceptional set, Rev. Roumaine Math. Pures et Appl. 43 (1998) 97-104] of a 1-convex manifold X of dimension 3 such that all holomorphic line bundles on X are trivial. We also point out several mistakes of [Vo Van Tan, On the quasiprojectivity of compactifiable strongly pseudoconvex manifolds, Bull. Sci. Math. 129 (2005) 501-522] concerning this topic.