Random attractors for asymptotically upper semicompact multivalue random semiflows

The present paper studied the dynamics of some multivalued random semi- flow.The corresponding concept of random attractor for this case was introduced to study asymptotic behavior.The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact,and this random attractor is random compact and invariant.Furthermore,if the system has ergodicity,then this random attractor is the limit set of a deterministic bounded set.     

Dynamics of delay induced composite multi-scroll attractor and its application in encryption

Time delay feedback has been shown to produce chaos from non-chaotic systems. In this paper, besides the single and double scroll chaotic attractors, a new composite multi-scroll attractor is found in stable systems with time delay feedback. From the viewpoint of the local stability analysis, conservation analysis, Lyapunov exponent spectrum and power spectrum, the composite multi-scroll attractor is shown to be a hyper-chaotic attractor. The phase trajectory in the new composite hyper-chaotic multi-scroll attractor diverges in multiple eigen-directions, which improves the security of secure communication and chaotic encryption. A paradigm using the multi-scroll attractor for encryption is proposed, demonstrating its potential applicability.     

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.     

Invariant Set and Attractor of Nonautonomous Functional Differential Systems: A Decomposition Approach

In this paper, the invariant set and attractor are addressed for the nonautonomous functional differential systems. An estimation of the existence range of the invariant set and attractor are given by using a decomposition approach and the properties of nonnegative matrices. In addition, an example is given to denote the application of the new results.     

Criteria for Strong and Weak Random Attractors

The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors.      

Ghost-Fluid Eulerian-Lagrangian方法及其应用

考察了将独立的Euler程序和Lagrange程序通过Ghost Fluid方法结合起来以处理流固耦合问题的算法。在Euler计算步中,采用基于物质界面建立的Levelset函数对被Lagrange域覆盖的Euler网格上的物理量进行外插,同时确保界面两侧压力和法向速度连续;而在Lagrange计算步中,根据界面所在Euler网格压力确定界面各个节点的受力情况,从而确定Lagrange单元的运动与变形。应用这种方法对瞬时起爆爆轰产物作用于爆炸容器问题进行了计算分析,给出了流场演化及容器各关键位置的超压与变形情况。计算表明,对长径比为2:1的椭球封头爆炸容器最大超压及最大应变均出现在封头顶部,这与封头顶部最易破坏的实际相符。     

Fuzzy approaching set and fuzzy approaching functional mapping

I.ProblemstoBeStudiedl.linmakingpredictiontothefuturestateofasystemaccordingtoitspaststate,thepredictionisusuallynotsimplytoextendthetimeseriescurvedescribingthepaststateofthesystemtotheonedescribingthefuturestateofthesystem,instead,mappingwhichmapsthetimeseriesfunctiondescribingthepaststateofthesystemtotheonedescribingthefLlturestateoftilesystem.Thatisbecausetheenvironmentconditionsinwhichthesystemliesareusuallydifferentbetweenthepastandthetexture.Meanwhile,slicingthetimeseriesfunctiondescri…     

Mohr-Coulomb准则主应力回映算法及在地基问题的应用

针对Mohr-Coulomb准则在应力空间中存在奇异点的问题,提出了主应力空间应力回映算法。分析了多屈服面下塑性流动法则,给出了应力更新过程中应力回映区域的判定方法,推导了不同映射区域下塑性因子的Newton-Raphson迭代求解式和应力更新方程,建立了对应的一致切线模量表达式。利用C++语言,编制了弹塑性有限元求解程序,并对岩土地基问题进行求解,计算结果的比对证明了所编程序的可行性和精确性。     

等参元逆变换算法在渗流—位移耦合场分析中的应用

在渗流 -位移耦合场分析中应用等参元逆变换算法解决了两个场之间的数据传递问题 ,所提出的逆变换算法是基于解析性质的新算法 ,具有简便、高效和高精度的特点 ,便于在实际工程中应用。     

A REGULAR VALUE OF COMPACT DEFORMATION

Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one value in a specific open ball. The proof of the result is constructive and based upon continuation methods.     

CONTINUITY OF GENERALIZED INVERSES OF LINEAR OPERATORS IN BANACH SPACES AND ITS APPLICATIONS

The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses were independent of the choice of the generalized inverse. Based on this result, two sufficient and necessary conditions for the lower semi-continuity of generalized inverses as the set-valued mappings are given.     

The adjoining cell mapping and its recursive unraveling,part II: Application to selected problems

Several applications of the adjoining cell mapping technique are provided here by employing the adaptive mapping unraveling algorithm to analyze smooth and pathological autonomous dynamical systems. The performance of an implementation of recursive unraveling algorithm is also illustrated regarding its low memory requirements for computational purposes when compared with the simple cell mapping method. The applications considered here illustrate the effectiveness of the adjoining cell mapping technique in its ability to determine limit cycles and to unravel nonstandard dynamics. The advantages of this new technique of global analysis over the simple cell mapping method are discussed.     

Chain recurrence,semiflows, and gradients

This paper is a study of chain recurrence and attractors for maps and semiflows on arbitrary metric spaces. The main results are as follows. (i) C. Conley's characterization of chain recurrence in terms of attractors holds for maps and semiflows on any metric space. (ii) An alternative definition of chain recurrence for semiflows is given and is shown to be equivalent to the usual definition. The alternative definition uses chains formed of orbit segments whose lengths are at least 1, while in the usual definition these lengths are required to be arbitrarily long. (iii) The chain recurrent set of a continuous semiflow is the same as the chain recurrent set of its time-one map. (iv) Conditions on a real-valued function are given that ensure that the semiflow generated by its gradient has only equilibria in its chain recurrent set. An example is given (onR ³) showing that a gradient flow may have nonequilibrium chain recurrent points if these conditions are violated.     

一种确定非线性振子多个共存周期解的数值方法

提出一种简洁高效数值方法，用以确定周期激励下非线性振子的多个共存周期响应。这是一种基于Ｐｏｉｎｃａｒé映射和二维自治系统奇点分类的几何方法，可在Ｐｏｉｎｃａｒé截面上得出多个周期运动的分布情况和类型。文中二个算例证实了该方法的有效性。     

The adjoining cell mapping and its recursive unraveling,part I: Description of adaptive and recursive algorithms

A new type of cell mapping, referred to as an adjoining cell mapping, is developed in this paper for autonomous dynamical systems employing the cellular state space. It is based on an adaptive time integration employed to compute an associated cell mapping for the system. This technique overcomes the problem of determining an appropriate duration of integration time for the simple cell mapping method. Employing the adjoining mapping principle, the first type of algorithm developed here is an adaptive mapping unraveling algorithm to determine equilibria and limit cycles of the dynamical system in a way similar to that of the simple cell mapping. In addition, it is capable of providing useful information regarding the behavior of dynamical systems possessing pathological dynamics and of systems with rapidly changing vector field. The adjoining property inherent in the adjoining cell mapping method, in general, permits development of new recursive algorithms for unraveling dynamics. The required computer memory for a practical implementation of such algorithms is considerably less than that required by the simple cell mapping algorithm since they allow for a recursive partitioning of state space for trajectory analysis. The second type of algorithm developed in this paper is a recursive unraveling algorithm based on adaptive integration and recursive partitioning of state space into blocks of cells with a view toward its practical implementation. It can find equilibria of the system in the same manner as the simple cell mapping method but is more efficient in locating periodic solutions.     

Existence of boundary value problems for TFD equation in quantum mechanics

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Dirichlet problem of higher order elliptic equation with perturbation both in differential operator and in boundary

This paper is the continuation of article [7]. It gives further results about the asymptotic expression for the solution of higher order elliptic equation in the case of boundary perturbation combined with operator perturbation. When unperturbed problemA ₀ is not on the spectrum, the asymptotic expression for the solution of perturbation problemA may be expanded with respect to the small parameter . WhileA ₀ is on the spectrum, the asymptotic expression of the solution contains negative powers of the small parameter . The approximation of arbitrary order to the solution is considered and the recursive formula for the general term and the estimation of remainder term are given.     

Asymptotic behaviors of solutions for dissipative quantum Zakharov equations

The dissipative quantum Zakharov equations are mainly studied. The existence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori estimate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated.     

一种高效的等参有限元逆变换算法

采用Ｔａｙｌｏｒ展开技术构造了一种具有线性迭代格式的等参有限元逆变换算法，对算法的收敛性和收敛速度分别给出了理论证明和数值检验。该算法不仅形式简单、便于程序实现，且适合于任何类型的等参单元，是一种高效实用的逆变换算法。文中还给出了算法的实施框图。     

Third-order nonlinear singularly perturbed boundary value problem

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