Codimension two bifurcation of a vibro-bounce system

A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.

Variable Separation and Derivative-Dependent Functional Separable Solutions to Generalized KdV Equations

Using the generalized conditional symmetry approach, a complete list of canonical forms for the Korteweg de-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained. The exact DDFSSs of the resulting equations are explicitly exhibited.

Folded Solitary Waves and Foldons in （2＋1） Dimensions

A general type of local/zed excitations, folded solitary waves and foldons, is defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess qnite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the real natural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universal formul is valid for some quite universal (2+1)-dimensional physical mode/s. The "universal" formula is also extended to a more general form with many more independent arbitrary functions.

Variable Separation and Derivative-Dependent Functional Separable Solutions to Generalized Nonlinear Wave Equations

Using the generalized conditional symmetry approach, we obtain a number of new generalized (1+1)-dimensional nonlinear wave equations that admit derivative-dependent functional separable solutions.

TWO FAST ALGORITHMS FOR COMPUTING POINT SCALAR MULTIPLICATIONS ON ELLIPTIC CURVES

The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Muller and Smart proposed two efficient algorithms for point scalar multiplications over even or odd finite fields respectively. This paper reduces the corresponding multiplier by modulo Υk-1 +…+Υ+ 1 and improves the above algorithms. Implementation of our Algorithm 1 in Maple for a given elliptic curve shows that it is at least as twice fast as binary method. By setting up a precomputation table, Algorithm 2, an improved version of Algorithm 1, is proposed. Since the time for the precomputation table can be considered free, Algorithm 2 is about (3/2) log2 q - 1 times faster than binary method for an elliptic curve over

Coordinated formation control of multiple nonlinear systems

A general method of controller design is developed for the purpose offormation keeping and reconfiguration of nonlinear systems with multiple subsystems, such as theformation of multiple aircraft, ground vehicles, or robot arms. The model consists of multiplenonlinear systems. Controllers are designed to keep the subsystems in a required formation and tocoordinate the subsystems in the presence of environmental changes. A step-by-step algorithm ofcontroller design is developed. Sufficient conditions for the stability of formation tracking areproved. Simulations and experiments are conducted to demonstrate some useful coordination strategiessuch as movement with a leader, simultaneous movement, series connection of formations, andhuman-machine interaction.

Solitary Waves in Relativistic Electromagnetic Plasma

Solitary waves in relativistic electromagnetic plasmas are obtained numerically. The longitudinal momentum of electrons has been taken into account in the problem. It is found that in the moving frame with electromagnetic field propagating the solitary waves can exist in both cases, where the vector potential frequency is larger or smaller than the plasma characteristic frequency.

Estimation and Testing for the Parameters of AR(p)-ARCH(q) under Ordered Restriction

Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-

On the Approaching Domain Obtained by Finite Element Method

The use of finite element method leads to replacing the initial domain by an approaching domain. Under some appropriate assumptions, we prove that there exists a W1,+∞-diffeomorphism from the original domain to the approaching domain.

A survey of ergodicity on the set-valued mappings

In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.

LD抽运的高性能微型绿光激光器

研制成高性能微型全固态绿光激光器。用独特的整体控温技术提高器件效率 ,全部元件固化为一个整体以提高激光输出功率和光束指向稳定性 ,用 1W的LD纵向抽运Nd∶YVO4 /KTP激光器 ,获得 195mW的TEM0 0 模 0 53μm连续激光输出。输出功率不稳定度≤± 2 % ,光束方向稳定性优于 0 0 1mrad/hr和 0 0 3mrad/ 2 4hrs。该器件体积小 ,效率高 ,使用方便。

关于具分形边界连通区域上的谱渐近及弱Weyl-Berry猜想

本文研究了连通分形鼓上的谱渐近，对满足“切口”条件的连通分形鼓以及一类自然连通的分形鼓，分别证明了弱Weyl－Berry猜想是成立的.

Heat Flow for the Minimal Surface with Plateau Boundary Condition

The heat flow for the minimal surface under Plateau boundary condition is defined to be a parabolic variational inequality, and then the existence, uniqueness, regularity, continuous dependence on the initial data and the asymptotics are studied. It is applied as a deformation of the level sets in the critical point theory.

The Entire Coloring of Series-Parallel Graphs

The entire chromatic number χ_(vef) (G) of a plane graph G is the minimalnumber of colors needed for coloring vertices, edges and faces of G such that no two adjacent orincident elements are of the same color. Let G be a series-parallel plane graph, that is, a planegraph which contains no subgraphs homeomorphic to K 4. It is proved in this paper that χ_(vef)(G)≤ max{8, Δ(G) + 2} and χ_(vef) (G) = Δ + 1 if G is 2-connected and Δ(G) ≥ 6.

ASYMPTOTIC BEHAVIOR OF THE NONLINEAR PARABOLIC EQUATIONS

This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces R^n. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data u0∈ L^2 ∩ L^r for 1 ≤ r ≤ 2, then the solutions decay in L^2 norm at t^-n/2(1/r-1/2). The decay rates are optimal in the sense that they coincide with the decay rates of the solutions to the heat equations with the same initial data.

Time-risk Discount Valuation of Life Contracts

In this paper a new approach is developed to value life insurance contracts by means of the method of backward stochastic differential equation. Such a valuation may relax certain market limitations. Following this approach, the values of single decrement policies are studied and Thiele's-type PDEs for general life insurance contracts are derived.