The transversal homoclinic points are dense in the codimension-1 Hénon-like strange attractors

We consider the codimension-1 Hénon-like strange attractors . We prove that the transversal homoclinic points are dense in , and that hyperbolic periodic points are dense in . Moreover the hyperbolic periodic points that are heteroclinically related to the primary fixed point ( transversal intersection of stable and unstable manifolds) are dense in .

     

Foliations with a Kupka component on algebraic manifolds

We consider codimension one holomorphic foliations in complex projective manifolds of dimension at least 3, having a compact Kupka component and represented by integrable holomorphic sections of the bundleTM ^*L, whereL denotes a very ample holomorphic line bundle. We will show that, if the transversal type is not the radial vector field andH ¹ (M,) = 0, then the foliation has a meromorphic first integral.Supported by Conacyt: 3398-E 9307     

Covering arrays with mixed alphabet sizes

Covering arrays with mixed alphabet sizes, or simply mixed covering arrays, are natural generalizations of covering arrays that are motivated by applications in software and network testing. A (mixed) covering array A of type is a k × N array with the cells of row i filled with elements from ? and having the property that for every two rows i and j and every ordered pair of elements (e,f) ∈ ? × ?, there exists at least one column c, 1 ≤ c ≤ N, such that A_i,c = e and A_j,c = f. The (mixed) covering array number, denoted by , is the minimum N for which a covering array of type with N columns exists. In this paper, several constructions for mixed covering arrays are presented, and the mixed covering array numbers are determined for nearly all cases with k = 4 and for a number of cases with k = 5. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 413–432, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10059     

Hyperbolic sets,transversal homoclinic trajectories,and symbolic dynamics for C1-maps in banach spaces

In an earlier paper we generalized the notion of a hyperbolic set and proved that the Shadowing Lemma remains valid, for C¹-maps which need not be invertible. Here we establish the existence of (generalized) hyperbolic structures along transversal homoclinic trajectories of C¹-maps. The hyperbolic structure and shadowing are then used to give a new proof of a result due to Hale and Lin (and ilnikov) on symbolic dynamics forall trajectories sufficiently close to a transversal homoclinic trajectory. The result is applied to a Poincaré map without continuous inverse, which is associated with a periodic orbit of an autonomous differential delay equation.     

On the Weakly Nonlinear,Transversal Vibrations of a Conveyor Belt with a Low and Time-Varying Velocity

In this paper the weakly nonlinear, transversal vibrations of aconveyor belt will be considered. The belt is assumed to move witha low and time-varying speed. Using Kirchhoff's approach a singleequation of motion will be derived from a coupled system ofpartial differential equations describing the longitudinal andtransversal vibrations of the belt. A two time-scalesperturbation method is then applied to approximate the solutionsof the problem. It will turn out that the frequencies of the belt speed fluctuations play an important role in the dynamic behaviourof the belt. It is well-known in linear systems that instabilitiescan occur if the frequency of the belt speed fluctuations is thesum of two natural frequencies. However, in the weakly nonlinearcase as considered in this paper this is no longer true. It turns out that the weak nonlinearity stabilizes the system.     

Class‐uniformly resolvable designs

We investigate Class‐Uniformly Resolvable Designs, which are resolvable designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present two general constructions. We primarily consider the case of block sizes 2 and 3, where we find two infinite extremal families and finish two other infinite families by difference constructions. We present tables showing the current state of knowledge in the case of block size 2 and 3 for all orders up to 200. © 2001 John Wiley & Sons, Inc. J Combin Designs 8: 79–99, 2001     

Melnikov方法和圆型平面限制性三体问题的横截同宿研究*

本文对由两自由度近可积哈密顿系统经非正则变换而得到的,具有高阶不动点的非哈密顿系统给出了判别横截同宿轨和横截异宿轨存在性的两条判据。对原二体质量比很小时近可积圆型平面限制性三体问题,采用本文判据证明存在横截同宿轨,从而存在横截同宿穿插现象;还在一定假设下证明了存在横截异宿轨;并给出了全局定性相图。     

Energy transfer in double plate system dynamics

The study of energy transfer between coupled subsystems in a hybrid system is very important for applications. This paper presents an analytical analysis of energy transfer between plates of a visco-elastically connected double-plate system in free transversal vibrations. The analytical analysis shows that the visco-elastic connection between plates is responsible for the appearance of two-frequency regime in the time function, which corresponds to one eigen amplitude function of one mode, and also that time functions of different vibration modes are uncoupled, but energy transfer between plates in one eigen mode appears. It was shown for each shape of vibrations. Series of the two Lyapunov exponents corresponding to the one eigen amplitude mode are expressed by using the energy of the corresponding eigen amplitude time component.     

完全单半群及完全正则半群的逆断面

指出完全单半群Ｓ的任何一个Ｆ－类是逆断面,且为Ｑ－逆断面,而Ｓ的任何一个逆断面必是一个Ｆ－类,因而所有逆断面同构。并且给出完全正则半群的逆断面存在的充要条件。