Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions

Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are studied. By establishing a local coordinate system and a Poincaré map near the homoclinic orbit, the existence and uniqueness of 1–homoclinic orbit and 1–periodic orbit are given. Also considered is the existence of 2–homoclinic orbit and 2–periodic orbit. In additon, the corresponding bifurcation surfaces are given. Project supported by the National Natural Science Foundation of China (No: 10171044), the Natural Science Foundation of Jiangsu Province (No: BK2001024), the Foundation for University Key Teachers of the Ministry of Education of China     

Measure equivalence rigidity and bi-exactness of groups

We get three types of results on measurable group theory; direct product groups of Ozawa's class S groups, wreath product groups and amalgamated free products. We prove measure equivalence factorization results on direct product groups of Ozawa's class S groups. As consequences, Monod-Shalom type orbit equivalence rigidity theorems follow. We prove that if two wreath product groups A?G, B?Γ of non-amenable exact direct product groups G, Γ with amenable bases A, B are measure equivalent, then G and Γ are measure equivalent. We get Bass-Serre rigidity results on amalgamated free products of non-amenable exact direct product groups.     

Self-dual codes from orbit matrices and quotient matrices of combinatorial designs

In this paper we give constructions of self-orthogonal and self-dual codes, with respect to certain scalar products, with the help of orbit matrices of block designs and quotient matrices of symmetric (group) divisible designs (SGDDs) with the dual property. First we describe constructions from block designs and their extended orbit matrices, where the orbit matrices are induced by the action of an automorphism group of the design. Further, we give some further constructions of self-dual codes from symmetric block designs and their orbit matrices. Moreover, in a similar way as for symmetric designs, we give constructions of self-dual codes from SGDDs with the dual property and their quotient matrices.     

一种新的永久周期磁铁聚焦的高功率宽带放大器

提出了一种新的高功率宽带放大器，它由速调管和自由电子脉塞组成，用永久周期磁铁聚焦。研究了这种器件的电子束聚焦、群聚和辐射。在速调管提供一阶调制系数为30%，波导管的半径1.51cm，摇摆器的磁场振幅0.16T，周期7.92cm，电子束的电压490kV，电流50A和半径0.368cm的条件下，预估这种器件的辐射波频率为11.4GHz，输出辐射功率为18MW，输出辐射带宽为44%。     

GNSS天线连接器同轴度误差测量技术

为测量GNSS天线连接器同轴度误差,构建了连接器分段旋转数学模型,提出了一种水平转台和机器视觉结合的非接触式测量方法,搭建测量装置并进行了测量实验.分析连接器运动方式和同轴度误差测量方法,确定各轴线之间的偏移关系,建立同轴度误差数学模型和测量模型.搭建测量装置,相机安装在水平转台上方,光轴平行于水平转台轴线.旋转水平转台,使用相机捕捉转接螺杆端面圆心位置并拟合轨迹,完成测量装置同轴度误差自标定.将连接器安置在水平转台上,旋转水平转台,测量连接器顶部螺纹杆轴线相对水平转台轴线的偏移.旋转连接器的承载器,测量连接器顶部螺纹杆轴线相对承载器轴线的偏移.最终,综合各轴线的偏移关系得到连接器同轴度误差的最大值.实验结果表明,测量装置对GNSS天线连接器同轴度误差的测量标准差为9μm,单次测量结果的扩展不确定度U=30μm(k=2),满足GNSS天线连接器0.1 mm至1 mm量级的同轴度误差的测量需求,使用连接器同轴度误差修正GNSS超短基线测量结果,可以显著提升基线测量精度.     

Transitivity and Chaos

Several different definitions of transitivity and their relationship are carefullydiscussed for general spaces, and it is proved that a continuous map on a metric space ischaotic in the sense of Devaney if and only if it is periodic orbit transitive or periodic orbitstrongly transitive.     

目标拦截的导引方法与仿真模拟

本文对目标拦截的导引方法进行了研究和模拟，是项目“军事指挥实时动态真实感模拟系统ＲＤＭＳＳ”的目标拦截模拟部分，主要内容是：对导弹的导引弹道进行了分析和模拟，并提出用样条预测的新方法进行目标导引；给出了模拟爆炸和火焰喷射的简易方法；最后在ＳＧＩ／Ｉｎｄｉｇｏ２上实现了一个简单的仿真模拟系统，对飞机的飞行、导弹及反导弹的发射和拦截过程作了成功的模拟，取得了良好的效果．     

Some small unipotent representations of indefinite orthogonal groups

We study a family of small unitary representations of indefinite orthogonal groups. These representations arise as analytic continuations of the discrete series and were studied extensively by Knapp in [K3]. We complete Knapp's analysis by proving that they are irreducible. In order to do so we prove that the representations are unipotent and have irreducible associated cycles in which all multiplicities are exactly one. Moreover, we prove that the K-type structure of each representation matches (up to a shift) the K-type structure of the ring of functions on the closure a nilpotent orbit on .     

On the edge-connectivity of graphs with two orbits of the same size

It is well known that the edge-connectivity of a simple, connected, vertex-transitive graph attains its regular degree. It is then natural to consider the relationship between the graph’s edge-connectivity and the number of orbits of its automorphism group. In this paper, we discuss the edge connectedness of graphs with two orbits of the same size, and characterize when these double-orbit graphs are maximally edge connected and super-edge-connected. We also obtain a sufficient condition for some double-orbit graphs to be λ^′-optimal. Furthermore, by applying our results we obtain some results on vertex/edge-transitive bipartite graphs, mixed Cayley graphs and half vertex-transitive graphs.     

Slice theorem and orbit type stratification in infinite dimensions

We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which the assumptions of this theorem are fulfilled. First, using Glöckner's inverse function theorem, we show that the linear action of a compact Lie group on a Fréchet space admits a slice. Second, using the Nash–Moser theorem, we establish a slice theorem for the tame action of a tame Fréchet Lie group on a tame Fréchet manifold. For this purpose, we develop the concept of a graded Riemannian metric, which allows the construction of a path-length metric compatible with the manifold topology and of a local addition. Finally, generalizing a classical result in finite dimensions, we prove that the existence of a slice implies that the decomposition of the manifold into orbit types of the group action is a stratification.