The number of powers of 2 in a representation of large even integers II

It is proved that for any integerk≥ 54 000, there isN _k >0 depending onk only such that every even integer ≥N _k is a sum of two odd prime numbers andk powers of 2. Project partially supported by RGC Research Grant (No.HKU 7122/97P) and Post-Doctoral Fellowship of the University of Hong Kong.     

滚动实验的另一种演示

介绍了另一种滚动演示实验,并对演示结果进行了理论分析和解释     

中国邮路问题的一个解法

本给出中国邮路问题的一个解法。虽然它仍只是初始方案，但因考虑了问题的足够信息，因而这种方案至少拉近了与最优解的距离。     

GENERALIZED CIRCLES AND THEIR CONFORMAL MAPPING IN A SUBSPACE OF A WEYL SPACE

The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation oil its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat.     

无滑动滚动时的摩擦力

通过一个演示实验 ,分析论证了纯滚动刚体所受摩擦力为静摩擦力 ,静摩擦力与物体的运动状态有关 ,与接触面性质无关 .     

Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.     

Orbifold fibrations of Eschenburg spaces

Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two points.      

A study of type I intermittency of a circular differential equation under a discontinuous right-hand side

In this paper we study a circular differential equation under a discontinuous periodic input, developing a quadratic differential equations system on S¹ and a linear differential equations system in the Minkowski space M³. The symmetry groups of these two systems are, respectively, PSOo(2,1) and SOo(2,1). The Poincaré circle map is constructed exactly, and a critical value αc of the parameter is identified. Depending on α of the input amplitude the equation may exhibit periodic, subharmonic or quasiperiodic motions. When α varies from α>αc to α<αc, there undergoes an inverse tangent bifurcation; consequently, the resultant Poincaré circle map offers one route to the quasiperiodicity via a type I intermittency. In the parameter range of α<αc the orbit generated by the Poincaré circle map is either m-periodic or quasiperiodic when n/m is a rational or an irrational number.     

复制缺陷型人泡沫病毒载体辅助质粒pΔGP的构建及转染小肠癌细胞的研究

在人泡沫病毒原病毒全长克隆pHRSV13的基础上,缺失突变gag和pol基因,并且用SV40polyA加尾信号替代人泡沫病毒的3′LTR,构建辅助质粒pΔGP.将复制缺陷型人泡沫病毒载体质粒pGPSNI EGFP和辅助质粒pΔGP分别转染和共转染小肠癌HIC细胞系,荧光显微镜检测发现共转染pGPSNI EGFP和pΔGP的HIC细胞能够强烈表达绿色荧光蛋白,转染有复制缺陷型人泡沫病毒载体质粒pGPSNI EGFP的HIC细胞能够表达少量的绿色荧光蛋白,而转染有辅助载体pΔGP的HIC细胞不表达绿色荧光.结果证明复制缺陷型人泡沫病毒载体的构建成功,表明人泡沫病毒env基因3′端的内部启动子IP具有弱启动子的活性,并且bel基因产生的调控蛋白能够反式激活人泡沫病毒内部启动子IP和5′LTR的启动子.     

用参考圆法演示简谐振动

对受迫振动仪进行了改进，通过参考圆法，演示了作镁速圆周运动的质点在直径方向上的投影所作的运动为简谐振动。