三次系统指标为正的奇点个数

本文证明了平面动力体系ｄｘ／ｄｔ＝Ｐｎ（ｘ，ｙ），ｄｙ／ｄｔ＝Ｑ２（ｘ，ｙ） （ｎ≥２）的有限远奇点中指标为正的 个数最多有（ｎ＋１）个，而系统ｄｘ／ｄｔ＝Ｐｎ（ｘ，ｙ），ｄｙ／ｄｔ＝Ｑ３（ｘ，ｙ） （ｎ≥３）的有限远奇点中指标为正的 个数最多不超过（３ｎ＋１）／２ ＋２个（ｎ≥３为奇数）或不超过 （ｎ为偶数）．进而得出系统Ｅ３：ｄｘ／ｄｔ＝Ｐ３（ｘ，ｙ），ｄｙ／ｄｔ＝Ｑ３（ｘ，ｙ） 的有限远奇点中指标为正的个数最多不超过７个．     

Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

开关布局中本质不同的开关线路计算

通过对开关布局问题的研究，来解决一类象开关线路一样比较特殊，比较复杂的布局优化问题。从而寻找出这类问题的全局优化算法。本应用对称群对集合的作用，轨道，不动点等讨论了开关布局问题，给出了本质不同的开关线路个数的计算公式。     

Vojta's Main Conjecture for blowup surfaces

In this paper, we prove Vojta's Main Conjecture for split blowups of products of certain elliptic curves with themselves. We then deduce from the conjecture bounds on the average number of rational points lying on curves on these surfaces, and expound upon this connection for abelian surfaces and rational surfaces.

     

Identifying Linking-Pin Organizations in Inter-Organizational Networks

Within the large literature on inter-organizational networks, there has been some discussion of linking-pin organizations and the role they play in integrating these networks. Based on this verbal specification of linking-pin organizations, we construct operational criteria and empirical methods for identifying these structurally important organizations in potentially large and complex inter-organizational networks. These methods are based on ideas drawn from blockmodeling, structural holes, centrality and centralization of networks, and identifying cut-points in networks. These methods are applied to a constructed example and then to real empirical inter-organizational networks. Implications and contrasts with other methods are discussed, together with some open problems.     

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.     

Dirac on Gauges and Constraints

We examine the relevance of Dirac's view on the use of transformation theory and invariants in modern physics to current reflections on the meaning of physical symmetries, especially gauge symmetries.     

Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Peritectic phase growth in directionally solidified Cu-70% Sn alloy

The growth mechanism of the peritectic η phase involving the peritectic reaction and peritectic transformation in Cu-70%Sn alloy was investigated under directional solidification. The results show that a major growth mechanism in thickening of the peritectic η-layer is not the peritectic reaction but the peritectic transformation. The transformation temperature and isothermal time play crucial roles in determining the volume fraction and the thickness of the peritectic η phase. With the increase of the temperature and isothermal time, the volume fraction of the peritectic η phase increases. The regressed data show that the relationship between the thickness of η phase (Δx) and the transformation temperature (T) meets the following equation In Δx=6.5−1673 1 / T. Additionally, there exists a relationship between the thickness of the η phase (Δx) and the isothermal time (t) at the 9 mm solidification distance below the peritectic reaction interface, Δx=0.72t ^1/2, which is consistent with the theoretical model. Supported by the National Science Foundation of China (Grant No. 50395102)