环面上近三角剖分地图的计数

本文提供了环面上带边数和根面次这两个参数的有根近三角剖分的函数方程及其参数表达式，并给出了根面次为1以边数为参数的有根近三角剖分地图的精确解．     

Structure of Lorentzian tori with a killing vector field

All Lorentzian tori with a non-discrete group of isometries are characterized and explicitly obtained. They can lie into three cases: (a) flat, (b) conformally flat but non-flat, and (c) geodesically incomplete. A detailed study of many of their properties (including results on the logical dependence of the three kinds of causal completeness, on geodesic connectedness and on prescribed curvature) is carried out. The incomplete case is specially analyzed, and several known examples and results in the literature are generalized from a unified point of view.

     

四维代数环群上无固定点的有理自同构群

本文解决K.Tahara提出的猜想,给出了所有四维代数环群上全部无固定点的有理自同构群.     

球环位形磁流体平衡的数值模拟

对原有的托卡马克平衡编码SWEQU进行了改进。使之适用于小环径比球形环装置的磁流体研究。用改进后的平衡编码SWEQU模拟了放电初始阶段等离子体平衡位形的演化及稳态阶段的双零偏滤器平衡位形。结果表明。不但町以得到球形环装置稳态阶段的平衡位形，也可以模拟等离子体电流上升阶段平衡位形的演化过程。     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.``     

Number of theoretical plates achievable by a toroidal capillary electrophoresis system

The ability of a method and instrument to separate very similar compounds is related to the “plate number,” a number indicating performance. The resolution between two neighboring peaks is proportional to the square root of the plate number. Currently available commercial capillary electrophoresis instruments easily reach plate numbers of a few million. In the present work, a capillary electrophoresis system with a toroidal platform is proposed and theoretically studied with the goal of extending the achievable plate number. In this new system, electrophoresis occurs in a nonstop continuous circulating mode within a closed loop capillary (toroid). Plate numbers upwards of one billion are theoretically predicted. This could resolve hundreds of unseparated mixtures of stereoisomers and other analytes that remain without a method for their analysis.     

Surfaces with high contact number and their characterization

The notion of contact number of a Euclidean submanifold was introduced in an earlier article (Proc. Edinb. Math. Soc. 47:69–100, 2004) as the highest order of contact of geodesics and normal sections on the submanifold. It was proved in (Proc. Edinb. Math. Soc. 47:69–100, 2004) that the contact number relates closely with the notions of isotropic submanifolds and holomorphic curves. One important problem concerning contact number is to construct Euclidean submanifolds with high contact number. The purpose of this article is thus to construct Euclidean surfaces with high contact number and to provide simple geometric characterization of such surfaces. Mathematics Subject Classification (2000) Primary 53C40, 53A10 Secondary 53B25, 53C42     

Stably and almost complex structures on bounded flag manifolds

We study the enumeration problem of stably complex structures on bounded flag manifolds arising from omniorientations, and determine those induced by almost complex structures. We also enumerate the stably complex structures on these manifolds which bound, therefore representing zero in the complex cobordism ring .

     

On complex and noncommutative tori

The ``noncommutative geometry' of complex algebraic curves is studied. As a first step, we clarify a morphism between elliptic curves, or complex tori, and -algebras , or noncommutative tori. The main result says that under the morphism, isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra of Riemann surfaces.