|
|
|
本科论文获奖者注意：所有的获奖者都必须出席2010年的颁奖典礼，颁奖典礼的时间暂定为2010年12月17日。金奖 (2项，排名不分先后) 姓名: Lam Ka Kit 论文题目: Achieving Capacity of Network 毕业学校: 香港中文大学 论文摘要: In any communication network, we always want to find ways to transmit information to maximize the throughput and have no errors. However, if the network is huge and complex, with many sources and receivers, such a problem will become nontrivial. One way to approach it is to employ coding in the intermediate nodes inside the network. And in our project, the achievability of capacity was investigated with an emphasis on designing non-Abelian group codes. Matroidal networks and properties of non-Abelian group codes were studied. Moreover, some decidability network problems about achieving capacity were also studied. 姓名: 赵亮 题目: 函数域上超几何函数的超越性 毕业学校: 清华大学 论文摘要: 本文利用J-Y. Yao所证明的超越性判别法,研究了在有限域的函数域上超几 何函数的超越性, 本文主要论证了以下两个结论: 1、当超几何函数中位于分子部分的参数个数严格少于位于分母部分的参数个数 时，若自变量取非零有理分式，则函数值在函数域上超越。 2、当超几何函数中位于分子部分的参数个数等于位于分母部分的参数个数时， 在某些情况下函数值在函数域上代数。 银奖(4项，排名不分先后) 姓名: 曹翔宇 论文题目: Mobius transform, moment-angle complexes and Halperin-Carlsson conjecture 毕业学校:复旦大学 论文摘要: In this paper, we give an algebra-combinatorics formula of the M\"obius transform for an abstract simplicial complex $K$ on $[m]=\{1, ..., m\}$ in terms of the Betti numbers of the Stanley-Reisner face ring of $K$. Furthermore, we employ a way of compressing $K$ to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex $\mathcal{Z}_K$ (resp. real moment-angle complex ${\Bbb R}\mathcal{Z}_K$) of $K$, we show that the Halperin-Carlsson conjecture holds for $\mathcal{Z}_K$ (resp. ${\Bbb R}\mathcal{Z}_K$) under the restriction of the natural $T^m$-action on $\mathcal{Z}_K$ (resp. $({\Bbb Z}_2)^m$-action on ${\Bbb R}\mathcal{Z}_K$).
姓名: 李超 论文题目: 计算机代数系统的数学原理 毕业学校: 清华大学 论文摘要: 本文主要讨论计算机代数系统的数学原理，由十六个章节组成. 内容包含高精度运算, 数论, 数学常数, 精确线性代数, 多项式, 方程求解, 符号求和, 符号积分, 微分方程符号解等九大部分, 涵盖了构建计算机代数系统的最基础也是最重要的内容. 许多内容是第一次被系统地整理出现在中文文献中, 一些领域也追踪到了最新进展.
姓名: 时代 论文题目: 定态薛定谔方程特征值个数的估计 毕业学校:复旦大学 论文摘要:本文给出了薛定谔方程特征值个数的估计式. 分别就一维定态, 中心势场, 广义函数势三个情形进行讨论. 相较Bargmann, Calogero等人的估计, 本文的结论在势函数u(x) 在无穷远处较慢速收敛时仍能给出有限估计, 这是他们办不到的. 本文还就Calogero估计式进行了推广, 使之不仅仅局限于单调函数. 针对某些例子, 还把本文结论和先前进行了比较. 最后, 本文还就现今物理上较热门的广义函数势情形估计了薛定谔方程特征值的个数.
姓名: Chao Xu 论文: 双曲Kahler-Ricci 流 毕业学校: 浙江大学 论文摘要: In this paper, I consider the hyperbolic Kaehler-Ricci flow introduced by Kong and Liu, that is, the hyperbolic version of the famous Kaehler-Ricci floow.. I explain the derivation of the equation and calculate the evolutions of various quantities associated to the equation including the curvatures. Particularly on Calabi-Yau manifolds, the equation can be simplified to a scalar hyperbolic Monge-Ampere equation which is just the hyperbolic version of the corresponding one in Kaehler-Ricciflow.. I briefly study its symmetries on Riemann surfaces and the symmetry theory of PDE is sketched in the appendix.
|
|