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Circle Packing相关研究取得进展
圆相切 欧氏圆 二维拟共形映射 Teichmuller 空间理论
2021/9/15
二十多年前，W. Thurston（菲尔兹奖得主），D. Sullivan（Wolf奖得主）等著名数学家引进了Circle Packing理论，它是复分析中复解析函数的一种离散表示，从而可以由计算机具体实现一个具体的解析函数，现在Circle Packing理论是复分析研究中一种非常重要的工具，在复解析动力系统、Kleinian群、双曲几何、计算机图形学等数学分支的研究中扮演着十分重要的角色。这些...
Packing ellipsoids with overlap
ellipsoid packing, trust-region algorithm, semide nite programming, chromosome territories
2012/4/17
The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulatio...
Abstract: Let $S$ be a set of $n$ points in the unit square $[0,1]^2$, one of which is the origin. We construct $n$ pairwise interior-disjoint axis-aligned empty rectangles such that the lower left co...
Abstract: Generalized $t$-designs, which form a common generalization of objects such as $t$-designs, resolvable designs and orthogonal arrays, were defined by Cameron [P.J. Cameron, A generalisation ...
Lagrangian blow-ups, blow-downs, and applications to real packing
Lagrangian blow-ups blow-downs applications real packing
2011/1/18
Given a symplectic manifold (M; !) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L.
Tuza conjectured that for every graph G, the maximum size of a set of edge-disjoint triangles and minimum size of a set of edges meeting all triangles, satisfy 2.
Hausdorff and packing dimensions of the images of random fields
Hausdorff packing dimensions the images of random fields
2010/11/24
Let $X=\{X(t),t\in\mathbb{R}^N\}$ be a random field with values in $\mathbb{R}^d$. For any finite Borel measure $\mu$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of t...
Edge-Colouring Hypergraphs Properly (Covering with Matchings) or Polychromatically (Packing Covers)
Edge-Colouring Hypergraphs Properly Polychromatically
2010/12/15
Let the chromatic index of a hypergraph be the smallest number of colours needed to colour the
edges such that similarly-coloured edges are disjoint. Likewise, let the cover index be the maximum numb...
Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut is at least k, then G contains k edge-disj...
The densest local packings of N three-dimensional identical nonoverlapping spheres within a
radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1...
Dense graphs with a large triangle cover have a large triangle packing
Dense graphs with large triangle cover large triangle packing
2010/11/29
It is well known that a graph with m edges can be made triangle-free by removing (slightly less
than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make
triangle-f...
A Simple Proof of Thue's Theorem on Circle Packing
Simple Proof Thue's Theorem Circle Packing
2010/12/10
Thue's theorem states that the regular hexagonal packing is the densest circle packing in the plane. The density of this circle con guration is p12 0:906 90:
Multiplying Pessimistic Estimators:Deterministic Approximation of Max TSP and Maximum Triangle Packing
derandomization approximation algorithms pessimistic estimators maximum traveling salesman problem
2012/12/3
We give a generalization of the method of pessimistic estimators, in which we compose estimators by multiplying them. We give conditions on the pessimistic estimators of two expectations, under which ...
对于六边形组合结构的circle packing, Rodin (1987年)证明了一个类似于解析函数的Schwarz引理. 本文中, 对于一般组合结构的circle packing, 我们证明了同样的Schwarz引理, 而且, 我们的方法比Rodin的方法更为简单. 同时, 我们得到了关于一般组合结构的circle packing的一个刚性性质.