基于MC算法的螺旋CT扫描数据的三维重建

在Marching Cubes(MC)算法的基础上，针对螺旋CT扫描数据的特点，提出一种改进的三维表面的快速绘制方法。通过使用体元描述表，并且对体元数据进行二值化处理，简化了数据，在绘制过程中，根据形体拓扑结构，优化了体元内部的等值面形成算法，提高了三维重建的速度和质量。     

受约束非线性控制系统正则方程的可解性分析

讨论了受约束条件下的非线性控制系统，通过Taylor一阶展开，在每一失代步中将问题转化成线性约束控制问题，进一步通过变分原理，对一般情况建立了约束变量的正则方程，进而建立了约事变量的极值变分原理，由此进行了正则方程的可解性分析，结果表明，约束变量二次型的系数阵满足可逆且负定的条件下，控制系统正则方程存在可解性，这对非线性控制系统的处理具有很大意义。     

不规则图形面积的一种计算机求解方法

本文利用计算机的图形显示技术,将平面作为面积元——象素的拼合,提出涂色计算象素数求解区域面积的方法。采用该方法可以很容易地求解不规则平面图形的面积。通过上机对规则区域面积的求解测试,表明其结果和计算结果基本吻合。     

几何造型中的裁剪曲面

在深入研究裁剪曲面的基础上，本文引入３种关于裁剪曲面的规范化操作及相应的逆操作，并运用扩展的欧拉公式给予合理性验证，并进一步提出了构造裁剪曲面几何（ＣＴＳＧ）这一概念，探索边界表示向构造实体几何（ＣＳＧ）转换的新途径。     

拟正则映射和变分关系

研究了ｐ－调和方程在拟正则映射作用下的一种不变性,并对得到的Ａ型调和方程建立了局部梯度Ｌｐ可积性及解的Ｈｌｄｅｒ连续性     

A uniform refinement property for congruence lattices

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt's construction or from the approach of P. Pudlák, M. Tischendorf, and J. Tuma. In a previous paper, we constructed a distributive algebraic lattice with compact elements that cannot be obtained by Schmidt's construction. In this paper, we show that the same lattice cannot be obtained using the Pudlák, Tischendorf, Tuma approach.

The basic idea is that every congruence lattice arising from either method satisfies the Uniform Refinement Property, that is not satisfied by our example. This yields, in turn, corresponding negative results about congruence lattices of sectionally complemented lattices and two-sided ideals of von Neumann regular rings.

     

A Basis for the Top Homology of a Generalized Partition Lattice

For a fixed positive integer k, consider the collection of all affine hyperplanes in n-space given by xi – xj = m, where i, j [n], i j, and m {0, 1,..., k}. Let Ln,k be the set of all nonempty affine subspaces (including the empty space) which can be obtained by intersecting some subset of these affine hyperplanes. Now give Ln,k a lattice structure by ordering its elements by reverse inclusion. The symmetric group Gn acts naturally on Ln,k by permuting the coordinates of the space, and this action extends to an action on the top homology of Ln,k. It is easy to show by computing the character of this action that the top homology is isomorphic as an Gn-module to a direct sum of copies of the regular representation, CGn. In this paper, we construct an explicit basis for the top homology of Ln,k, where the basis elements are indexed by all labelled, rooted, (k + 1)-ary trees on n-vertices in which the root has no 0-child. This construction gives an explicit Gn-equivariant isomorphism between the top homology of Ln,k and a direct sum of copies of CGn.     

广义正则半群 广义逆半群

推广正则半群，逆半群为广义正则半群，广义逆半群，并得到相应的结果。     

A Classification of Regular Embeddings of Graphs of Order a Product of Two Primes

In this paper, we classify the regular embeddings of arc-transitive simple graphs of order pq for any two primes p and q (not necessarily distinct) into orientable surfaces. Our classification is obtained by direct analysis of the structure of arc-regular subgroups (with cyclic vertex-stabilizers) of the automorphism groups of such graphs. This work is independent of the classification of primitive permutation groups of degree p or degree pq for p q and it is also independent of the classification of the arc-transitive graphs of order pq for p q.