四边形的等积三角剖分

1970年Monsky证明了著名的Richman猜想: 正方形不能剖分成奇数个面积相等的三角形。近年来Stein等人研究一类特殊类型的四边形的等积三角剖分问题;获得了许多重要结果。该文进一步研究四边形等积三角剖分的待解决问题。      

关于适约三角剖分的计数

众所周知,适约三角剖分在地图运算中有着重要作用．本文对于平面上这种三角剖分的数目进行了探讨．同时,也提供了含有两个变量的精确公式．     

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．     

三角剖分上的仿射迭代函数系统分形插值曲面

对二维平面上三角形区域进行三角剖分,构造仿射变换,由二元分形插值函数引入第三维的值,构成迭代函数系统(IFS).利用此IFS构造了一类山状分形插值曲面.通过数值实验对比分析表明:它比人们以往用矩形剖分得出的分形图形效果更逼真,更接近于自然.     

关于二元样条空间下的三角剖分的分解

本文指出，在一定条件下，对于一个二元样条空间，所考虑的三种剖分中的某些胞腔和网线可以消去，而前后两个三角剖分下样条空间的结构有着紧密的联系，从而可以用简单划分下的空间结构表示复杂剖分下的空间结构。该分解剖分的步骤可以递推的进行，尤其对Ｓ＾１ｓ。据此，本文还分析了剖分对Ｓ＾１２的奇异性并给出一组奇异的剖分。     

关于4-连通三角剖分的计数

本文讨论4-连通极大平面地图的计数问题.从地图对偶的角度考虑,它等价 于强3-连通3-正则有根平面地图的计数问题.在此,我们获得了具有一个和两个变 量的精确计数公式.本文的结果简化并推广了文[1,2]中的相应结果.     

一类三角剖分下样条空间S13(Δ)维数

首次提出了一种判别样条空间S13(Δ)维数不依赖剖分几何性质的协调条件.依此,在一类较一般的三角剖分下,获得了S13(Δ)的维数.     

少圈二重覆盖平面近三角剖分图的生成元

令Ｇ为一具有ｎ个节点的平面近三角剖分图,Ｃ为Ｇ的一个少圈二重覆盖（ＳＣＤＣ）．本文首先给出了Ｇ的一些生成元,由此可以得到Ｇ的一个ＳＣＤＣ．若Ｇ为一外平面近三角剖分图,得到 ｜Ｃ｜≤ｎ－２的一充分必要条件;若 Ｇ至少有一个内点,得到｜Ｃ｜≤ｎ－２的一充分条件．     

一类三角剖分下样条空间S_3~1(Δ)维数

首次提出了一种判别样条空间S13(Δ)维数不依赖剖分几何性质的协调条件·　依此 ,在一类较一般的三角剖分下 ,获得了S13(Δ)的维数·     

完全图K19在可定向曲面的三角剖分嵌入数

首先由完全图K19的两种电流图满足KCL电流定律,建立线性方程组,利用计算机求出方程组的所有解,由一组解对应K18电流图的一种电流赋值方式,得到两种电流图的不同电流赋值方式数为34和6,然后求出K19两种电流图的基础图在可定向曲面上分别有16种不同的单面嵌入;由上面的结论得到完全图K19在可定向曲面上至少有640种不同...     

Continuous spectrum, point spectrum and residual spectrum of operator matrices

Let M_C denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?_C∈B(K,H)σ_r(M_C) are, respectively, characterized completely, where σ_c(·) denotes the continuous spectrum, σ_p(·) denotes the point spectrum and σ_r(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given.     

Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.     

Remarks on Q-integral complete multipartite graphs

A graph is Q-integral if the spectrum of its signless Laplacian matrix consists entirely of integers. In their study of Q-integral complete multipartite graphs, [Zhao et al., Q-integral complete r-partite graphs, Linear Algebra Appl. 438 (2013) 1067–1077] posed two questions on the existence of such graphs. We resolve these questions and present some further results characterizing particular classes of Q-integral complete multipartite graphs.     

Around the Proof of the Legendre–Cauchy Lemma on Convex Polygons

We briefly describe the history of the proofs of the well-known Cauchy lemma on comparison of the distances between the endpoints of two convex open polygons on a plane or sphere, present a rather analytical proof, and explain why the traditional constructions lead in general to inevitable appearance of nonstrictly convex open polygons. We also consider bendings one to the other of two isometric open or closed convex isometric polygons.     

Complete Surjections and Complete Epimorphisms over Completely Distributive Lattices

Generators and lattice properties of the poset of complete homomorphisic images of a completely distributive lattice are exploited via the localic methods. Some intrinsic and extrinsic conditions about this poset to be a completely distributive lattice are given. It is shown that the category of completely distributive lattices is co-well-powered,and complete epimorphisms on completely distributive lattice are not necessary to be surjections. Finally, some conditions about complete epimorphisms to be surjections are given.     

Several classes of complete permutation polynomials

In this paper, three classes of monomials and one class of trinomials over finite fields of even characteristic are proposed. They are proved to be complete permutation polynomials.