Nther-type theorem of piecewise algebraic curves on triangulation

The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space.In this paper,using the properties of bivariate splines,the Nther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.     

Geometric graphs which are 1-skeletons of unstacked triangulated polygons

We give sufficient (and necessary) conditions of local character ensuring that a geometric graph is the 1-skeleton of an unstacked triangulation of a simple polygon.     

Coloring-flow duality of embedded graphs

Let be a directed graph embedded in a surface. A map is a tension if for every circuit , the sum of on the forward edges of is equal to the sum of on the backward edges of . If this condition is satisfied for every circuit of which is a contractible curve in the surface, then is a local tension. If holds for every , we say that is a (local) -tension. We define the circular chromatic number and the local circular chromatic number of by and , respectively. The invariant is a refinement of the usual chromatic number, whereas is closely related to Tutte's flow index and Bouchet's biflow index of the surface dual .

From the definitions we have . The main result of this paper is a far-reaching generalization of Tutte's coloring-flow duality in planar graphs. It is proved that for every surface and every 0$">, there exists an integer so that holds for every graph embedded in with edge-width at least , where the edge-width is the length of a shortest noncontractible circuit in .

In 1996, Youngs discovered that every quadrangulation of the projective plane has chromatic number 2 or 4, but never 3. As an application of the main result we show that such `bimodal' behavior can be observed in , and thus in for two generic classes of embedded graphs: those that are triangulations and those whose face boundaries all have even length. In particular, if is embedded in some surface with large edge-width and all its faces have even length , then . Similarly, if is a triangulation with large edge-width, then . It is also shown that there exist Eulerian triangulations of arbitrarily large edge-width on nonorientable surfaces whose circular chromatic number is equal to 5.

     

Colorability of Planar Graphs with Isolated Nontriangular Faces

By a hole graph we mean a 2-connected planar graph where no two nontriangular faces have a vertex in common. We give necessary and sufficient conditions for a hole graph to be 3-colorable.Acknowledgments. This paper was prepared in framework of the exchange program between the Austrian and Slovak Academies of Sciences. The third author was active at Department of Mathematics, Vanderbilt University and Fakulta prírodných vied, ilinská univerzita v iline.Mathematics Subject Classification (1991): 05C15     

Bounding edge degrees in triangulated -manifolds

In this note we prove that every closed orientable -manifold has a triangulation in which each edge has degree , or .

     

激光同步扫描三角测距成像系统的理论分析

本文介绍了激光同步扫描三角测距成像系统的基本原理和特点,从理论上推出了一般意义的轨迹圆方程,并得出系统所能测量的最大和最小范围,确定了横向测量范围、系统景深、系统分辨率等系统性能与系统参数的关系。在分析系统参数对分辨率和系统测量范围的影响后,本文给出了一些系统设计的建议。     

光刀中心自适应阈值提取法

在讨论了常用的各种光刀中心提取法的基础上,提出了一种光刀中心自知应阈值提取法。该方法结合了极值法、阈值法和重心法,避开了它们各自的缺点,消除了噪声,从而实现了光刀中心的精确定位。该方法具有稳定性好、精度高、速度快等特点。     

A method for computing curved meshes via the linear elasticity analogy,application to fluid dynamics problems

We propose and analyze an algorithm for the robust construction of curved meshes in two and three dimensions. The meshes are made of curved simplexes. The algorithm starts from a mesh made of straight simplexes, and using a linear elasticity analogy applied on well‐chosen data, one can generate a curved mesh. Note that if the initial mesh has a boundary layer, this method allows to conserve it on the final mesh. This algorithm is used on several airfoils in two and three dimensions, including a turbulent M6 wing. Copyright © 2014 John Wiley & Sons, Ltd.