某些曲面上有根近-4-正则欧拉迹的计数

In this article the rooted planar near-4-regular Eulerian trails are enumerated and an explicit formula for such maps is presented. Further, the rooted near-4-regular Eulerian maps on the torus are counted in an exact way.     

COUNTING FAIR NEAR-TRIANGULATIONS ON THE DISC

1IntroductionAp1anarmaPisrootedifauedgeandadirectionalongonesideofitaredistinguished;atriangulationissucharootedplanarmapwhosefaCesareall3-gons;anear-triangulationonthe8phereordiscisarootednonseparableplanarmapsuchthatallofitsfacesexceptpossiblytheroot-faCehavevalencythree.TheenumerationoftriangulationswasfitStintroducedbyTUtteinthebeginningofsixtiesIv9].Infact,thetopicsheworkedweremuchconcentratedonplanartriangularmapsforthesakeofattackingFourColorProblem.Manyelegantresultsrelatedtononsep…     

ENUMERATING ROOTED EULERIAN PLANAR MAPS

1 IntroductionSince Thtte's papers oll enunlerating planar InaPs in [7,8] published iu the beginlling Ofsixties, the enumerative theory has been developed greatly up to now. The enumeration ofgenera1 Eulerian planar maps is dependent on two paranleters as the valency of rooted vertexalld the uunther of edges Of the nmps. Y.P.Liu found tl1e functional equation firstly for thenlaPs aud then obtained the number of general rooted Elllerian planar maPs with the nuntherof edges given in 1989[1].…     

射影平面上不可分近三角剖分地图的计算

众所周知,由于本质圈(或不可收缩圈)的作用,使得一般的曲面上要得到带有两到三个参数的地图计算公式(尤其是显式公式)变得十分困难。该文集中讨论射影平面上不可分近三角剖分地图的计算。通过引入含有面次,边数和内部面数的参数表达式与Lagrangian反演,作者得到了含有正项系数的显式公式用以计算射影平面上三角剖分地图 。     

球面和射影平面上不可分地图的色和

给出了球面和射影平面上带根不可分地图的色和方程,从色和方程导出了球面和射影平面上带根一般不可分地图、二部地图的计数函数方程. 利用色和理论,研究不同类地图的计数问题,得到了一种研究计数问题的新方法. 此外,还得到了一些计数显示表达式.     

ENUMERATIONS OF ONE-VERTEX MAPS WITH FACE PARTITION ON THE PLANE

In addition to the known method given in [1],authors provide other three methods to the enumeration of one-vertex maps with face partition on the plane.Correspondingly,there are four functional equations in the enufuntion .It is shown that the four equations are equivalent.Moreover,an explicit expression of the solution is found by expanding the powers of the matrix of infinite order directly.This is a new complement of what appeared in [1].     

BISINGULAR MAPS ON SOME SURFACES

A map is bisingular if each edge is either a loop (This paper only considersplanar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies thenumber of rooted bisingular maps on the sphere and the torus, and also presents formulaefor such maps with three parameters: the root-valency, the number of isthmus, and thenumber of planar loops.     

THE NUMBER OF ROOTED NEARLY CUBIC C-NETS

1. IntroductionW.T. Tutte's original papers[1--3) on the enumerative theory of rooted planar maps havebrought forth a series of papers on enumerating triangulations. The enumeration of generalrooted planar maps has then also been investigated and a number of elegant results havebeen obtained, although relatively fewer than that of triangulations. As the dual case oftriangulations, the enumerative theory of cubic maps has also been developed, though thereare a lot of problems waiting for solut…     

Counting rooted near-4-regular Eulerian maps on some surfaces

In this article the rooted planar near-4-regular Eulerian trails are enumerated and an explicit formula for such maps is presented. Further, the rooted near-4-regular Eulerian maps on the torus are counted in an exact way.     

CYCLE SPACES OF GRAPHS ON THE SPHERE AND THE PROJECTIVE PLANE

Cycle base theory of a graph has been well studied in abstract mathematical field such matroid theory as Whitney and Tutte did and found many applications in pratical uses such as electric circuit theory and structure analysis, etc. In this paper graph embedding theory is used to investigate cycle base structures of a 2-(edge)-connected graph on the sphere and the projective plane and it is shown that short cycles do generate the cycle spaces in the case of ““““small face-embeddings““““. As applications the authors find the exact formulae for the minimum lengthes of cycle bases of some types of graphs and present several known results. Infinite examples shows that the conditions in their main results are best possible and there are many 3-connected planar graphs whose minimum cycle bases can not be determined by the planar formulae but may be located by re-embedding them into the projective plane.     

Enumerating near-4-regular maps on the sphere and the torus

In this paper rooted near-4-regular maps on the plane and the torus are counted with formulae with respect to four parameters: the root valency, the number of edges, the inner faces, and nonroot-vertex loops. In particular, the number of rooted near-4-regular maps on those surfaces with exactly k nonroot-vertex loops is investigated.     

(x)方程解的关于参数依赖性

本文作者研究拟凸域上的(x)-方程解关于参数的解析依赖性.     

AN EXPONENTIAL STABILITY PROBLEM ON THE SMALL DELAY LINEAR SYSTEM

1IntroductionLetXbea'Banachspace,andB(X)betheBanachspaceofcontinuouslinearoperatorsfromXintoX.LetT(t)bea(CO)selltigroup,andletAbeitsinfinitesilllalgenerator.WedenotethedomainandtherangeofAbyD(A)andR(A).LetBbelongtoB(X).FOrthelinearsystem:andthedelaylinearsystem:wherer>0,((.)EC([--.,o],x)={fif:[--r,oj~X,fiscontinuous},r(t)EC[o,.)'05r(t)5r.Weconsidertileexponentialstabilityequivalencebetweellthesolutionof(1)and(2),whichllleans:ifthereexistM,a>0,sllththatIIS(f)II5Me--"'(f20),whereS(…     

THE NAGUMO EQUATION ON SELF－SIMILAR FRACTAL SETS

The Nagumo equationut ut=△u+bu(u-a)(1-u),t＞0 is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the“pathological” property of the fractal. However, it is shown that a global Hoelder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl‘s formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.     

关于P4P问题解数的一些研究

本文研究了计算机视觉中P4P问题的多解问题,运用几何方法,分析了P4P问题的多解现象,获得了P4P问题存在5个解的必要条件.     

关于图的L(2,1)标号核图

图的L(2,1)标号核图来自频率分配问题而导致的图论问题.在本文中,我们证得(i)对任意简单图G,存在G的一个标号核图Gcore,使得L(G)=L(Gcore)和L(G)≥|V(Gcore)|-1;(ii)设图G有p个顶点且边集|E(G)|≠φ,存在路 Pi G(1≤i≤m)和路Hs G(1≤s≤n),其中在G中V(Pi)∩V(Pj)=φ(i≠j),在G中V(P,)∩V(Pt)=φ(s≠t),则有m∑t=1|V(Pt)|+n∑s=1|V(Hs)|-(m+n)≥p;(iii)G是p(p≥5)个顶点的简单图,则有p+3≤L(G)+L(G)≤3p-4.     

数值求解Euler方程的UCGVC差分格式的注记

１．引言 近年来高精度差分格式的研究引起国内外的普遍重视,目的是更准确地模拟复杂流场的流动．众所周知,传统的二阶ＴＶＤ类格式虽然能较好地捕捉激波,但却存在局部极值点降阶的问题,而且由于一些格式的数值粘性过大,当用该格式计算粘性流特别是高雷诺数问题时,格式本身的数值粘性可能掩盖了流场的物理粘性,从而降低了格式对边界层的分辨率,因而无法正确计算热流值。文献［３］指出,采用高精度格式可适当放松对网格雷诺数的要求,因此发展三阶或三阶以上的格式是需要的。近年来,人们已经发展了一些无伪振荡的高阶格式,如ＥＮ…     

曲面上图的拉普拉斯谱半径

本文研究了图嵌入到给定紧致曲面上的拉普拉斯谱半径,确定了将顶点数为n、最大度为△的图分别嵌入到亏格为g的定向曲面和亏格为h的不可定向曲面上的新上界.     

关于Je(s)manowicz猜想的一个注记

本文研究了Je(s)manowicz于1956年提出的关于丢番图方程(1.1)解的猜想.利用数论中的一些方法,得到了丢番图方程(1.2)的所有正整数解,证明了Je(s)manowicz猜想在这类情况下的正确性.