VORONOI POLYHEDRA OF UNIT BALL PACKINGS WITH SMALL SURFACE AREA

In this note, first, we give a very short new proof of the theorem which yields a lower bound for the surface area of Voronoi cells of unit ball packings in E ^d and implies Rogers' upper bound for the density of unit ball packings in E ^d for all d ≥ 2. Second we sharpen locally a classical result of Gauss by finding the locally smallest surface area Voronoi cells of lattice unit ball packings in E ³. This revised version was published online in August 2006 with corrections to the Cover Date.     

ON THE CONVERGENCE OF CIRCLE PACKINGS TO THE QUASICONFORMAL MAP

Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.     

REALIZATION OF PEETRE K-MODULUS ON THE SPHERE

1IntroductionandNotationsLetfi={p=(x,yiz)ER3,IPI=1}betheunitsphereintheEuclideanspaceR3.ByC(O)andLP(O),1SP相似文献   

关于单位圆内代数体函数的聚值点

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ON THE GROWTH OF THE SOLUTIONS FOR 1ST KIND OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN THE UNIT DISC

In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order.     

模恒为1的并非常值的向量值解析函数

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关于球面上的一种Hermite插值

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ON THE MINIMUM COVERING NUMBER FORMULA OF GRAPHS

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关于Rn中实单位球上M-调和BMO函数的Carleson测度特征

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一类循环码的极小距离

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关于球面上的Lagrange插值

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THE DISTRIBUTION OF LATTICE POINTS IN ELLIPTIC ANNULI

We study the distribution of the number of lattice points lyingin thin elliptical annuli. It has been conjectured by Bleherand Lebowitz that if the width of the annuli tends to zero andtheir area tends to infinity, then the distribution of thisnumber, normalized to have zero mean and unit variance, is Gaussian.This has been proved by Hughes and Rudnick for circular annuliwhose width shrinks to zero sufficiently slowly. We prove thisconjecture for ellipses whose aspect ratio is transcendentaland strongly Diophantine, also assuming the width shrinks slowlyto zero.     

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.     

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