不变的赋值函数与Cauchy投影公式(英文)

本文研究了Rn中凸集上不变的赋值函数与凸体的投影问题.利用赋值函数的方法,我们获得了凸体在任意维平面上投影的Cauchy公式和Kubota公式,这些结果推广了经典的Cauchy公式和Kubota公式.     

一类特殊网格的几何概率

本文研究了以正六边形和菱形为基本区域的复合网格中的Buffon 问题. 利用积分几何理论和运动测度工具, 获得了上述复合网格与长针相交的概率表达式, 推广了长针与复合网格相交的概率问题.     

一类特殊网格的几何概率

本文研究了以正六边形和菱形为基本区域的复合网格中的Buffon问题.利用积分几何理论和运动测度工具,获得了上述复合网格与长针相交的概率表达式,推广了长针与复合网格相交的概率问题.     

几何概型测度的类型及应用

几何概型是一种特殊的随机事件概率模型,是概率问题的几何形式．求解此类问题时可把每个基本事件理解为从某个特定的可度量的几何区域D内随机取一点,区域D内的每一点被取到的可能性大小相同,即点在区域D内是均匀分布的;     

几何概型测度的类型及应用

几何概型是一种特殊的随机事件概率模型,是概率问题的几何形式.求解此类问题时可把每个基本事件理解为从某个特定的可度量的几何区域D内随机取一点,区域D内的每一点被取到的可能性大小相同,即点在区域D内是均匀分布的;     

利用不变测度消除Bertrand奇论

通过不变测度的引入,消除了Bertrand奇论.     

平移积分几何中的对偶运动公式

本文利用对偶混合体积建立平移积分几何中的对偶运动公式.这些公式是将关于均质积分的基本运动公式推广到对偶均质积分和对偶混合体积情形.     

乘积空间上 Carleson 测度的一点注记及其应用

本文通过对 Carleson 测度的进一步研究,讨论了极大函数及平方函数之分布函数不等式,进而给出了 Str(o|¨)mberg H_φ 空间的极大函数及平方函数特征.新方法的优点在于它不依赖于欧氏空间的平移及伸缩结构,可用于某些一般情形.     

Rn中线性子空间束与凸体相交的几何概率

利用超曲面的平均曲率积分的概念及性质给出Rn中三个与凸体K相交的线性子空间彼此在K内相交的几何概率,并重点讨论超平面束的情形.在此基础上给出超平面束分别与特殊凸体:球体、正方体以及长方体相交时的几何概率,并讨论这些概率序列的单调性、收敛性以及大小关系.     

Lebesgue积分几何意义的推广

证明了非负有界函数的Lebesgue上积分等于函数下方图形的Lebesgue外测度,其Lebesgue下积分等于函数下方图形的Lebesgue内测度,从而将积分的几何意义从可测情形推广到一般情形.     

Harmonic Calculus on Fractals - A Measure Geometric Approach I

Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights.     

关于Alexander猜想的几何不等式

本文获得了一类关于度量如单形的体积和外接超球半径的几何不等式,作为其应用,给出了一些重要的推论。     

On the Orthogonality of Geometric Codes

We solve some problems concerning the orthogonality of geometric codes associated with sets of i- and j-dimensional subspaces of PG(n, q). Various applications are found, and we discuss all the interesting cases in small dimensional spaces.     

On Variational Measures Related to Some Bases

We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.     

The Spectrum of a Random Geometric Graph is Concentrated

Consider n points, x ₁,... , x _n , distributed uniformly in [0, 1] ^d . Form a graph by connecting two points x _i and x _j if . This gives a random geometric graph, , which is connected for appropriate r(n). We show that the spectral measure of the transition matrix of the simple random walk on is concentrated, and in fact converges to that of the graph on the deterministic grid.      

Measures of Association for Hilbertian Subspaces and Some Applications

Measures of association are introduced for Hilbertian subspaces, that are defined by a few axioms and are shown to be symmetric nondecreasing functions of the canonical coefficients. When particular subspaces are considered, classical measures of association are obtained as particular cases. Moreover, the proposed framework allows one to introduce new approaches for measuring partial noncorrelation, partial independence and linear predictability of a stationary process.     

一个几何不等式的一般形式

文 [1 ]建立了关于 n维单形的棱长、体积与外接球半径的一个不等式 ,本文给出了这一结论的一般形式     

On Geometric Graph Ramsey Numbers

For any two-colouring of the segments determined by 3n − 3 points in general position in the plane, either the first colour class contains a triangle, or there is a noncrossing cycle of length n in the second colour class, and this result is tight. We also give a series of more general estimates on off-diagonal geometric graph Ramsey numbers in the same spirit. Finally we investigate the existence of large noncrossing monochromatic matchings in multicoloured geometric graphs. Research partially supported by Hungarian Scientific Research Grants OTKA T043631 and NK67867.     

Hermite interpolation and its numerical differentiation formula involving symmetric functions

By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula.And the corresponding error estimates are also provided.