n-Colour self-inverse compositions

MacMahon’s definition of self-inverse composition is extended ton-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.     

Odd length for even hyperoctahedral groups and signed generating functions

We define a new statistic on the even hyperoctahedral groups which is a natural analogue of the odd length statistic recently defined and studied on Coxeter groups of types $A$ and $B$. We compute the signed (by length) generating function of this statistic over the whole group and over its maximal and some other quotients and show that it always factors nicely. We also present some conjectures.     

Diameter of a direct power of a finite group

We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gⁿ with respect to each generating set is at most n(|G|?rank(G)); and the second one states that there exists a generating set 𝒜, of minimum size, for Gⁿ such that the diameter of Gⁿ with respect to 𝒜 is at most n(|G|?rank(G)). We will establish evidence for each of the above mentioned conjectures.     

一类扩展Euler和的表示问题

应用Parseval定理和Nielsen广义多重对数函数的性质,给出了非线性扩展Euler和的Riemann Zeta函数表示.对来自于实验数学中的扩展Euler和∑n=1∞H2n/n2的经验公式给出了严格的理论证明.此方法也适用于求其它扩展Euler和的计算问题.     

Analytic combinatorics of connected graphs

We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, that is, generating function manipulations, we derive a formula for the coefficients of the complete asymptotic expansion. The same result is derived for connected multigraphs.     

一种基于物体质心的图像自动化校准方法

图像校准是将任意相邻两图像都具有公共部分的一列图像合成一副全图的图像处理过程.而图像自动化校准的难点在于对一组图像公共部分特征信息的提取和自动匹配,尤其是自动匹配和图像校准的误差分析.本文基于放射变换不变性,给出了一种基于特征信息质心的自动匹配方法,与目前国际上主流特征提取和特征校准方法相比,本文方法较准确,且适用于卫星图片及一些MRI和CT 图片.本文方法的另一优点是具有线性计算复杂度.     

VALUE-AT-RISK的核估计理论

如何根据历史数据估计Value-at-Risk（VaR）;是风险分析与管理中一个重要的基本问题.木文基于非参数核估计方法,通过拟合实际数据过程的分布,构造了VaR的估计.在合适的相依数据条件下,证明了该估计量的渐近正态性,并给出了渐近方差的估计.由此表明:本文所构造的估计量不仅比参数模型具有更广泛的适应性,而且如同参数模型具有n~（-1/2）的收敛速度.本文假设的数据过程避免使用混合性,可很好地适用于金融管理中广泛应用的ARMA与GARCH模型族及非线性模型.     

First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups

We study the first-order definable, Diophantine, and algebraic subsets in the set of all ordered sets generating a group or generating a group as a normal subgroup for some relatively free solvable groups.