关于四边形的两个定理在平面及空间中的拓广

文[1]介绍了关于四边形的两个定理:中线定理:如图凸四边形ABCD中,E,F,G,H是各边中点,EF,GH是两条中线,则2(EF2-GH2)＝AD2+BC2-AB2-CD2.对角线定理:如图凸四边形ABCD中,对角线AC,BD的夹角为a,a的对应边为AD,BC,则2AC·BDcos a＝(AB2+CD2-AD2-BC2)/2.     

对"两个有趣的几何发现"一文的修正及改进

文[1]给出了两个几何结论及一个猜想,具体如下: 定理1:若凸m边形内有互不相同且任意三点都不共线的n(n∈N*)个点,把这n个点再加上m边形的m个顶点共有m+n个点作为顶点,连线组成互不重叠的小三角形,则一共可以组成的小三角形的个数为f(m,n)=m+2n-2.     

长方体同心球的几条性质

《数学通报》数学问题1813是:正方体内切球的半径为R,P为球上任一点,P到正方体各面的距离分别为PNi(i=1,2,…,6).证明:∑6i=1PN2i=8R2,∑6i=1PN3i=12R3.此题凸显了长方体同心球的一些性质.所谓长方体的同心球,是指球心在长方体中心的球,长方体的外接球是它的特例,当长方体正好是正方体时,其内切球也是它的同心球.     

Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable

Thompson’s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson’s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.     

Global existence of solutions for stochastic impulsive differential equations

In this paper we obtain some results on the global existence of solution to Itô stochastic impulsive differential equations in M([0,∞),? ⁿ ) which denotes the family of ? ⁿ -valued stochastic processes x satisfying sup_t∈[0,∞) \(\mathbb{E}\)|x(t)|² < ∞ under non-Lipschitz coefficients. The Schaefer fixed point theorem is employed to achieve the desired result. An example is provided to illustrate the obtained results.     

Operator-Valued Fourier Multipliers on Multi-dimensional Hardy Spaces

The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces H ^p ($ \mathbb{T} $ \mathbb{T} ^d ;X), where 1 ≤ p < ∞, d ∈ ℕ, and X is an AUMD Banach space having the property (α). The sufficient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of sets of bounded linear operators. It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers. When the underlying Banach space does not have the property (α), a sufficient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given.     

Hopf Superquivers

In this paper, a super version of the Hopf quiver theory is developed. The notion of Hopf superquivers is introduced. It is shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra structures. A complete classification of such graded Hopf superalgebras is given. A superquiver setting for general pointed Hopf superalgebras is also built up. In particular, a super version of the Gabriel type theorem and the Cartier-Gabriel decomposition theorem is given.     

分担处于一般位置超平面的亚纯映射唯一性定理

本文研究从Cn到复射影空间PN(C)上亚纯映射唯一性问题.根据杨乐处理重值的方法和Dethloff、Quang、Tan等人的技巧,我们分别得到了两个广泛的唯一性定理,改进和推广了一些分担处于一般位置超平面的亚纯映射唯一性结果.     

α混合随机变量序列部分和乘积的几乎处处中心极限定理

利用子序列等方法,获得α混合随机变量序列部分和乘积的几乎处处中心极限定理的更优结果,改进了相关文献的结果.