章鱼图由Laplacian谱确定

如果与图G同谱的图都与G同构,则称图G由它的谱确定.重合星图K1,q的中心点和圈图Cn的一个点得到章鱼图.证明了这一类单圈图由Laplacian谱确定.     

Hilbert空间中φ-强伪压缩映像的一个注记

在cn‖xn-Txn‖2→0(n→∞)的条件下,在Hilbert空间中研究了一类未必连续,甚至未必有界的φ-强伪压缩映像的不动点的迭代序列逼近问题,获得了一个强收敛定理.     

Reissner板的中值定理

The mean-value theorem of Reissner's plate is first presented and proved. Letting Cs and Cn approach infinite, the mean-value theorem of elastic thin plate can be obtained.     

介值定理和它的两个应用

在映射观点理解介值定理的基础上,推广介值定理.运用所推广的介值定理将Li-York定理推广到多变量情形,并给出单位Cn球Bloch空间上复合算子的下有界性特征.     

两类非连通图优美性的研究

给出了两类非连通图(K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi)和(K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1(k=1,2), 并证明了如下结论:对自然数n, m, m1, m2, m3, 设s=〖JB(［〗〖SX(〗n〖〗2〖SX)〗〖JB)］〗, n≥9, m1≥s+2, 则图(K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi)是一个优美图; 对 k=1,2,设n, m≥3, G(k)n-1是一个具有n-1条边的k-优美图,则图(K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1是一个优美图。 其中,K2是一个具有2个顶点的完全图,K2〖TX-〗是图K2的补图,K2〖TX-〗∨Cn是图K2和n圈Cn的联图, St(m)是一个具有m+1个顶点的星形树。     

星体的弦长积分

首先引入星体弦长积分的概念,研究了其性质并建立了有关星体弦长积分的不等式.作为应用,给出相交体的星对偶的Brunn-Minkowski型不等式.     

一类差分方程的频率振动解

本文讨论了一类差分方程的解的频率振动性,建立了新的频率振动性定理,给出了如下中立型差分方程的解的频率振动的充分条件,从而简化和改进了文献[3]中的相应条件与结论：△（xn＋cnxn-k）=f（n,xn-1）,n=0,1,2,…其中k≥1与l≥1均为正整数,1Cn∩∞n=0是一实数列,f是定义在Z×R上的函数。     

A generalized funk’s section theorem for measures

If L is a star body in R~n whose central(n-i)-slices have the same(n-i)-dimensional measure μ_(n-i)(with appropriate density)as the central(n-i)-slices of an origin-symmetric star body K,then the corresponding n-dimensional measures μ_n of K and L satisfy μ_n(K)≤μ_n(L).This extends a generalized Funk’s section theorem for volumes to that for measures.     

C~n中(p,q)型微分形式的-闭开拓

文中研究对给定在C~n中一域的边界上的C~(2)类(p,q)型微分形式越过边界的?闭开拓问题,得到了可以?闭开拓的二个充分必要条件和 Hartogs 与Bochner 型定理。     

几类图的均匀邻点可区别全染色

 邻点可区别全染色是在正常全染色的定义下,使得任两相邻顶点的色集不同。设G（V,E）为一个简单图,f为G的一个k-邻点可区别全染色,若f满足||Vi∪Ei|－|Vj∪Ej||≤1（i≠j）,其中,Vi∪Ei={v|f（v）=i}∪{e|f（e）=i},记C（i）=Vi∪Ei,则称f为G的k-均匀邻点可区别全染色,简记为k-EAVDTC,并称χeat（G）=min{k|G存在k－均匀邻点可区别全染色}为G的均匀邻点可区别全染色数。本文给出了路、圈、风车图K t 3、图Dm,4和齿轮图■n的均匀邻点可区别全染色,以及它们的均匀邻点可区别全色数的确切值。     

On the Dual <Emphasis Type="Italic">p</Emphasis>-Measures of Asymmetry for Star Bodies

Recently, the connection between p-measures of asymmetry and the L_p -mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p -measures of asymmetry for star bodies (naturally for convex bodies) is introduced first. Then the connection between dual p -measures of asymmetry and L_p -dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.     

星体的p-极曲率映象与p-仿射表面积

引进了星体的p-极曲率映象的概念,建立了p-极曲率映象不等式,并给出了一些特殊几何体的p-极曲率映象与其极体的p仿射表面积乘积的界.作为p-极曲率映象的一个应用,同时研究了p-混合仿射表面积的p-Minkowski型不等式的推广.     

星半环的亚直分解定理

引入了星半环、半环的星同态、星半环的亚直积和亚直既约等概念,证明了星半环的亚直分解定理.     

集值映射的Ky Fan不等式

利用广义的截口定理，本文讨论在集值映射和锥的情形下的Ky Fan不等式．     

A compact system of small planets around a former red-giant star

Planets that orbit their parent star at less than about one astronomical unit (1?AU is the Earth-Sun distance) are expected to be engulfed when the star becomes a red giant. Previous observations have revealed the existence of post-red-giant host stars with giant planets orbiting as close as 0.116?AU or with brown dwarf companions in tight orbits, showing that these bodies can survive engulfment. What has remained unclear is whether planets can be dragged deeper into the red-giant envelope without being disrupted and whether the evolution of the parent star itself could be affected. Here we report the presence of two nearly Earth-sized bodies orbiting the post-red-giant, hot B subdwarf star KIC 05807616 at distances of 0.0060 and 0.0076?AU, with orbital periods of 5.7625 and 8.2293 hours, respectively. These bodies probably survived deep immersion in the former red-giant envelope. They may be the dense cores of evaporated giant planets that were transported closer to the star during the engulfment and triggered the mass loss necessary for the formation of the hot B subdwarf, which might also explain how some stars of this type did not form in binary systems.     

一类弱凹（凸）函数及其应用

本文引进了一类弱凹（凸）函数，讨论了与之相关的ＫＫＭ映象，Ｋｙ·Ｆａｎ不等式定理与截口定理，并给出了一些应用．     

Nother-type theorem of piecewise algebraic curves

The piecewise algebraic curve is a generalization of the classical algebraic curve. This paper describes the improvement of the Nother-type theorem of piecewise algebraic curves on the star region. Moreover, the Nother-type theorem of piecewise algebraic curves on the cross-cut partition is discussed.     

Nöther-type theorem of piecewise algebraic curves

The piecewise algebraic curve is a generalization of the classical algebraic curve.This paper describes the improvement of the Nother-type theorem of piecewise algebraic curves on the star region.Moreover,the Nother-type theorem of piecewise algebraic curves on the cross-cut partition is discussed.     

亚幂零半群及其同余格

本文研究了亚幂零半群的基本性质及幂等元分离同余,并给出了同余交换的有限阶亚幂零半群的完全分类。