无穷维情形下的Rolle定理

设Ω是自反的实Banach空间X中的有界开凸集,Y为一实赋范线性空间。证明了一个无穷维情形下的Rolle定理：如果算子A∶Ω→Y在Ω上强连续,在Ω内Frèchet可微,并且存在Y上的非0连续线性泛函f,使得f（Ax）=0对一切x∈Ω成立,则至少存在一点∈Ω,使对一切u∈X,都成立f（A′（x）u）=0。     

2-连通无爪图的Hamilton性

Hamilton问题是图论中重要的问题之一，已经得到了很多很好的结果，但一个图是Hamilton图的充分必要条件到现在还没有得出，文章应用幅度的概念，使用反证法，通过构造最长圈并得出矛盾的方法，给出了2-连通无爪图，若θ(G)≥1/2(n-δ-2)时，G为Hamilton图这一充分条件，为进一步讨论Hamilton提供了一种新的思路。     

域k上三次一般方程式的解的计算

我们已经研究了域k上的n（n≥5）次一般方程在特征标为0的情形下关于幂根是不可解的，而对于n≤4是可解的。本文利用n次循环域的拉格朗日分解式及循环群σ∈G（K/k）的结构，推出域k上的三次一般方程在特征标为0的情形下一般解的计算公式。     

关于非扩张映像的修正粘滞迭代格式

设H是Hilbert空间,X是Banach空间,C是H或X中的非空闭凸子集,T是C→C的非扩张映射,且f是C→C的压缩映射。受H．K．Xu对粘滞迭代算法讨论的启发,提出一种新的粘滞迭代算法,xn＋1=T[（1-αn）xn＋αnf（xn）],n≥0,其中x0∈C,C是Banach空间中的非空闭凸子集,分别在Hilbert空间和Banach空间框架下证明了序列{xn}是强收敛的。     

一类边传递图

令G=（α,β｜α^n=β^2=1,α^β=α^r）,r＆^2≡1（modn），是图Г的一个自同构群。目的是研究关于G一边传递图的性质．运用置换群和代数图论的相关理论，获得了这类图的完全分类，它们是一些互不相交的圈和完全二部图的并。     

2K＋1正则图的自由边

本文利用 Tutte 定理,给出并证明了满足一定条件的2k 1正则图中的每个边都是自由边的结论。     

Primordial Helium and ΔY/ΔZ from H II Regions and from Fine Structure in the Main Sequence Based on Hipparcos Parallaxes

The primordial helium abundance YP is important for cosmology and the ratio Y/Z of the changes relative to primordial abundances constrains models of stellar evolution. While the most accurate estimates of YP come from emission lines in extragalactic H II regions, they involve an extrapolation to zero metallicity which itself is closely tied up with the slope Y/Z. Recently certain systematic effects have come to light in this exercise which make it useful to have an independent estimate of Y/Z from fine structure in the main sequence of nearby stars. We derive such an estimate from Hipparcos data for stars with Z Z and find values between 2 and 3, which are consistent with stellar models, but still have a large uncertainty.     

二重积分中值定理中间点的进一步讨论

众所周知,二重积分中值定理一般表述为：“设Ｄ为平面上有界闭区域,ｆ（ｘ,ｙ）在Ｄ上连续,ｇ（ｘ,ｙ）在Ｄ上可积且不变号,则至少存在一点（ζη）∈Ｄ,使得∫∫Ｄｆ（ｘ,ｙ）ｇ（ｘ,ｙ）ｄｘｄｙ＝ｆ（ζη）∫∫Ｄｇ（ｘ,ｙ）ｄｘｄｙ。”进一步证明了中间点（ζη）可选为Ｄ的内点,其结论与方法完全可推广到一般多重积分中值定理。     

Ureilites

Ureilites are a rare group of five stony meteorites — feldsparless achondrites containing diamonds of preterrestrial origin the total weight of them being 315 carats. The whole carbon content in ureilites makes up 1.5–4.1%. Ureilites substantially differ from the other stony meteorites. In comparison with chondrites they are enriched in Mg but depleted in metal, troilite, alkaline elements. All ureilites are very similar by their structure. They contain elongated cavities generally stretched in the same direction. The structure of ureilites is an achondritic porphyric one. These meteorites consist of large olivine grains, there is less clinopyroxene (pigeonite). They contain kamacite (Ni content being 1.5–4%), troilite FeS, chromite. Carbon material is represented by diamond, graphite and organic material being present in a disequilibrium state. Two ureilites (North Haig and Dingo Pup Donga) were considerably oxidized during terrestrial weathering and contain secondary iron oxides.Diamonds are present in ureilites in thin intergrowths with graphite being disposed between silicate grains more or less evenly in the meteorite. The sizes of such black diamond-graphite aggregates are 0.3–0.9 mm. The sizes of the micromonocrystals of diamond and graphite are less than 1. The diamond-graphite aggregates contain dispersed particles of kamacite, troilite, chromite, nickelchrome, being present in very thin intergrowths with one another. Besides the usual diamond there is an admixture of lonsdaleite in the aggregates representing a hexagonal diamond with a würtzite-like structure. Lonsdaleite has been identified in the ureilites Novo Urei, Goalpara, North Haig. The diamonds of ureilites are characterized by inhomogeneities in the crystalline structure which are at least partly caused by the presence of donor nitrogen. According to the isotopic carbon composition the diamond in the meteorite Novo Urei has the value C¹³ = -5.7.The structure peculiarities of ureilites bear witness of the fact that these meteorites had been subject to the action of dynamic pressure about 300–600 kbar. The impact had taken place in cosmic space. All ureilites subdivide into two types: the first type are Novo Urei, Dyalpur, Dingo Pup Donga, the second type are Goalpara, North Haig according to the following signs: (1) olivine grains are finer in ureilites of the second type; (2) twinning is more typical of clinopyroxenes of ureilites belonging to the first type; (3) in ureilites of the first type a net-like iron distribution is observed, in ureilites of the second type kamacite plates are chiefly present between silicate grains; (4) the size of diamondgraphite intergrowths in ureilites of the first type does not exceed 0.3 mm, in ureilites of the second type it reaches 0.9 mm. Ureilites of the first type have undergone a less intensive impact than ureilites of the second type. Certain similarity of the material composition of ureilites and of the material composition of carbonaceous chondrites, the distinction of these two groups of meteorites from all other meteorites bear witness of the fact that ureilites have formed from carbonaceous chondrites during a collision of asteroid bodies in cosmic space, diamonds having been formed from the carbon material of carbonaceous chondrites.     

单侧容限对应实际存活率的预测

 研究了单侧容限系数法中子样容量ｎ、置信度γ及名义存活率Ｐ与实际存活率α之间的定量关系,导出了α的预测公式。计算结果表明：在ｎ较小,γ与Ｐ搭配不当时,将出现α小于Ｐ的不合理情况。此时,名义存活率Ｐ将过高地表示了安全性,从而使人盲目乐观。本文指出：在飞机或直升机结构可靠性分析中,子样容量ｎ通常远小于４３,因此,某些文献中建议取γ＝９０％,Ｐ＝０．９９９９９９是不合理的,本文提出了新的建议。