A classification of regular embeddings of hypercubes Q_(2m) with m odd

In this paper we give a classification of the orientable regular embeddings of Q_n for n=2m with m odd.Actually we prove that the known examples given by Kwon are the only regular maps of Q_n when n=2m (m odd).     

k-smooth Points of m(Ω,R)

ｋ－ｓｍｏｏｔｈＰｏｉｎｔｓｏｆｍ（Ω，Ｒ）ＷａｎｇＳｈｕｓｈｉ（王漱石）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｚｈｏｕＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｈｕｚｈｏｕ，Ｚｈｅｊｉａｎｇ，３１３０００）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐｏｐｅｒ...     

F型树F(m,n)可由其Laplacian谱唯一确定

讨论了“哪些图由它的Laplacian谱确定？”的问题，一棵树称为F型树，如果其由一梳图的一个2度顶点与一条路的悬挂点邻接而成。本文利用同谱图的线图的特点，证明了，型树可由它的Laplacian谱确定。     

关于t(n)、F(m,n)分布数字特征的计算

在统计推断中，需用统计量来估计未知参数θ或ｇ（θ）的数值，如要进一步分析一个估计量的好坏，就需知道估计量的分布，或至少要知道统计量的某些数字特征．众所周知，ｔ统计量、Ｆ统计量在参数的点估计、区间估计、假设检验中起着重要的作用．文献［１］中介绍了几种重...     

AgL(m,n)的gL(m,n)模结构

设g=g_(-1)+g_0+g_1是由阶化向量空间V=V_0+V_1的线性变换所构成的李超代数。通过上诱导模,定义了外代数Λ(g_1)的g模结构,这儿g_1=V_1(?)V_0~*,并决定了它的全部子(g_0+g_1),(g_0+g_(-1))、g模。     

Total Chromatic Number of the Join of K_(m,n) and C_n

The total chromatic number XT(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no adjacent or incident pair of elements receive the same color. G is called Type 1 if XT(G)=Δ(G) 1. In this paper we prove that the join of a complete bipartite graph Km,n and a cycle Cn is of Type 1.     

B(m→m)中的等距逼近问题

本文利用B(m→m)的算子表(?)定(?)中元的性质,解决了B(m中的“等距与几乎等距算子的关系(?)问题,(?)得到如下结果:设0≤ε<1/3,,则对B(m→m)中任意“ε—等距算子”(?) T,必存在B(m→m)中的等距算子U,使‖T-U‖(?)4ε。 定义Ⅰ 记号m表示(复)有界数列空间,记号同_0表示N上复值“简单函数”空间,(?)     

A characterization of a class of hyperplanes of DW(2n−1,F)

A hyperplane of the symplectic dual polar space $DW(2n?1,\mathbb{F})$, $n\ge 2$, is said to be of subspace-type if it consists of all maximal singular subspaces of $W(2n?1,\mathbb{F})$ meeting a given $(n?1)$-dimensional subspace of $\text{PG}(2n?1,\mathbb{F})$. We show that a hyperplane of $DW(2n?1,\mathbb{F})$ is of subspace-type if and only if every hex $F$ of $DW(2n?1,\mathbb{F})$ intersects it in either $F$, a singular hyperplane of $F$ or the extension of a full subgrid of a quad. In the case $\mathbb{F}$ is a perfect field of characteristic 2, a stronger result can be proved, namely a hyperplane $H$ of $DW(2n?1,\mathbb{F})$ is of subspace-type or arises from the spin-embedding of $DW(2n?1,\mathbb{F})?DQ(2n,\mathbb{F})$ if and only if every hex $F$ intersects it in either $F$, a singular hyperplane of $F$, a hexagonal hyperplane of $F$ or the extension of a full subgrid of a quad.     

Finite Dimensional Lie Superalgebras W(m,n,t) and S(m,n,t) of Cartan Type

设Ｌ＝Ｗ或Ｓ，Ｆ是特征数大于２的域．本文证明了Ｆ上的有限维单李超代数Ｌ（ｍ，ｎ，ｔ）的自然滤过是不变的．进而得出了Ｌ（ｍ，ｎ，ｔ）与Ｌ（ｍ′，ｎ′，ｔ′）同构的充要条件是ｍ＝ｍ′，ｎ＝ｎ′和ｔｉ＝τ（ｔ′ｉ），ｉ＝１，２，…，ｍ，这里τ是｛１，２，…，ｍ｝的一个置换．     

Regularity and explicit representation of (0,1,...,m−2,m) interpolation on the zeros of (1−x 2)P n −2/(α,β) (x)

Necessary and sufficient conditions for the regularity andq-regularity of (0,1,...,m–2,m) interpolation on the zeros of (1–x ²)P _n ^–2/(,) (x) (,>–1) in a manageable form are established, whereP _n ^–2/(,) (x) stands for the (n–2)th Jacobi polynomial. Meanwhile, the explicit representation of the fundamental polynomials, when they exist, is given. Moreover, we show that under a mild assumption if the problem of (0,1,...,m–2,m) interpolation has an infinity of solutions then the general form of the solutions isf ₀(x)+C f(x) with an arbitrary constantC.This work is supported by the National Natural Science Foundation of China.     

Chromatic Uniqueness of the Complement of T_m(l, 4, m - 6)

In the paper, we prove that the complement of Tm(1,4,m - 6)(m > 10) is chromatically unique if and only if m ≠5k(k ≥ 2).     

环F2m+uF2m+u2F2m+u3F2m上线性码及其对偶码的Gray像

本文研究了环F2m+uF2m+u2 Fm+u3F2m上线性码.利用环是Frobenius环,证明了环上线性码C及其自对偶码的Gray像为F2m上的线性码和自对偶码.同时,给出了上循环码C的Gray像ψ(C)为F2m上的拟循环码.     

系数在模李超代数W(m,3,1)上的gl(2,F)的一维上同调

研究了系数在模李超代数W(m,3,1)上的gl(2,F)的一维上同调,其中F是一个素特征的代数闭域且gl(2,F)是系数在F上的2×2阶矩阵李代数.计算出所有gl(2,F)到模李超代数W(m,3,1)的子模的导子和内导子.从而一维上同调H~1(gl(2,F),W(m,3,1))可以完全用矩阵的形式表示.     

Three classes of smooth Banach submanifolds in B(E,F)

Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. ＜ ∞ or codim R(T) = const.＜ ∞} and {T ∈ R(E, F) RankT =const.＜∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry.     

弱(F)-反演半群上的模糊(F)-核正规系

借助于模糊(F)-核正规系刻画了弱(F)-反演半群S(P)上的强(F)-同余.证明了S(P)上的每一个模糊强(F)-同余都是由它的模糊(F)-核正规系所唯一决定的.     

Generalized Taylor series for the class of functions H(ρ,m)

The nonquasianalytic class of functions H(, m) is constructively described by generalized Taylor series. Nonredundant discrete information in this connection is given with the help of first and second differences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 1007–1009, July, 1990.     

A_2(F)在G_2(F)中的扩群及其泛正规性

域Ｆ上Ａ２型Ｃｈｅｖａｌｌｅｙ群Ａ２（Ｆ）可视为Ｆ上Ｇ２型Ｃｈｅｖａｌｌｅｙ群Ｇ２（Ｆ）的子群．当 Ｆ是特征不为 ２，３的域且 Ｆ＝Ｆ３时，本文给出了 Ａ２（Ｆ）在 Ｇ２（Ｆ）中的所有扩群及其泛正规性．