弱拟正则映射的正则性

对于低于自然可积指数Sobolev类Wloc1,p(Ω,Rn)(1＜p＜n)的弱拟正则映射,建立了其广义微商可积指数提高到大于空间维数n结果,从而得出拟正则映射的可去奇异集的Hausdorff维数大于零的结论.本文是从弱拟正则映射定义出发对Iwaniec的有关结果给出一个简化证明.     

Heisenberg群上弱拟正则映射正则性的自我改善

考虑定义在Heisenberg群上的弱拟正则映射其水平微商可积性的自我改善. 在广义水平微商可积指数低于第1层空间维数的情况下, 通过接触映射的Jacobian和广义水平微商Jacobian的关系, 建立了逆向H\"older不等式, 从而得到其可积指数的自我提升.     

退化弱拟正则映射的正则性

本文考虑退化弱拟正则映射.利用Hodge分解、逆Holder不等式等工具,证明了其正则性结果:存在指数q₁=q₁（n,l,K）1,q_1loc(Ω,Rⁿ)，都有f∈W^1,l_loc(Ω,Rⁿ) ，即f为退化拟正则映射.     

退化（K1，K2）—拟正则映射的正则性

对于n维欧氏空间中一类退化(K1,K2)-拟正则映射,设其n×n阶Jacobi矩阵的秩为l1≤l≤n,得到了它的局部Lp可积性(p(l,n,K1,K2)＞l)和具有指数为的Holder连续性内估计(当时).     

弱 (K1, K2) -拟正则映射的正则性

给出空间弱(K₁, K₂) -拟正则映射的定义, 并以Hodge分解及弱逆Hölder不等式为工具, 得到了其正则性结果：对任意满足 的q1, 都存在可积指数 使得对任意弱 (K₁, K₂) -拟正则映射 都有 即f为通常意义下的(K₁, K₂) -拟正则映射.     

弱(L1,L2)-BLD映射的正则性

本文首先将文[1]中的BLD映射推广为弱(L1,L2)-BLD映射,并证明了如下正则性结果存在两个可积指数p1=p1(n,L1,L2)＜n＜q1=q1(n,L1,L2),使得对任意弱(L1,L2)-BLD映射,∈W1(Ω,Rn),都有,∈(Ω,Rn),即,为(L1,L2)-BLD映射.     

弱拟正则映射的若干性质

本文应用Ｈｏｄｇｅ分解,得到了弱拟正则映射的逆Ｈ　　ｌｄｅｒ不等式,Ｌｐ可积性与其分量函数的弱单调性结果．     

关于空间(k1,k2)-拟正则映射

本文考虑空间 (k1,k2 ) -拟正则映射的 Lp(p >n)可积性 ,以及当 k1→ 1 ,k2 → 0时 p的渐近行为 .     

退化弱(L1,L2)-BLD映射的正则性

本文给出空间退化的弱(L1,L2)-BLD映射的定义.利用Hodge分解,弱逆Holder不等式等工具,证明了其正则性结果对任意满足0＜L2lnl/2l2n+l×100n2[23l/2.(24l+n+1)](l-q1)＜1的q1,都存在可积指数p1=p1(n,l,q1,L1,L2)＞l,使得对任意退化的弱(L1,L2)-BLD映射f∈W1,q1 loc(Ω,Rn),都有f∈W1,p1 loc (Ω,Rn),即f为通常意义下的退化的(L1,L2)-BLD映射.     

退化弱(L1,L2)-BLD映射的正则性

本文给出空间退化的弱(L1,L2)-BLD映射的定义.利用Hodge分解,弱逆Holder不等式等工具,证明了其正则性结果:对任意满足Ol,使得对任意退化的弱(L1,L2)-BLD映射f∈Wloc1,q1(Ω,Rn),都有f∈Wloc1,p1(Ω,Rn),即f为通常意义下的退化的(L1,L2)-BLD映射.     

多元多项式齐次方程组的一个解法

本文对多元多项式齐次方程组给出一种解法，并给出其解子模的基所含向量的个数在最坏情况时的下界。     

SOLUTION OF A RESEARCH PROBLEM

ＳＯＬＵＴＩＯＮＯＦＡＲＥＳＥＡＲＣＨＰＲＯＢＬＥＭＷＵＳＨＩＱＵＡＮ（巫世权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，Ｃｈａｎｇｓｈａ４１００７３，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

The Siegel norm,the length function and character values of finite groups

In this paper we present some new results on the connection between the Siegel norm, the length function and irreducible character values of finite groups. In addition, we provide algorithms to compute the length of a cyclotomic integer and the set of cyclotomic integers with Siegel norm bounded by a given positive real number.     

The Formula of General Term of the Sum of Equal Powers of Natural Numbers

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｏｆｉｎｄｔｈｅｇｅｎｅｒａｌｔｅｒｍｆｏｒｍｕｌａｏｆｃａｌｃｕｌａｔｉｎｇｗａｓａｎｏｌｄｅｓｔｐｒｏｂｌｅｍｉｎＮｕｍｂｅｒＴｈｅｏｒｙ．Ｅａｒｌｙｉｎ３００Ｂ．Ｃ．,Ａｒｃｈｉｍｅｄｏ,ｔｈｅｍａｔｈｅｍａｔｉｃｉａｎｏｆａｎｃｉｅｎｔＧｒｅｅｃｅ,ｗｏｒｋｅｄｏｕｔｔｈｅｆｏｒｍｕｌａ∑ｎｋ＝１ｋ＝ｎ（ｎ＋１）２ａｎｄ∑ｎｋ＝１ｋ２＝ｎ（ｎ＋１）（２ｎ＋１）６．Ｓｏｆａｒ,ｐｅｏｐｌｅｈａｖｅｇｏｔｍａｎｙｆｏｒｍｓｏｆｅｐｒｅｓｓｉｏｎｏｆｔｈｅｇｅ…     

用AHP法建立教学质量评估体系

以AHP为理论基础,结合Delphi方法,对高校教师教学质量评估体系进行尝试性建构。通过构建结构→个体判断→群判断处理→量化指标体系生成的分步操作,来达到科学、民主、公正、客观的评价目标。     

The diffeomorphic types of the complements of arrangements in ??3 II

For any arrangement of hyperplanes in ℂℙ³, we introduce the soul of this arrangement. The soul, which is a pseudo-complex, is determined by the combinatorics of the arrangement of hyperplanes. In this paper, we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other. In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected. This generalizes our previous result on hyperplane point arrangements in ℂℙ³. This work was partially supported by NSA grant and NSF grant     

The diffeomorphic types of the complements of arrangements in CP~3Ⅱ

For any arrangement of hyperplanes in CP~3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP~3.     

A generalization of Alon–Aydinian–Huang theorem

Let $S_{n,k}^m$ be the collection of sets of real numbers of size n, in which every subset of size larger than k has a sum less than m, where $n\ge k+1$, and m is some real number. Denote by $a_{n,k}^m$ the maximum number of nonempty subsets of a set in $S_{n,k}^m$ with a sum at least m. In particular, when $m=0$, Alon, Aydinian, Huang ((2014) [1]) proved that $a_{n,k}^0={\sum }_{i=0}^{k?1}\left(\begin{array}{c}n?1\\ i\end{array}\right)$, where two technical proofs, based on a weighted version of Hall's theorem and an extension of the nonuniform Erd?s–Ko–Rado theorem, were presented. In this note, we extend their elegant result from $m=0$ to any real number m, and show that $a_{n,k}^m=\{\begin{array}{cc}{\sum }_{i=0}^{k?1}\left(\begin{array}{c}n?1\\ i\end{array}\right)\hfill & \text{ if }m\ge 0\hfill \\ {\sum }_{i=1}^k\left(\begin{array}{c}n\\ i\end{array}\right)\hfill & \text{ if }m<0\hfill \end{array}$. Our proof is obtained by exploring the recurrence relation and initial conditions of $a_{n,k}^m$.     

A Note on the Theorems of Church-Turing and Trachtenbrot

We sketch proofs of the theorems of Church-Turing and Trachtenbrot using a semi-monomorphic axiomatization. Mathematics Subject Classification : 03B10, 03B25.