一类Hardy型空间H0p,q,8(Rn)

本文定义了一般意义下的原子,引入了一类Hardy型空间H₀^p,q,s(Rⁿ)。同时,用推广的Lusin面积积分得到了该空间的一个等价刻划。     

Extensions of the D(?k2)-triples {k2, k2 ± 1, 4k2 ± 1}

Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square. Let k be a positive integer. In this paper, we show that if {k ², k ² + 1, 4k ² + 1, d} is a D(−k ²)-quadruple, then d = 1, and that if {k ² − 1, k ², 4k ² − 1, d} is a D(k ²)-quadruple, then d = 8k ²(2k ² − 1).     

On hypersurfaces of H2×H2

In this paper, we study hypersurfaces of H²× H². We first classify the hypersurfaces with constant principal curvatures and constant product angle functions. Then we classify homogeneous hypersurfaces and isoparametric hypersurfaces, respectively. Finally, we classify the hypersurfaces with at most two distinct constant principal curvatures, as well as those with three distinct constant principal curvatures under some additional conditions.     

广义函数x+λ和x-μ的乘积

For any complcx λ≠integral, and any natural number n, the product is calcuated and Hadmard''s finite part of obtained. The product is also obtained when λ+μ is a complex number of any other possible kind, and μ is a complex number ≠ integral. The products are also calculated. Any special example of these kinds of products has not yet been calculated.     

Hα∞到Hβ∞复合算子的线性组合

设B是N维复空间C^N中的开单位球,φ_i为B上的解析自映射,H_α^∞表示定义在单位球上的加权解析函数空间.本文主要研究的是从空间H_α^∞到H_β^∞上的复合算子线性组合■的紧致性,其中λ_i(i=1,2,…,M)是非零常数.另外,根据紧致性等价条件,得出算子差分对(C_φ1-C_φ2)-(C_φ3-C_φ1)是紧致的当且仅当C_φ1-C_φ2与C_φ3-C_φ1都是紧致的算子.     

泛系分析：数学.方法论.相对论.辩证思维

基于对广义系统、泛导、泛对称、泛箱原理、泛系相对性提出了新的分析模式与新的相对数学化的简化强化的定义，发展了泛系方法论与泛系相对论的框架与理法，具体内容涉及相对普适的数学化的泛系，200类对偶，对偶转化，泛对称转化，泛系辩证，八畴方法，泛系数学方法，广义量化，逼近转化原则，泛等价定理，供求分析，思维实验，广义灰色系统，等等     

Y2=X3-p3上的无穷阶点

首先用(12)上的模函数参数化椭圆曲线y²=x³+1,然后利用虚二次域Q((-p)^1/2)上的类域论和Shimura互反律构造了当p≡7(mod24)为一素数时Y²=X³-p³上的一个无穷阶点.     

Embedding into l ∞2 Is Easy, Embedding into l ∞3 Is?NP-Complete

We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair within a set of n points) into ℝ² Cartesian space preserving their l _∞ (or l ₁) metric distances. Its expected time is (i.e., within a poly-log of the size of the input) beating the previous algorithm. In contrast, we prove that detecting l _∞³ embeddings is NP-complete. The problem is also NP-complete within l ₁² or l _∞² with the added constraint that the locations of two of the points are given or alternatively that the two dimensions are curved into a three-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded in l _∞³; however, it can be embedded if any single point is removed. This research is partially supported by NSERC grants. I would like to thank Steven Watson for his extensive help on this paper.     

关于复平面上H∞空间,βp空间以及β0p空间的几个问题

本文讨论了单位圆中Hardy空间H^∞到p-Bloch空间β^p的复合算子T_1,φ加权复合算子T_ψ,φ的有界性,也讨论了H^∞到小p-Bloch空间β₀^p的复合算子T_1,φ的有界性问题;另外还讨论了小p-Bloch空间到H^∞空间的点乘子及小p-Bloch空间上复合算子的紧性等.     

关于Diophantine 方程xn+2kyn=pz2

设p 为奇素数且对任意的整数m, d, p≠(2^m±1)=/d², 则对任意的素数n > p^8p2, 方程xⁿ+2^kyⁿ=pz², k≥2 没有整数解(x, y, z) 使得x, y, z 两两互素且均不为0.     

探究x0x+y0y=r2与x0x+y0y=x02+y02的几何意义

问题背景苏教版教材必修二P105有这样一道习题:已知圆C的方程是x2+y2=r2,求经过圆C上一点M(x0,y0)的切线的方程.同学们在处理该问题时给出以下的解答过程:如图1,设切线的斜率为k,半径OM的斜率为k1,因为圆的切线垂直于过切点的半径,于是k=     

SL(2,R)上一类极大算子的(H∞,s1,L1)型

本文我们引入了函数类B_δ(G//K)={φ∈L¹(G//K)||φ(t)|≤Δ^-1(t)(1+t)^1-δ,δ>0),对f∈L^p(G//K),1≤p≤∞,和极大算子(?),证明了这类算子是(H_∞,s¹,L¹)型的.     

Hardy-Orlicz-Lorentz空间*

论文利用极大刻画方法介绍了带一般参数的Hardy空间.作为特殊情况, 它们包含了经典H^p空间, Hardy-Lorentz 空间H^p,^q和广义的Hardy-Lorentz空间H^p(φ).     

Small solutions of the congruencea1x12 +a2x22 +a3x32 +a4x42 ≡c(modp)

For any integersa ₁,a ₂,a ₃,a ₄ andc witha ₁ a ₂ a ₃ a ₄≢0(modp), this paper shows that there exists a solutionX=(x ₁,x ₂,x ₃,x ₄) ∈Z ⁴ of the congruencea ₁ x ₁ ² +a ₂ x ₂ ² +a ₃ x ₃ ² +a ₄ x ₄ ² ≡c(modp) such that

d8(C3v*)EPR理论与CsMgCl3:Ni2+的光、磁性质研究

本文给出了O_h点群表象中的d^2,8(C_3v^*)完全强场矩阵,并借助于这种矩阵的特征值和特征矢量,建立了CsMgX₃:Ni²⁺(X=Cl,B,I)类晶体的全组态混合EPR理论。应用这一理论,对CsMgCl₃晶体中的Ni²⁺杂质离子的光学吸收谱、基态零场分裂参量D、顺磁g因数、基态Zeeman分裂以及EPR条件(B,hv₀)进行了统一的计算。结果与观测非常一致,从而首次对CsMgCl₃:Ni²⁺的光、磁性质作出了统一的理论解释。