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1.
严绍宗  朱建中 《中国科学A辑》1987,30(11):1139-1146
本文主要是给出Hilbert空间上满足方程 λA2+μA*2=αA*A+βAA* (λ,μ,α,β都是复数)的有界线性算子A的全部形式,并给出它的应用。  相似文献   

2.
孔荫莹  罗茜 《数学学报》2018,61(2):347-352
本文给出新Dirichlet级数Σn=0aneλns的收敛横坐标σc、一致收敛横坐标σu和绝对收敛横坐标σa的定义.通过指数λn和系数an的关系去估计三个横坐标,并补充证明两类Dirichlet级数Σn=0aneλns和Σn=0anens的收敛条件是一致的.  相似文献   

3.
该文研究了广义Besov类Bp,θΩ在一致和随机框架下由Gel'fand方法的逼近问题. 利用Maiorov的离散化方法和pseudo-s-scale的性质, 给出了这一逼近问题在某些情况下的渐近阶.  相似文献   

4.
本文利用余瑞璜的“固体与分子经验电子理论”提出:(1)2型多元置换、间隙型固溶体的价电子结构计算模型;(2)未知键距结构固溶体的键距差(BLD)分析方法;(3)BLD分析中解的不唯一性的处理。  相似文献   

5.
保继光 《中国科学A辑》1998,41(7):613-616
在较弱的条件下 ,证明了以给定的具有紧支集的非负函数为Gauss曲率 ,以已知的空间曲线为边界的凸曲面是整体C1,1的 .有例子表明这个正则性是最佳的.  相似文献   

6.
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.  相似文献   

7.
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  相似文献   

8.
设B是N维复空间CN中的开单位球,φi为B上的解析自映射,Hα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Hα到Hβ上的复合算子线性组合■的紧致性,其中λi(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(Cφ1-Cφ2)-(Cφ3-Cφ1)是紧致的当且仅当Cφ1-Cφ2与Cφ3-Cφ1都是紧致的算子.  相似文献   

9.
柯召  孙琦 《中国科学A辑》1981,24(12):1453-1457
对于丢番图方程x3±1=Dy2,D>2,D无平方因子且不能被3或6k+1形的素数整除。本文用初等的方法证明了除开平凡解x=±1,y=0以外,均无其它的整数解。此外,本文指出,用类似的方法还可证明丢番图方程x3±1=3Dy2除开平凡解x=±1,y=0以外,均无其它的整数解,D的条件同前。  相似文献   

10.
张绍伟 《中国科学A辑》1995,38(6):561-564
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.  相似文献   

11.
吴华明 《数学学报》2010,53(1):205-208
根据四次Diophantine方程的已知结果,运用初等数论方法证明了:椭圆曲线y~2=x~3+27x-62仅有整数点(x,y)=(2,0)和(28844402,±154914585540).  相似文献   

12.
It is proved that the equation of the title has a finite number of integral solutions (x, y, n) and necessary conditions are given for (x, y, n) in order that it can be a solution (Theorem 2). It is also proved that for a given odd x0 there is at most one integral solution (y, n), n ≥ 3, to x03 + 3y3 = 2n and for a given odd y0 there is at most one integral solution (x, n), n ≥ 3, to x3 + 3y03 = 2n.  相似文献   

13.
The three numbers 1, 5, 10 have the property that the product of any two numbers decreased by 1 is a perfect square. In this paper it is proved that there is no other positive integer N which shares this property with 1, 5, and 10.  相似文献   

14.
 We compute, up to an element of a fixed number field, the critical values of the L-function of a pair of automorphic, cuspidal, cohomological representations of any GL(r). The result is expressed as a product of cohomological periods divided by an archimedean integral. The main tool used is the rationality of the cohomology of the three representations involved in the Rankin–Selberg integral. As an intermediate step, we also obtained the rationality of the Eisenstein cohomology. Received: 14 February 2002 / Revised version: 17 September 2002 Published online: 14 February 2003  相似文献   

15.
张纯洁 《数学学报》2010,53(4):741-750
证明一类带粗糙核平方函数的加权及l~r-向量值不等式,其中所用的权函数为径向权.作为推论,我们得出了带H~1-核的Marcinkiewicz积分μ_Ω的相应不等式.  相似文献   

16.
A fairly old problem in modular representation theory is to determine the vanishing behavior of the Hom groups and higher Ext groups of Weyl modules and to compute the dimension of the ℤ/(p)-vector space for any partitions λ, μ of r, which is the intertwining number. K. Akin, D. A. Buchsbaum, and D. Flores solved this problem in the cases of partitions of length two and three. In this paper, we describe the vanishing behavior of the groups and provide a new formula for the intertwining number for any n-rowed partition.  相似文献   

17.
Some general remarks are made concerning the equation f(x, y) = qn in the integral unknowns x, y, n, where f is an integral form and q > 1 is a given integer. It is proved that the only integral triads (x, y, n) satisfying x3 + 3y3 = 2n are (x, y, n) = (?1, 1, 1), (1, 1, 2), (?7, 5, 5,), (5, 1, 7).  相似文献   

18.
We consider *-automorphisms and *-antiautomorphisms of real and complex factors. We establish both the uniqueness of the class of *-automorphisms (with ) of a real injective factor and the uniqueness of the class of *-antiautomorphisms (with ) of a complex injective factor. It is well known that, for complex factors, the notions of hyperfiniteness and injectivity are equivalent. Here we prove that, for real factors, the two notions are no longer equivalent. Bibliography: 15 titles.  相似文献   

19.
Diophantine方程y~2=px(x~2+2)   总被引:2,自引:0,他引:2  
陈历敏 《数学学报》2010,53(1):83-86
设p是大于3的奇素数.本文证明了:当p≡5或7(mod 8)时,方程y~2=px(x~2+2)无正整数解(x,y);当p≡1(mod 8)时,该方程至多有1组解;当p≡3(mod 8)时,该方程至多有2组解.  相似文献   

20.
亚纯函数在角域内的波莱耳方向   总被引:2,自引:0,他引:2       下载免费PDF全文
杨乐 《中国科学A辑》1979,22(Z1):149-162
Suppose that f(z) is a meromorphic function of order λ(0<λ≤∞) and of lower order μ(0≤μ<∞) in the plane. Let ρ(μ≤ρ≤λ) be a finite positive number. B: arg z=θ0(0≤θ0 <2π) is called a Borel direction of order ρ of f(z), if for any complex number a, the equality holds, except at most for some a belonging to a set of linear measure zero. For the exceptional values a, we have ρ(θ0, a)>ρ, except two possible values. With the above hypotheses on f(z), λ, μ and ρ, We have the following lemmas. Lemma 1. There exists a sequence of positive numbers (rn) such that(?)=∞ and that Lemma 2. If f(z) has a deficient value a0 with deficiency δ(a0, f), then we have where (rn) is the sequence defined in the Lemma 1 and when a_0=∞, we have to replace(?)by (?) in the left hand side of (*). Lemma 3. Suppose that B_1 : arg z =θ1 and B2 : arg z=θ2 (0≤θ12<2π+θ1) are two half straight lines from the origin and there are no Borel directions of order≥ρ(ρ>1/2) of f(z) in θ10, the inequality holds as n is sufficiently large, where K1 is a positive number not depending on n andεand when a0=∞, it is necessary to replace we have θ21≤π/ρ. Theorem 1. Suppose that f(z) is a meromorphic function of order λ (1/2<λ≤+∞) and of lower order μ(0≤μ<+∞) in the plane. Let p be a number such that μ≤ρ≤λ and that 1/2<ρ<+∞If f~((k))(z) has p(1≤P<+∞) deficient values ai (i=1,2,…,p) with deficiencies δ(ai,f(k)), then f(z) has a Borel direction of order ≥ρ in any angular domain, the magnitude of which is larger than It is convenient to consider Julia directions as Borel directions of order zero.Under this assumption, We have the following. Theorem 2. Suppose that f(z) is a meromorphic function of order λ and of finite lower order μ in the plane and that ρ(μ≤ρ≤λ) is a finite number. If p denotes the number of deficient values of f(z) and q denotes the number of Borel directions of order ≥p of f(z), then we have p≤q.  相似文献   

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