A Note on the ω-Global Transform of Mori Domains

Let R be a domain and let Rωg be the ω-global transform of R. In this note it is shown that if R is a Mori domain, then the t-dimension formula t- dim(Rωg) = t-dim(R)-1 holds.     

A Note on Lp Boundedness for Maximal Singular Integrals on Product Domains

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＳｔａｔｅｍｅｎｔｓｏｆＲｅｓｕｌｔｓ　Ｉｔｉｓｗｅｌｌ ｋｎｏｗｎｔｈａｔｔｈｅｍａｘｉｍａｌｓｉｎｇｕｌａｒｉｎｔｅｇｒａｌｏｎｐｒｏｄｕｃｔｄｏｍａｉｎｓｉｓｖｅｒｙｕｓｅｆｕｌｌｉｎｈａｒｍｏｎｉｃａｎａｌｙｓｉｓ.Ｈｅｒｅｗｅｌｉｓｔｔｗｏｒｅｓｕｌｔｓｒｅｌａｔｅｄｔｏｔｈｉｓｐａｐｅｒ.Ｓｅｅ [1 ] ,[2 ]ａｎｄｔｈｅｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ .　Ｆｒｏｍ [1 ] ,ｗｅｋｎｏｗｔｈｅｆｏｌｌｏｗｉｎｇｆａｃｔ.　ＳｕｐｐｏｓｅｔｈａｔＫ(ｘ,ｙ)ｉｓｌ…     

On t-Dimension over Strong Mori Domains

In this note we prove that if R is a strong Mori domain with t-dim R = n and with countably many prime v-ideals, then there is a chain of rings between R and R^w R1=R belong to R2……belong to Rn lohtuin in R^w such that each R, is also a strong Mori domain and t-dim Rk=n - k ＋ 1 for k = 1,2,..., n.     

欧氏环上特殊正交群的一类极大子群

定出欧氏环上特殊正交群的一类极大子群,得到如下结果:设R是带有欧氏映射σ的特征不为2的欧氏环且不是域,SO(2m,R)为R上的特殊正交群,R*=R\{0},l=min{σ(x)|x∈R*\U(R)},任取a∈R*\U(R)使σ(a)=l,记a在R中生成的主理想为M.那么当m≥3时,AB CD∈SO(2m,R)|B∈Mm×m是SO(2m,R)的一个极大子群.     

A Note on Boundary Unique Contination for Harmonic Functions in Non-Smooth Domains

In this note, we prove the boundary unique continuation property for harmonic function dfined on convex domain     

双调和泊松方程的新解法

本文用Fourier变换法求解了区域为带形区域和上半平面的双调和Po isson方程的边值问题。     

关于拟连续Domain的一个注记

证明了:(1)具有性质M的dcpo为拟连续domain当且仅当其上的下拓扑开集格在集合包含序下为连续格;(2)对于dcpo L,L为拟连续domain当且仅当ΣL的Hoare空间为局部强紧空间.     

整环上Moore-Penrose逆的刻画

若A为整环上的n阶可逆矩阵,则X=A-1是满足方程rank■=rank(A)的唯一矩阵.把它推广到满足Rao条件的整环上得到关于矩阵A的Moore-Penrose逆A+的刻画.     

On the Ascent of Properties Related to Unique Factorization Domains

In this article, we develop equivalent conditions for a certain class of monoidal transform to inherit either the property of being a completely integrally closed domain that satisfies the ascending chain condition on principal ideals, the property of being a Mori domain, the property of being a Krull domain, or the property of being a unique factorization domain, respectively. Such a class of monoidal transform is given in terms of an (analytically) independent set that forms a prime ideal in the base domain. Characterizations are provided illustrating the necessity of the “prime ideal” hypothesis when the base domain is a Noetherian unique factorization domain.     

关于极大前缀码的刻划的一个注记

设X*是字母表X上的自由幺半群,以X*为顶点集构造一个语言图Γ(X*),引入语言图Γ(X*)的横截集的概念,给出了前缀码为极大前缀码的一个刻划,并推广了相关文献的结果.     

关于Fourier级数的一点推广

以２ｌ为周期的函数ｆ（ｘ）也可看作周期为４ｌ．设ｆ（ｘ）满足 Ｄｉｒｉｃｈｌｅｔ充分条件,按［１］方法展开的以 ２ｌ为周期的 Ｆｏｕｒｉｅｒ 级数和以 ４ｌ为周期的 Ｆｏｕｒｉｅｒ 级数则对应于不同表达式．本文证明了这两种表达形式是一致的     

网络最小割计算的一点注记

给出了具有单一源和单一汇网络割的数目,完善了一些文献中的不完整之处.     

关于积域上的粗糙奇异积分算子的一点注记

讨论积域上的奇异积分算子：ＴΩｆ（ｘ,ｙ） ＝ ｐ．ｖ．∫Ｒｎ×ＲｍΩ（ｕ,ｖ）｜ｕ｜ｎ｜ｖ｜ｍ ｆ（ｘ － ｕ,ｙ － ｖ）ｄｕｄｖ的Ｌｐ 有界性,及相应的Ｍａｒｃｉｎｋｉｅｗ ｉｃｚ积分的Ｌ２ 有界性． 其中Ω为类似文［４］中引进的函数类．     

A Note on Sequences with the Shift and Add Property

A sequence of elements from a finite field satisfies the shift and add property if the componentwise sum of any two shifts of the sequence is either a shift of the sequence or the all zero sequence. A sequence whose elements lie in an arbitrary group satisfies the shift and multiply property if the componentwise product of any two shifts of the sequence is either a shift of the sequence or the all identity sequence. The paper classifies sequences which have the shift and add property or the shift and multiply property.     

A Note on Property of Cauchy Integral on Classical Domains

In[1],ZhengXueanprovedthat:letRI(n×n)befirstclassicaldomain,Unbecharacteris-ticboundaryofRI,x∈Un,f(x)∈L2(Un).Asz=rx(0≤r<1)→x,Cauchyintegral∫Unf(y)det(I-zy′)-ndyconvergetoafunctioninL2(Un).Inthispaper,wewillfacusourselfonCauchyintegralofL2onclassicaldomains[2]andgetsomeproperties.Themainresultisfollowing:Theorem　LetRbeoneofclassicaldomains,LbecharacteristicboundaryofR,f∈L2(L),H(z,ξ)beCauchykernelofRandF(z)=∫Lf(u)H(z,u)u　z∈R,(1)wheretherightisLebesgueintegral;uist…     

拟连续Domain与广义完全分配格

本文证明了(1)在合适的态射下,拟连续domain范畴与广义完全分配范畴等价;(2)对有界完备的拟连续domain P,(P,σ(P))为极大极限空间.     

A Note on Maximal Inequality for Stochastic Convolutions

Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution

一种基于Eno-Haar小波变换二维遗传算法

A two-dimensional genetic algorithm of wavelet coefficient is presented by using the ENO wavelet transform and the decomposed characterization of the two-dimensional Haar wavelet.And simulated by the ENO interpolation the article shows the affectivity and the superiority of this algorithm.     

The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg Flat Domains

We study the inhomogeneous conormal derivative problem for thedivergence form elliptic equation, assuming that the principalcoefficients belong to the BMO space with small BMO semi-normsand that the boundary is -Reifenberg flat. These conditionsfor the W^{1, p}-theory not only weaken the requirements on thecoefficients but also lead to a more general geometric conditionon the domain. In fact, the Reifenberg flatness is the minimalregularity condition for the W^{1, p}-theory. 2000 MathematicsSubject Classification 35R05 (primary), 35J15 (secondary).