IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS

In basic homological algebra,the flat and injective dimensions of modules play an important and fundamental role.In this paper,the closely related I F P-flat and I F P-injective dimensions are introduced and studied.We show that I F P-fd(M) = I F P-id(M +) and I F P-fd(M +)=I F P-id(M) for any R-module M over any ring R.Let IIn(resp.,IFn) be the class of all left(resp.,right) R-modules of IFP-injective(resp.,I F P-flat) dimension at most n.We prove that every right R-module has an IF npreenvelope,(IF n,IF n⊥) is a perfect cotorsion theory over any ring R,and for any ring R with I F P-id(RR) ≤ n,(II n,II n⊥) is a perfect cotorsion theory.This generalizes and improves the earlier work(J.Algebra 242(2001),447-459).Finally,some applications are given.     

微分多项式的Picard集

设 f(z)为超越整函数,F=f~N(N≥3,N 为自然数),设复序列(?)={λ_n)满足|(λ_(n+1))/(λ_n)|>q>1.Anderson,I.M.等人在文[3]中证明了 F′在(?)中取任意非零复数ω∈(?)无限多次,并提出以下两个问题:(a)(?)对整函数能否扩大到含有无穷多个小圆盘?(b)相似的结论对 F=f~nQ[f](Q[f]是 f 的微分多项式)是否也成立?1983年,Langley,J.K.,对 F=f~N 形式将(?)扩大到含有无穷多个小圆盘,从而对(a)作出肯定回答.本文将[1]的结论推广到 F=f~NQ[f]的形式,从而对(b)作出肯定回答.     

REPETITIVE CLUSTER-TILTED ALGEBRAS

Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and C F m be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in C F m and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of C F m , and prove that the tilting graph KCFm of C F m is connected.     

ON THE FIRST KIND OF RELATIVE k-JET COHOMOLOGY OF SINGULARITIES OF MAPGERMS

In this paper the author generalizes the computations about the first kind of k-jetcohomology in[5]to mapgerms.The main results are as follows:H~p(Ω_(,k-.,x))=0,0相似文献   

圆内接三角形的一个性质

设I为△ABC的内心,射线A I、B I、C I与△ABC的外接圆分别交于点D、E、F,EF与AD交于点P,DF与BE交于点M、DE与CF交于点N,则I是△PMN的内心.图1证明连结AF(如图1),∵∠1=∠4,∠2=∠5,∴∠1 ∠2 ∠3=∠4 ∠5 ∠3.∵内心是三角形三条内角平分线的交点,∴∠4 ∠5 ∠3=90°即∠1 ∠2     

综合题新编选登

题 73　 双曲线 x2a2- y2b2 =1(a >0 ,b >0 )的左、右焦点分别为F1,F2 ,点P(x0 ,y0 )是双曲线右支上一点 ,且x0 >2a .I为△PF1F2 的内心 ,直线PI交x轴于Q点 ,若 |F1Q| =|PF2 | ,当a ,b变化时 ,求I分PQ的比λ的取值范围 (见图 1) .解　设双曲线半焦距为c ,则c =a2 +b2 .∵I为PQ的内分点 ,则λ =PIIQ=|PI||IQ| .由内角平分线定理知|PI||IQ| =|PF1||F1Q| =|PF2 ||F2 Q| .又∵ |F1Q| =|PF2 | .∴|PI||IQ| =|PF1||PF2 | ,可得|PI| - |IQ||IQ| =|PF1| - |PF2 ||PF2 | =2a|PF2 | ,|PI||IQ| =|F1Q||F2 Q| ,可得|PI| …     

求解超越方程的n+1信息的2~n阶迭代

设f(x)是实变量的实单值函数,且在零点a的邻域有若干阶连续导数.[1]中概述了用迭代法逼近a的多种方法。并指出多点I.F.(迭代函数)往往可用较少的信息得到较高的敛速.     

极值Beltrami系数的Hamilton序列

考虑了Strebel点与Hamilton序列之间的关系.这个问题是Gardiner F.P.最早研究的(见[Approximation of infinite-dimensional Tcichmiiller spaces,Trans.Amer.Math.Soc.,1984,282(1):367-383]).在无限小Teichmiiller空间中,证明了范金华在[On infinitesimal Teichmüller space,Bull.Austral Math.Soc.,2008,78:293-300]中得到的使{φ_n}成为Hamilton序列的充分条件不是必要的.     

泛函微分方程的循环多步法

其中泛函F:1×C~1(I)×C~0(I)→R,I表示区间[0,T],满足下列条件: A_1.对于给定的x∈C~1(I),映射t→F(t,x(·),x′(·))在I上连续. A_2.算子F满足Lipschitz条件:     

一类特殊分布纪录值之和的中心极限定理

摘要：设{X，Xn,n≥1)为独立同分布的服从某连续分布F的随机变量序列，X^(1)=X1，X^(2),X^(3),…为其纪录值序列．令ψ(u)=F^-1(1-e^-u)．其中F^-1是F的反函数．本文研究当ψ(u)=log^pu时Tn=∑k=1^nX^(k)=^dn∑k=1^nψ(Sn)的极限性质．解决了户为所有正整数时Tn的中心极限定理．     

ADDITIVE FAMILIES OF INVARIANTS OF FORMS OF DEGREE d

Abstract

Let d be a positive integer, and F be a field of characteristic zero. Suppose that for each positive integer n, I _n, is a GL _n,(F)- invariant of forms of degree d in x₁, …, x _n, over F. We call {I _n} an additive family of invariants if I _p+q (f ⊥ g) = I _p(f).I _q(g) whenever f; g are forms of degree d over F in x _l, …, x _p; …, x _q respectively, and where (f ⊥ g)(x _l, …, x _p+q) = f(x ₁, …, x _p,) + g (x _p+1, …, x _p+q). It is well-known that the family of discriminants of the quadratic forms is additive. We prove that in odd degree d each invariant in an additive family must be a constant. We also give an example in each even degree d of a nontrivial family of invariants of the forms of degree d. The proofs depend on the symbolic method for representing invariants of a form, which we review.     

一类pnm阶群的构造

本文研究了一类特殊的pnm阶有限群的构造.利用求解数论同余方程的方法和群的扩张理论,得到了具有m阶循环正规子群,其补子群为循环群的Pnm阶有限群的构造及相关的计数定理.     

COMPARISON OF PRODUCTS OF THE VARIETIES OF LIE ALGEBRAS

Abstract

In Fortes (2001), we introduced a notion of order for associative pairs and we obtained a Goldie-like characterization of left orders in a semiprime pair coinciding with its socle. In this paper, we take up again that notion of order to establish a Faith-Utumi theorem, which studies left orders in a prime pair coinciding with its socle.     

函数集的完全性

1.:敲g(x)篇〔一二,二]上之非降的有界缝差两数,业具有性鬓(K)s‘二一0,一。(:);f--:.,。g。尹(:)!d:一郁匕,(‘一”,”;dg)篇在〔一二,司上定羲业且满足修件:,一{户,(柳dg(·)}青<一,>l的可测蝮值函数族{f(幻}.封龄一徊乙“(一二,侧d刃中之子族凌B(幻},若由f(劣)(乙,(一二,二:dg),夕>1生+上夕q=1,及f--:ha”“’“““’一0纷{B(x)}之任何B(哟成立必滇致f(幻在〔一二,司上规乎虚虚等焚零则释{B(x)}在乙“(一二,侧dg)中完全. 函数族的完全性是舆函数横造的一些简题很有阴保的.徙【l]我们知道{e‘”}豁。是在乙,(一二,州dg),,>1,中完全的,…     

有限Abel群上子集等价类的计数

设G为一有限Abel群，|G|=v,D1,D2是G的两个子集，如果存在t∈Zv,(t,v)=1,s∈G使D1＝tD2 s，则称D1与D2是等价的。文中给出了G的k-子集等价类的计数公式，同时也给出了G的的所有子集等价类的计数公式。     

ESTIMATES OF N-FUNCTION AND m-FUNCTION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS

We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.