弱Hopf代数的扭曲理论

本文研究了弱Hopf代数的扭曲理论的对偶问题.利用了弱Hopf代数上的弱Hopf双模的(辫子)张量范畴与扭曲弱Hopf代数上的弱Hopf双模的(辫子)张量范畴等价方法,得到Long模范畴是Yetter-Drinfel'd模范畴的辫子张量子范畴.推广了Oeckl(2000)的结果.     

THE RADICALS OF HOPF MODULE ALGEBRAS

ＴＨＥＲＡＤＩＣＡＬＳＯＦＨＯＰＦＭＯＤＵＬＥＡＬＧＥＢＲＡＳＺＨＡＮＧＳＨＯＵＣＨＵＡＮ＊ＡｂｓｔｒａｃｔＴｈｅｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＨ－ｐｒｉｍｅｒａｄｉｃａｌｉｓｇｉｖｅｎｉｎｍａｎｙｗａｙｓ．Ｍｅａｎｔｉｍｅ，ｔｈｅｒｅｌａｔｉ...     

HOPF代数的右伴随作用构造的上循环模(英文)

本文研究了上循环模,对于特征为O的域k上满足S~2=id_H的Hopf代数H,和左H-模代数A,利用日的右伴随作用以及H在A上的模作用,构造了上循环模(C)_H~#(A),并且证明了由H的右伴随作用和左伴随作用分别诱导的上循环模(C)_H~(#)(A)和(C)_H~(#)(A)足同构的.     

弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.     

Smash积代数和量子模范畴中的Hopf代数的新对偶

本文引入模代数的一种新对偶,它推广了代数的有限对偶概念,并证明:通过这种新对偶,模代数的对偶为余模余代数,从而形成Smash余积,而且证明了Smash积的对偶是Smash余积,即有(A#H)~0 _HA~0×H~0余代数同构,最后证明量子模范畴中的Hopf代数通过这种新对偶是自对偶的。     

THE HOPF BIFURCATION OF QUADRATIC SYSTEM (I)_(n=0)

δlm is the parameter space of quadratic system (I)n=0. A partition of parameters corresponding to the existence and nonexistence of the limit cycle of the system is given in detail. The Hopf bifurcation surfaces of (I)m=0 are obtained, and the sketch of Hopf bifurcation surfaces of (I)n=0 are drawn.     

与广义Baouendi-Grushin算子相关的二阶退化椭圆方程的Hopf型引理

本文研究与广义Baouendi-Grushin(B-G)算子相关的二阶退化椭圆方程.利用广义B-G向量场的拟齐性质建立了相关的拟齐度量,证明了与广义B-G算子相关的退化椭圆方程的Hopf型引理,并给出了有关应用及推广.     

ERROR ESTIMATES FOR THE RECURSIVE LINEARIZATION OF INVERSE MEDIUM PROBLEMS

This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, Inverse Problems 13（1997）, pp.253-282] is established for solving the acoustic inverse scattering problem.     

Chemostat系统中Hopf分支的存在性

本文应用Hopf分支理论研究了具有内在代谢形式的Chemostat系统存在Hopf分支的条件,同时得到周期解的存在性及稳定性的结果.     

正则乘子Hopf代数上Yetter-Drinfel'd模范畴中的自同构代数

本文研究了正则乘子Hopf代数上Yetter-Drinfel''d模范畴中自同构代数的问题.利用乘子Hopf代数以及同调代数理论中的方法,获得了Yetter-Drinfel''d模范畴中两个自同构代数是同构的结果,推广了Panaite等人在Hopf代数中的结果.     

找约束方程组最佳解的递推算法

本文利用关于Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆的Ｇｒｅｖｉｌｌｅ算法及其有关参数的性质，导出了找约束方程组Ａｘ＝ｂ，ｘ∈Ｔ最佳解的两类递推算法，其中后者是与求解通常线性方程组的ＡＢＳ算法类似的。     

THE BLOSSOM APPROACH TO THE DIMENSION OF THE BIVARIATE SPLINE SPACE

1. IntroductionLet fi C mZ be a closed simply connected polygonal region, andA:~ {fit}!=,, fi = .6 fitz= 1its regular triangulation, i.e. the trianglesfit, ioj, i / i,can have in common only a vertex or a whole edge. Let V de'note the set of innervenices, E the set of inner edges, and E the set of all edges of a. PutmV:= IVI, mE:~ IEI.The planar graph G:~ (V, E) clearly describes A. However, it's sometimes useful toconsider also the dual planar graph Q:= (V,e), where venices i E V co…     

A RIEMANN-HILBERT APPROACH TO THE INITIAL-BOUNDARY PROBLEM FOR DERIVATIVE NONLINEAR SCHRODINGER EQUATION

We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit （x, t） dependence, and it has jumps across {ξ∈C｜Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a（ξ）, b（ξ）}, {A（ξ）, B（ξ）}, and {A（ξ）, B（ξ）}, which in turn are defined in terms of the initial data q0（x） = q（x, 0）, the bound- ary data g0（t）= q（0, t）, g1（t） = qx（0, t）, and another boundary values f0（t） = q（L, t）, f1（t） = qx（L, t）. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.     

Cayley-Bacharach定理在沿平面代数曲线插值问题中的应用

1 引 言 本文是讨论关于沿平面代数曲线的Lagrange插值问题,该问题与在二维实平面R~2上的二元Lagrange插值有关.设n为非负整数并且e_n=1/2(n+1)(n_2).P_n代表所有全     

A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS

The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.     

指数分布场合下加速寿命试验的Bayes方法

当寿命分布为指数分布时,本文用Bayes方法对由恒定或步进应力加速寿命试验得到的数据进行统计分析,得到了满足顺序约束的参数的估计,模拟结果表明这个方法较好。     

球面稳定同伦群中的一个新元素族b1g0(γ)s

设P≥7素数,A为模P的Steenrod代数．我们利用Adams谱序列证明了球面稳定同伦群π*S中,存在由所表示的新的非平凡元素族,其中q=2(p-1),3≤s相似文献   

A note on recursive completions of the countable atomless Boolean algebras

The Baire category theorem for compact Hausdorff spaces is used to show that any recursive completion ℬ^ϕof the countable atomless Boolean algebra ℬ is ℬrecursively closed." Also, a theorem of R.D. Anderson on the simplicity of Aut(ℬ) is used to show that uncountably many automorphisms of ℬ extend to ℬ^ϕ. This revised version was published online in June 2006 with corrections to the Cover Date.     

ON THE SUFFICIENT CONDITION FOR A CONVEX DOMAIN TO CONTAIN ANOTHER IN R_(2n)

1IntroductionandSomeLemmasInplalle,tileclassicalresultsontilesufficielltcollditiolll'oradonlailltocontaillallotherareobtainedinH.Hadwiger's['t,]first.Renobtaillstileeqllivalentformwhichisllloresilllplein[1],i.e.,TheoremLetDoandDIbethedomainsboulldedbythes…