全稳定Q过程构造的一个等价条件

给出了Q过程构造的等价条件,证明了Q过程的构造等价于一个条件方程组的解,以此方法求出了所有的Q过程、F过程、B过程及BF过程的等价条件。     

THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_?~*(β, A, B), strong and almost spirallike mappings of type βand order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.     

球面区域上buckling特征值的万有估计(英文)

本文研究了球面域上的buckling特征值问题.通过引入新的参数和使用Cauchy不等式,优化了Wang-Xia在文献[12]中的不等式.     

DIMENSIONS OF THE RING OF INVARIANT OPERATORS ON BOUNDED HOMOGENEOUS DOMAINS

Let \[{\cal D}\] be the bounded homogeneous domain, \[G({\cal D})\]be the group of the auto- morphism of \[{\cal D}\]. A differential operator T of (k,l) type is called invariant, if and only if it is commutative with the actions of the \[G({\cal D})\] . The ring of the (k,l) type invariant differential operators is denoted by \[{I_{k,l}}({\cal D})\]. This paper gives a formula for caculating the dimension of \[{I_{k,l}}({\cal D})\]. Obviously, these dimensions are the invarians of \[{\cal D}\] in analytical equivalence, By means 〇f the results in the famous work of A,, Selberg⁴, and applying the theory of group representations, we have proved the following Theorem. \[\dim {I_{k,l}}({\cal D})/\sum\limits_{({k^'},{l^'}) < (k,l)} {{I_{{k^'},{l^'}}}({\cal D})} = \int_K^{} {\cal X} (k,0,...,0)(A)\overline {{\cal X}(k,0,...,0)(A)} \dot A\]K where K is the group formed by the linear parts of the isotropy of \[G({\cal D})\] at \[0 \in {\cal D}\] and \[{{\cal X}(k,0,...,0)(A)}\] is the character of the irreducible representation of the unitary group U(n) with Young index (k, 0, ???, 0). Using this formula, we caculate the dimensions for some concrete cases, including those with the classical symmetric domain, and with a Siegel domain that is not symmetric.     

PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

In this paper,we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains.By the analytical characteristics and distortion results of subclasses of biholomorphic mappings,we conclude that the modified Roper-Suffridge operators preserve the properties of S_Ω~*(β,A,B),almost starlike mapping of complex orderλ on Ω_(n,p2,…,pn).Sequentially,we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order a,strongly pirallikeness of type β and order α,almost starlikeness of order α on Ω_(n,p2,…,pn).The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.     

區域的映照半徑與格林函數

<正> §1.設a_1,a_2是z平面上兩個不同的有限點,G_1和G_2是z平面上不相重疊的兩個單連區域,a_i∈G_i,i=1,2.記R(a_i,G_i)是區域G_i關於a_i真的映照半徑.記     

CONVERGENCE OF CHORIN-MARSDEN FORMULA FOR THE NAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

1.IntroductionDifferentkindsoffractionalstepmethodshavebeenappliedtosolvetheinitialboundaryvalueproblemsoftheNavier--Stokesequationsforviscousincompressibleflow.Thevortexmethoddevelopedin[5]byChorinisaschemewiththreeintermediatestepswheretheeffectsofconvectionandviscosityareseparated,andvortexsheetsarecreatedalongtheboundary.Asetofvortexblobsisintroducedtoapproximatethevorticityfield.Thesevortexblobsmovealongtheparticletrajectoriesintheconvectionstep,andtheymoverandomlyinthediffusionstep.The…     

THE BLOCH CONSTANT OF LOCALLY BIHOLOMORPHIC MAPPINGS ON BOUNDED SYMMETRIC DOMAINS

51.IntroductionIn[11,westudiedtheboundsofBlochconstantofholomorphicmappingsonirreducibleboundedsymmetricdomains.ThispaperisasuccessivepaPerof[1].WestudytheboundsoftheBlochconstantoflocallybiholomorphicmappingsonirreducibleboundedsymmetricdomains.AllthenotationsofthispaPerarethesameasthoseweusedin[1].LetDbeadomain,whichcontainstheorigin.AholomorphicmappingonDisdefinedasaBlochmappingifthefamilyofmappingsFj={g:g(z)=f(rk(z))-j(gh(o)),forallrkEAut(D)},isanormalfamily.TheBlochnormofaBlochmapp…     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。     

L-Fuzzy Domain上的广义Scott拓扑

本文研究了L-fuzzy domain上的广义Scott拓扑,利用[1]中引入的L-fuzzy domain.获得了其上的广义Scott拓扑,它是Domain上Scott拓扑的推广,证明了一个L-fuzzy单调映射是L-fuzzy Scott连续映射当且仅当它关于L-fuzzy domain上的广义Scott拓扑连续.     

ON THE STRUCTURE OF PRIMITIVE RINGS

In this paper the author introduces two concepts, i. e. the concept of so-colled v-socles of primitive rings and the concept of a pair of dual modules. Then the author establishes a general structure theorem for primitive rings with v-socles, which implies the well-known structure theorem for primitive rings with usual non-zero socles.     

WHEN CAN THE STABLE ALGEBRA DETERMINE THE STRUCTURE OF A C^＊-ALGEBRA ？

ＷＨＥＮＣＡＮＴＨＥＳＴＡＢＬＥＡＬＧＥＢＲＡＤＥＴＥＲＭＩＮＥＴＨＥＳＴＲＵＣＴＵＲＥＯＦＡＣ－ＡＬＧＥＢＲＡ？￥ＷＵＬＩＡＮＧＳＥＮＡｂｓｔｒａｃｔ：ＬｅｔＡａｎｄＢｂｅＣ－ａｌｇｅｂｒａｓ．ＳｕｐｐｏｓｅｔｈａｔＫｉｓｔｈｅａｌｇｅｂｒａｏｆａ...     

ON THE ASYMPTOTIC BEHAVIOR OF HOLOMORPHIC ISOMETRIES OF THE POINCARE DISK INTO BOUNDED SYMMETRIC DOMAINS

In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometrics up to normalizing constants with respect to the Bergman metric, showing in particular that the graph 170 of any germ of holomorphic isometry of the Poincar6 disk A into an irreducible bounded symmetric domain Ω belong to C^N in its Harish-Chandra realization must extend to an affinealgebraic subvariety V belong to C × C^N = C^N＋1, and that the irreducible component of V ∩ （△ × Ω） containing V0 is the graph of a proper holomorphic isometric embedding F ： A→ Ω. In this article we study holomorphie isometric embeddings which are asymptotically geodesic at a general boundary point b ∈ δ△. Starting with the structural equation for holomorphic isometrics arising from the Gauss equation, we obtain by covariant differentiation an identity relating certain holomorphic bisectional curvatures to the boundary behavior of the second fundamental form σ of the holomorphie isometric embedding. Using the nonpositivity of holomorphic bisectional curvatures on a bounded symmetric domain, we prove that ‖σ‖ must vanish at a general boundary point either to the order 1 or to the order 1/2, called a holomorphie isometry of the first resp. second kind. We deal with special cases of non-standard holomorphic isometric embeddings of such maps, showing that they must be asymptotically totally geodesic at a general boundary point and in fact of the first kind whenever the target domain is a Cartesian product of complex unit balls. We also study the boundary behavior of an example of holomorphic isometric embedding from the Poincare disk into a Siegel upper half-plane by an explicit determination of the boundary behavior of holomorphic sectional curvatures in the directions tangent to the embedded Poincare disk, showing that the map is indeed asymptotically totally geodesic at a general boundary point and of the first kind. For the metric computation we make use of formulas for symplectic geometry on Siegel upper half-planes.     

关于G逆半群的构造

本文讨论一类重要的半群即Ｇ逆半群,文中给出Ｇ逆半群的主要的几例子,并详尽地讨论了Ｇ逆半群的构造。     

Hamilton半群的结构

每个子半群是左理想的半群，称为左Ｈａｍｉｌｔｏｎ半群，本文给出左Ｈａｍｉｌｔｏｎ半群的刻划，并将左Ｈａｍｉｌｔｏｎ半群表示为有向森林，最后给出左Ｈａｍｉｌｔｏｎ半群同构的充要条件。     

關於區域的映照半徑

<正> §1.設α_1,α_2,…,α_n是z平面上n個相異的點,G_1,G_2,…,G_n是z平面上n個不互相重叠的有限區域,α_k屬於G_k,記G_k對於α_k的映照半徑為     

关于稳定流形的扰动

本文中,M~n 普遍表一紧致的 n 维 C~∞ Riemann 流形,n≧2,(?)(M~n)表 M~n 上所有 C~1 常微系统作成的线性空间.如通常,后者赋以 C~1模‖o‖_1成为一 Banach 空间.任给一系统 S∈(?)(M~n).考虑 S 的一条双曲轨道.这等价于说这轨道在|M~n 中的闭包为 S 的双曲集,特别地,它可以是 S 的双曲奇点或双曲周期轨道.问题.设 S 过一点 c∈M~n 的轨道的 ω-极限集合г_c 与它的一条双曲轨道 P 相交.     

ON THE STRUCTURE OF THE JACOBSON RADICAL OF GRADED RINGS

Abstract

We introduce a new large class of semigroups S including all locally finite, completely regular and strongly π-regular linear semigroups. For any semigroup S in the class and any S-graded ring R, the structure of the Jacobson radical of R is reduced to the radicals of subrings graded by the maximal subgroups of S. Many results on radicals follow from this reduction in a unified way. In two special cases the reduction is simplified.     

c~n中有界强拟凸域上Bergman空间的复合算子

设D是Cn中具有光滑边界的有界强拟凸域,φ:D-D是D的全纯自映射.本文研究D上Bergman空间的复合算子Cφ,通过η-Carleson测度给出Cφ:LηPa(D)-Lηpa(D)(0相似文献