Finite Element Approximation of Conformal Mappings to Unbounded Jordan Domains

In two-dimensional Euclidean space, a simply connected unbounded domain whose boundary is a Jordan curve is called an unbounded Jordan domain. In this article, we discuss a piecewise linear finite element approximation of conformal mappings from the unit disk of the plane to unbounded Jordan domains. Some convergence results and error analysis are presented. Numerical examples are also given.     

多连通域之间的共形映射及其Schwarz导数

证明了扩充复平面C的多连通子区域之间的共形映射的一个分解定理,并利用此定理给出了定义在C的多连通子区域内的单叶全纯函数的双曲上确界范数的一致有界性的一个简单证明.     

有界凸域上拟共形映射的Holder连续性

该文利用曲线族的模,得到了n维空间中的有界凸域 D 到单位球 Bⁿ上的 K -拟共形映射f的全局Holder连续性, 且Holder指数α=K^1/(1-n)是最佳的.     

外部边界球可达域上拟共形映射的Lipschitz连续性

定义了外部边界球可达域,利用曲线族的模获得如下结果:设D是R~n中的有界拟凸域,f:D→B~n是K-拟共形映射,若D是外部边界球可达域,则f∈Lip_α(D),其中α=K~(1/(1-n)).     

On Secondary Modules over Dedekind Domains

The aim of this paper is to classify the indecomposable secondary modules over local dedekind domains and to establish a connection between the indecomposable secondary modules and the indecomposable pure-injective modules over such domains.     

On Jordan Triple Derivations and Related Mappings

In this article we study certain functional equations and systems of functional equations related to (generalized) derivations on semiprime rings. In particular, we prove that any generalized Jordan triple derivation on a 2- torsion free semiprime ring is a generalized derivation. We also prove that any (generalized) Jordan triple *-derivation on a 2-torsion free semiprime *-ring is a (generalized) Jordan *-derivation. The second author was supported in part by the Ministry of Science, Education and Sports of the Republic of Croatia (project No. 037-0372784-2757).     

On Jordan Triple Higher Derivable Mappings on Rings

Let R be a ring and \({\mathbb{N}}\) be the set of all non-negative integers. A family of maps \({D=\{d_n\}_{n \in\mathbb{N}}}\) is said to be Jordan triple higher derivable if \({d_n(aba)=\sum \nolimits_{p+q+r=n} d_p(a)d_q(b)d_r(a)}\) holds for all \({a,b \in R}\), where d ₀ = I _R , (the identity map on R). In this paper, we determine Jordan triple higher derivable map on a ring R, which contains a nontrivial idempotent which is automatically additive. An immediate application of our main result shows that every Jordan triple higher derivable map becomes higher derivation on R.     

内部边界球可达域和拟共形映射的H(o)lder连续性

定义了内部边界球可达域,利用曲线族的模证明了D是Rn中的有界Jordan域,f:Bn→D是K-拟共形映射,若D是内部边界球可达域,则f∈H1/K(Bn).     

On the Banach-Steinhaus Theorem and the Continuity of Bilinear Mappings

In this paper, the BANACH-STEINHAUS theorem is extended from its usual locally convex topological vector space setting to the much broader framework of convergence vector spaces. It is used to derive theorems yielding the joint continuity of separately continuous bilinear mappings. These results are used, in turn, to show that the convolution mapping ?? is a jointly continuous bilinear mapping when the distribution spaces ? and ?? carry the canonical convergence vector space structures.     

Jordan Modules and Jordan Ideals of Reflexive Algebras

Let ${\mathcal{L}}$ be a completely distributive subspace lattice on a Banach space and alg ${\mathcal{L}}$ the associated reflexive algebra. Suppose that the following $$\mbox{Condition A:}\dim(F/F\wedge F_-)\ne1\;\; \mbox{for all}\;\;F\in\mathcal{L}$$ holds; note that if ${\mathcal{L}}$ is an atomic Boolean subspace lattice, this condition means that every atom of ${\mathcal{L}}$ has dimension at least two. It is shown that every reflexive Jordan Alg ${\mathcal{L}}$ -module is an associative Alg ${\mathcal{L}}$ -module. We give an example which shows that if the Condition A is removed, then the conclusion is not necessarily true. Moreover, we prove that all reflexive Jordan ideals of Alg ${\mathcal{L}}$ are associative ideals in the case that no the Condition A is assumed. The same conclusions hold for weakly closed Jordan modules and weakly closed Jordan ideals if the rank one subalgebra of Alg ${\mathcal{L}}$ is weakly dense in Alg ${\mathcal{L}}$ .     

Concave Shells of Continuity Modules

Ukrainian Mathematical Journal - We prove the inequality$$ \overline{\omega}(t)\le \underset{s>0}{\operatorname{inf}}\left(\omega \left(\frac{s}{2}\right)+\frac{\omega (s)}{s}t\right), $$...     

Jordan Homomorphisms and Harmonic Mappings

 We show that each Jordan homomorphism R → R′ of rings gives rise to a harmonic mapping of one connected component of the projective line over R into the projective line over R′. If there is more than one connected component then this mapping can be extended in various ways to a harmonic mapping which is defined on the entire projective line over R. Received December 7, 2001; in revised form April 28, 2002 Published online January 7, 2003     

拟共形映射和Plump域

设fL:Rn→Rn是一同胚,证明了f是K-拟共形映射当且仅当对任给的常数c≥1,存在c*≥1,使得任一 c-Plump域在f下的像是c*-Plump域.其中在必要性中c*=c*(n,K,c)是仅与n,K和c有关的常数,在充分性中K=K(n,c,c*)是仅与n,c和c*有关的常数.     

拟共形映射与John域

本证明了有界一致域必定是Hohn域和Jphn域的拟共不变性．     

集值映射的可测性与连续性

引进《集D关于集β对于关系《是正常的》这个概念,由两个单值映射组成,再通过取凸包和闭包,构造了可测集值映射、上下半连续集值映射和连续集值映射.     

Conformal Conjugacies in Baker Domains

Let F be a meromorphic function in the complex plane. We investigatethe behaviour of the iterates of F in a Baker domain B. In particular,we describe the dynamics of the orbits with the help of conformalconjugacies; that is, we determine a function which is univalentin a large simply connected subdomain of B such that (F(z))=T((z))holds throughout B. Here T is either a parabolic or hyperbolicMöbius transformation mapping either a half plane or Conto itself. This functional equation is always solvable ina Baker domain if F has only finitely many poles. Moreover,there is an example of a function with infinitely many poleswhere one cannot find an appropriate conformal conjugacy inan invariant Baker domain.