Computable Carathéodory Theory

The conformal Riemann mapping of the unit disk onto a simply-connected domain W is a central object of study in classical Complex Analysis. The first complete proof of the Riemann Mapping Theorem given by P. Koebe in 1912 is constructive, and theoretical aspects of computing the Riemann map have been extensively studied since. Carathéodory Theory describes the boundary extension of the Riemann map. In this paper we develop its constructive version with explicit complexity bounds.     

Semilattice decompositions of semigroups

The purpose of this paper is to develop a general theory of semilattice decompositions of semigroups from the point of view of obtaining theorems of the type: A semigroup S has propertyD if and only if S is a semilattice of semigroups having property β. As such we are able to extend the theories of Clifford [3], Andersen [1], Croisot [5], Tamura and Kimura [14], Petrich [9], Chrislock [2], Tamura and Shafer [15], Iyengar [7] and Weissglass and the author [10]. The root of our whole theory is Tamura's semilattice decomposition theorem [12, 13]. Of this, we give a new proof. The results of this paper were obtained by the author between January and July of 1971, while an undergraduate at the University of California, Santa Barbara.     

交换半群的强半格

本文刻划交换半群的强半格上的最小半格同余，并证明由此得到的商半群为对应的每个交换半群的商半群的强半格。     

Semilattice composition of ordered semigroups

We study the semilattice composition of ordered semigroups (a concept opposite to that of the semilattice decomposition), using the ideal extensions. The text was submitted by the authors in English.     

正则带的半格结构

Petrich解决了一般带的构造定理（见[1]或[2]），在此基础上，我们将证明正则带（满足等式axya=axaya的带）的一些特征，并给出一个带为正则带或右似正规带（满足等式xya=xaya的带）的充分必要条件，这些结果是Yamada和Kimura的关于正规带（满足等式axya=ayxa的带）的结果的推广，正规带被他们描述为矩形带的强半格（见[1]或[3]）。     

The Stone-Cech Compactification of a Semilattice

We study properties of particular right topological semigroups, namely the Stone-Cech compactifications of semilattices. In particular, we extend some of the results of Grainger's paper on the Stone-Cech compactification of the semilattice of finite subsets of an infinite set.     

半格与Domain的表示

引入一种半格———Ｄ 半格，建立了Ｄ－半格的表示理论，利用它得到了Ｌ ｄｏｍａｉｎ（即局部代数格）的表示理论；证明了Ｌ ｄｏｍａｉｎ与稳定映射范畴对偶等价于稳定Ｄ 半格与Ｄ－半格同态范畴．     

群的正则带的KG-强半格分解

推广了著名的Petrich的完全正则半群为群的正规带当且仅当它为完全单半群的强半格的结果，证明了完全正则半群为群的正则(或右拟正规)带当且仅当它是完全单半群的HG(LG)-强半格．     

Semilattice transversals of regular bands I

Every regular band can be isomorphically embedded into a regular band which has a semilattice transversal. The latter constitute the variety of regular split bands, whose subvariety lattice is isomorphic to the lattice of regular band varieties.     

Computable Linearizations of Well-partial-orderings

We analyze results on well-partial-orderings from the viewpoint of computability theory, and we answer a question posed by Diana Schmidt. We obtain the following results. De Jongh and Parikh showed that every well-partial-order has a linearization of maximal order type. We show that such a linearization can be found computably. We also show that the process of finding such a linearization is not computably uniform, not even hyperarithmetically.     

Derivatives of Computable Functions

As is well known the derivative of a computable and C¹ function may not be computable. For a computable and C∞ function f, the sequence {f⁽ⁿ⁾} of its derivatives may fail to be computable as a sequence, even though its derivative of any order is computable. In this paper we present a necessary and sufficient condition for the sequence {f⁽ⁿ⁾} of derivatives of a computable and C^∞ function f to be computable. We also give a sharp regularity condition on an initial computable function f which insures the computability of its derivative f′.     

A Dedekind Criterion over Valued Fields

Siberian Mathematical Journal - Let $ (K,nu) $ be an arbitrary-rank valued field, let  $ R_{nu} $ be the valuation ring of  $ (K,nu) $ , and let  $ K(alpha)/K $ be...     

Semilattice transversals of regular bands II

A band is a regular band if and only if it can be embedded into a band in which every element belongs to a semilattice transversal.     

左$C$-Wrpp 半群的加细半格结构

本文研究了左$C$-wrpp半群的加细半格结构,证明了左$C$-wrpp半群是左-${cal R}$可消带的加细半格当且仅当它是一个$C$-wrpp半群和一个左正则带的织积.