Finite Derivation Type for Semigroups and Congruences

We consider a congruence ρ on a semigroup S as a subsemigroup of the direct product S × S. We prove that if ρ has finite derivation type (FDT), then so does S.     

Polynomial Basins of Infinity

We study the projection p: M_d ? B_d{\pi : \mathcal{M}_d \rightarrow \mathcal{B}_d} which sends an affine conjugacy class of polynomial f : \mathbbC ? \mathbbC{f : \mathbb{C} \rightarrow \mathbb{C}} to the holomorphic conjugacy class of the restriction of f to its basin of infinity. When B_d{\mathcal{B}_d} is equipped with a dynamically natural Gromov–Hausdorff topology, the map π becomes continuous and a homeomorphism on the shift locus. Our main result is that all fibers of π are connected. Consequently, quasiconformal and topological basin-of-infinity conjugacy classes are also connected. The key ingredient in the proof is an analysis of model surfaces and model maps, branched covers between translation surfaces which model the local behavior of a polynomial.     

Polynomial Trace Estimates for Semigroups

For semigroups (e ^tA ) _t0 of operators on a Hilbert space, we give conditions guaranteeing trace estimates of the polynomial type 0$$ " align="middle" border="0"> , where denotes the trace class. As an application we present higher order analogues of results due to E.B. Davies, B. Simon and M. van den Berg of the type 0$$ " align="middle" border="0"> , for certain unbounded domains , e.g. spiny urchin domains.     

The Full Transformation Semigroups of Finite Rank are Amalgamation Bases for Finite Semigroups

In this article, we prove that the full transformation semigroup on a finite set is an amalgamation base for finite semigroups.     

Mappings of Finite Distortion of Polynomial Type

Suppose f:? ⁿ →? ⁿ is a mapping of K-bounded p-mean distortion for some p>n?1. We prove the equivalence of the following properties of f: the doubling condition for J(x,f) over big balls centered at the origin, the boundedness of the multiplicity function N(f,? ⁿ ), the polynomial type of f, and the polynomial growth condition for f.     

Equational Theories for Classes of Finite Semigroups

It is proved that there exists an infinite sequence of finitely based semigroup varieties such that, for all i, an equational theory for and for the class of all finite semigroups in is undecidable while an equational theory for and for the class of all finite semigroups in is decidable. An infinite sequence of finitely based semigroup varieties is constructed so that, for all i, an equational theory for and for the class of all finite semigroups in is decidable whicle an equational theory for and for the class of all finite semigroups in is not.     

Opial Type Inequalities for Semigroups

Various L_p form Opial type inequalities are given for semigroups with applications.     

Fibers of Polynomial Mappings at Infinity and a Generalized Malgrange Condition

Let f be a complex polynomial mapping. We relate the behaviour of f at infinity to the characteristic cycle associated to the projective closures of fibres of f. We obtain a condition on the characteristic cycle which is equivalent to a condition on the asymptotic behaviour of some of the minors of the Jacobian matrix of f. This condition generalizes the condition in the hypersurface case known as Malgrange's condition. The relation between this condition and the behavior of the characteristic cycle is a partial generalization of Parusinski's result in the hypersurface case. We show that the new condition implies the C-triviality of f.     

On the Monodromy at Infinity of a Polynomial Map, II

To a polynomial map f : Cn + 1 C one can attach a monodromy transformation on the complex cohomology of its generic fiber that reflects its asymptotic behaviour. In this paper this transformation is determined for a class of generic polynomials in terms of data attached to projective hypersurfaces with isolated singularities.     

Finite Nilpotent Semigroups of Small Coclass

The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this article a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are classified. Presentations for all such semigroups and formulae for their numbers are obtained. The classification is provided up to isomorphism as well as up to isomorphism or anti-isomorphism. Commutative and self-dual semigroups are identified within the classification.     

Computing Finite Semigroups, I: The First Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this first part describe the first row of the multiplication table in detail and provide a numerical profile with which it can be compared to other rows.     

扰动双参数C_0半群的直接范数连续性

双参数半群理论是研究Markov过程的一种重要方法.本文首先证明了双参数C_0半群在有界扰动下生成一个双参数C_0半群;其次证明了如果双参数C_0半群是直接范数连续的,那么在有界扰动下生成的双参数C_0半群也是直接范数连续的.     

The Berman Conjecture Is True for Finite Surjective Semigroups and Their Inflations

A semigroup S is called surjective if S ² =S . The aim of this paper is to prove that p _n -sequences of finite surjective semigroups are eventually strictly increasing, except in few well known cases, when they are bounded. Also, some further types of finite semigroups, obtained by means of subdirect products, are shown to have the same property.     

Hille-Yosida算子非线性Lipschitz扰动半群的直接紧性

研究非自反Banach空间中Hille-Yosida算子的非线性Lipschitz扰动半群的直接紧性保持问题.具体地,在非线性Lipschitz半群的框架下,利用外推空间理论,证明非线性扰动半群保持原半群的直接紧性质.获得的研究结果是线性算子半群相应结果的非线性推广.     

Computing Finite Semigroups,II: The First Nonconstant Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this second part assume a left zero element, describe the first nonconstant row of the multiplication table in detail, and provide a numerical profile with which it can be compared to other rows.     

巴拿赫空间的吸引盆及其应用

利用吸引盆为工具,我们把巴拿赫空间的全局同胚问题转化为讨论纯量微分方程解的存在有限性．推广了Hadamard-Levy定理,并应用于区间分析和微分方程,推广了一些现有定理．