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Abstract  

This paper was inspired by a monograph by Bratteli and Jorgensen, and the work of Kawamura. We introduce two new semigroups: a wide inverse submonoid of the polycyclic inverse monoid, called the gauge inverse monoid, and a Zappa-Szép product of an arbitrary free monoid with the free monoid on one generator. Both these monoids play an important role in studying arbitrary, not necessarily transitive, strong actions of polycyclic inverse monoids. As a special case of such actions, we obtain some new results concerning the strong actions of P 2 on ℤ determined by the choice of one positive odd number. We explain the role played by Lyndon words in characterising these repesentations and show that the structure of the representation can be explained by studying the binary representations of the numbers
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{1} {p},\frac{2} {p}, \ldots \frac{{p - 1}} {p}$$ \end{document}
. We also raise some questions about strong representations of the polycyclic monoids on free abelian groups.
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University Press. The Extended Phenotype. DOISE, W. (1993): Debating Social Representations. In Breakwell, G. M. and Canter, D. (eds

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We are studying the representations of Artin’s braid group B n .

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We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.

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Acta Mathematica Hungarica
Authors:
Shigeki Akiyama
,
Tibor Borbély
,
Horst Brunotte
,
Attila Pethő
, and
Jörg M. Thuswaldner

Summary We are concerned with families of dynamical systems which are related to generalized radix representations. The properties of these dynamical systems lead to new results on the characterization of bases of Pisot number systems as well as canonical number systems.

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flowering of formal phonological theory, which both provoked the rehabilitation of syllable structure in mainstream phonological theory, and led to the introduction of novel hierarchical organisation in autosegmental representations both below and above the

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This study explores the representations of Ottoman interpreters in a number of selected paintings and engravings by western artists. The purpose of the paper is to describe and analyse the position of the interpreter as a political and diplomatic figure within the pictorial composition, basing itself in historical facts about Ottoman interpreters. I will start the paper by a brief discussion on the history of the interpreting profession in the Ottoman Empire and then move on to exploring the paintings where I will touch upon issues such as the traditional costumes, postures and physical positions of interpreters. I will question whether these elements were uniform in different representations by different artists or whether they displayed certain variances.

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We describe the representations of (2, n )-semigroups, i.e., sets with n binary associative operations, by partial n -place functions and prove that any such representation is a union of some family of representations induced by Schein’s determining pairs.

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Abstract

Perceptual learning is the improvement in perceptual task performance with practice or training. The observation of specificity in perceptual learning has been widely associated with plasticity in early visual cortex representations. Here, we review the evidence supporting the plastic reweighting of readout from stable sensory representations, originally proposed by Dosher and Lu (1998), as an alternative explanation of perceptual learning. A task-analysis that identifies circumstances in which specificity supports representation enhancement and those in which it implies reweighting provides a framework for evaluating the literature; reweighting is broadly consistent with the behavioral results and almost all of the physiological reports. We also consider the evidence that the primary mode of perceptual learning is through augmented Hebbian learning of the reweighted associations, which has implications for the role and importance of feedback. Feedback is not necessary for perceptual learning, but can improve it in some circumstances, and in some cases block feedback is also helpful — all effects that are generally compatible with an augmented Hebbian model (Petrov, Dosher and Lu, 2005). The two principles of perceptual learning through reweighting evidence from stable sensory representations and of augmented Hebbian learning provide a theoretical structure for the consideration of issues such as task difficulty, task roving, and cuing in perceptual learning.

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Abstract  

We present several series and product representations for γ, π, and other mathematical constants. One of our results states that, for all real numbers µ s>0, we have

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma = \sum\limits_{k = 0}^\infty {\frac{1} {{(1 + \mu )^{k + 1} }}\sum\limits_{m = 0}^k {\left( {_m^k } \right)} \left( { - 1} \right)^m \mu ^{k - m} S(m),}$$ \end{document}
where S(m) = ∑ k=1 1/2 k +m.

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