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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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representations of finite groups , (Springer-Verlag, 1977). Serre J.-P. Linear representations of finite groups 1977

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Dudek, W. A. and Trokhimenko, V. S. , Representations of Menger (2, n )-semi-groups by multiplace functions, Commun. Algebra 34 (2006), 259–274. MR 2194765 Trokhimenko V. S

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Learning pop-out detection: Building representations for conflicting target-distractor relationships Vision Research 38 3095 3107

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. , Some families of hypergeometric polynomials and associated integral representations, J. Math. Anal. Appl. , 294 (2004), 399–411. Srivastava H M Some families of hypergeometric

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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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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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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 1/2k+m.

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