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] Erdőos , P. , Some Problems and Results on the Irrationality of the Sum of Infinite Series , J. Math. Sci. , 10 ( 1975 ), 1 – 7 . [4

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Studying groups through their actions on different sets and algebraic structures has become a useful technique to know about the structure of the groups. The main object of this work is to examine the action of the infinite group \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $H = \langle x,y : x^{2} = y^{4} = 1\rangle$ \end{document} where \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $x (z) = \frac{-1}{2z}$ \end{document} and \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $y (z) = \frac{-1}{2(z+1)}$ \end{document} on the real quadratic field \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}\left(\sqrt{n}\,\right)$ \end{document} and find invariant subsets of \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}\left(\sqrt{n}\,\right)$ \end{document} under the action of the group \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $H$ \end{document}. We also discuss some basic properties of elements of \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}\left(\sqrt{n}\,\right)$ \end{document} under the action of the group H.

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half of the figure illustrates the mood compensation pathway to compulsive buying behavior; the lower half illustrates the irrational cognitive pathway Irrational cognitive factors have also been implicated in

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; Yeon, 2006 ), including cognitive error, which is a very critical factor in maintaining gambling behavior. It often allows the prediction of recurring gambling problems. An irrational belief in gambling that leads to winning could also lead to excessive

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way problematic gambling may develop. For example, problematic gamblers are losing or winning players, irrational or rational in their game perception, and their playing styles can be uncontrolled or controlled. It seems that online poker challenges

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Overimitation in the Transmission of Artifact Culture. Philosophical Transactions of the Royal Society B, 366 (1567), 1158–1167. Mak, B. S. K. (2005). Peer Imitation in 4-year-old Children: Rational or Irrational? Paper presented at

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Journal of Behavioral Addictions
Authors: Roser Granero, Fernando Fernández-Aranda, Susana Valero-Solís, Amparo del Pino-Gutiérrez, Gemma Mestre-Bach, Isabel Baenas, S. Fabrizio Contaldo, Mónica Gómez-Peña, Neus Aymamí, Laura Moragas, Cristina Vintró, Teresa Mena-Moreno, Eduardo Valenciano-Mendoza, Bernat Mora-Maltas, José M. Menchón, and Susana Jiménez-Murcia

systematically report relevant cognitive distortions related with the onset of problematic gambling, its maintenance and the difficulty overcoming this dependence. Studies have shown that irrational thoughts are pervasive in most forms of problematic gambling

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Abstract  

We continue the study of sums of the form

\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\limits_{m_j p \leqq x} {Y_{mj} X_p e(\alpha m_j p)} ,$$ \end{document}
begun by Indlekofer and Kátai. Here |Y n|,|X p| ≦ 1 and α is irrational. We prove one conjecture of Kátai, disprove another by both authors, and give what may be a close to best possible result valid for all irrational α.

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Abstract  

We prove that the space C c(X) of the real-valued continuous functions with the compact-open topology is quasi-Souslin iff it is K-analytic. This implies that C c(X) is K-analytic iff it is dominated by the irrationals.

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Creative memory is the dominant feature in the writing process of Nabokov’s prose in general, and that of the novel The Gift in particular. Mnemosyna in Nabokov’s word has many faces, such as memory concrete, creative recollection, mystic-transcendental as well as cultural-reminiscential memory. The concrete memory of an event produces the illusion of lifelikeness; the rest of Mnemosyna’s hypostases weave a magic fabric of artistic endeavour. It can be observed in the specific style of Nabokov’s prose: loyalty to reality of life blended organically with fantasy and irrational-transcendental epiphanies of the artist-demiurge.

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