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150 159 Chang, S. S. and Cho, Y. J. , The implicit iterative processes for asymptotically nonexpansive mappings, Nonlinear Anal. Appl. 1 (2003), 369

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Abstract  

To find presumed regularities by means of analysing observations on physical phenomena is a problem which frequently arises in calculation practice. An attempt is made to provide a general mathematical formulation of this problem and to connect its occurrence to an effective research strategy. A general calculational approach to the analysis of latent regularities, based on regularized and autoregularized iteration processes for solving non-linear problems, is suggested. Some particular classes of problems are discussed and actual numerical examples are given.

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The central problem of this paper is the question of denseness of those planar point sets \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} \(\mathcal{P}\) \end{document}, not a subset of a line, which have the property that for every three noncollinear points in \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} \(\mathcal{P}\) \end{document}, a specific triangle center (incenter (IC), circumcenter (CC), orthocenter (OC) resp.) is also in the set \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} \(\mathcal{P}\) \end{document}. The IC and CC versions were settled before. First we generalize and solve the CC problem in higher dimensions. Then we solve the OC problem in the plane essentially proving that \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} \(\mathcal{P}\) \end{document} is either a dense point set of the plane or it is a subset of a rectangular hyperbola. In the latter case it is either a dense subset or it is a special discrete subset of a rectangular hyperbola.

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A two-level hierarchic system of fields and subfields of the sciences, social sciences and arts and humanities is proposed. The system was specifically designed for scientometric (evaluation) purposes with the ultimate goal of classifying every single document into a well-defined category. This goal was achieved using a three-step iterative process. The basic concepts and some preliminary results are presented.

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Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979.  The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.

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A large sample INAA (LS-INAA) was conducted based on available experimental conditions. Four different materials, e.g., a quartz-sand and three wastes from an incineration plant were analyzed on sample size of 1 kg. The neutron flux spatial distribution was determined by irradiation of flux monitors in the sample. The gamma-ray apparent counting efficiency was evaluated based on the effective-solid angle concept, using linear attenuation coefficients calculated from an iteration process. The k 0- and the modified monostandard methods were modified for the LS-INAA. To check the LS-INAA performance, a conventional small sample INAA was carried out for the quartz sand and a waste. All detected elements in the LS-INAA are presented and the discussion is conducted to explore the sources of errors in the LS-INAA. As a pilot experiment, the information from this work will be used in constructing irradiation and counting devices for the new FRM-II neutron source in Garching, Germany.

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Physical considerations permit the asymmetry of the photopeak in scintillation γ-spectra to be represented by a second Gaussian peak of lower intensity, accompanying the principal peak. The problem of finding the peak parameters is described as one reduced to solving an over-determined system of non-linear equations, when the numbers of counts in the channels of the analyzer are given. The nature of ill-conditioned linear steps is discussed for the case of solving the problem by Newton's method. A solution procedure based on the regulation of the iteration process is proposed, and the concept of ‘α-approximative solution’ of the given problem is introduced. The calculation procedure is illustrated on actual numerical examples by tables and diagrams, and the possibilities of checking the physical hypothesis and of additional control of the experimental conditions are described.

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