The sharp radius of convexity of the classes consisting of normalized analytic functions f defined in the open unit disk is determined such that the condition | f'/g' -1| < 1 is satisfied in the unit disk f...
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The sharp radius of convexity of the classes consisting of normalized analytic functions f defined in the open unit disk is determined such that the condition | f'/g' -1| < 1 is satisfied in the unit disk fora univalent function g with the quantities zg'(z)/g(z) or 1 +zg''(z)/g'(z) lying in the certain regions of the right-half plane. This, in turn, yields the sharp radius of convexity of the functions f satisfying z f '/ f ? ez and zf'/ f ? z + v1 + z(2) in the unit disk.
Complications arise when ratios are used to present environmental data because ratios are an unbounded, multiplicative scale that can lead to asymmetrical (skewed) data distributions. Enantiomeric ratios (ERs), histor...
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Complications arise when ratios are used to present environmental data because ratios are an unbounded, multiplicative scale that can lead to asymmetrical (skewed) data distributions. Enantiomeric ratios (ERs), historically used in discussions of chiral signatures, often are published as mean ER +/- single-value standard deviation. Application of statistical summaries, such as the widely used sample mean and standard deviation, to skewed ratio data is misleading and often inappropriate. Comparison of statistically summarized ER and enantiomer fraction (EF) data (which are based on a bounded, additive scale) for a range of hypothetical values reveals substantial discrepancies when conversion between ER and EF formats is used. These discrepancies are largest when the ratio data are greater than one and have large variability, because the data are more skewed. In many cases, the use of fractions instead of ratios can help to minimize misrepresentation of environmental data, including chiral data. The use of nonparametric statistical summaries, e.g., median and percentiles, provides a more robust indicator of the typical value and spread for both ER and EF data. (C) 2003 Elsevier Ltd. All rights reserved.
In this paper we develop and derive the computational cost of an -approximation algorithm for a class of global optimization problems, where a suitably defined composition of some ratio functions is minimized over a c...
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In this paper we develop and derive the computational cost of an -approximation algorithm for a class of global optimization problems, where a suitably defined composition of some ratio functions is minimized over a convex set. The result extends a previous one about a class of Linear Fractional/Multiplicative problems.
Papadimitriou and Reiss have independently shown how a rational x = p/q, p, q positive integers with p,q≤N can be found in O(logN) queries of the form 'is x≤y?' We examine some of the algorithmic implication...
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In this short note we comment on the mean-standard deviation ratio problem analyzed recently by Chung (1992) and present an alternative framework for its treatment. It is shown that this problem is just one of the man...
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