منابع مشابه
Basic Properties of Even and Odd Functions
In this paper x, r are real numbers. Let A be a set. We say that A is symmetrical if and only if: (Def. 1) For every complex number x such that x ∈ A holds −x ∈ A. Let us note that there exists a subset of C which is symmetrical. Let us observe that there exists a subset of R which is symmetrical. In the sequel A denotes a symmetrical subset of C. Let R be a binary relation. We say that R has s...
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We solve the problem of finding optimal entire approximations of prescribed exponential type (unrestricted, majorant and minorant) for a class of truncated and odd functions with a shifted exponential subordination, minimizing the L1(R)-error. The class considered here includes new examples such as the truncated logarithm and truncated shifted power functions. This paper is the counterpart of t...
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Aliphatic polyamides derived from odd diamine or odd dicarboxylic acid units cannot adopt a conventional sheet structure when molecular chains have an all trans conformation. However, typical fiber diffraction patterns of this sheet structure were observed in several polyamides derived from odd units such as nylons 65 and 56. Consequently, a new structure based on the establishment of intermole...
متن کاملAbsolute testing of flats by using even and odd functions.
We describe a modified three-flat method. In a Cartesian coordinate system, a flat can be expressed as the sum of even-odd, odd-even, even-even, and odd-odd functions. The even-odd and the odd-even functions of each flat are obtained first, and then the even-even function is calculated. All three functions are exact. The odd-odd function is difficult to obtain. In theory, this function can be s...
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The celebrated odd-even exchange algorithm by Batcher provides the quantity average number of exchanges, which was a mystery a few years ago and is still tricky today. We provide an approach that is purely based on generating functions to provide an explicit expression. The asymptotic analysis was done several years ago but never published in a journal and is thus provided here. It is a combina...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2003
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700003086