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Dong Li CHEN Jing Jing FENG Chun Hui MA .School of Science Xi’an University of Architecture Technology Shaanxi P.R.China .Department of Basic Courses Xi’an Peihua University Shaanxi 《数学研究与评论》2011,31(2)
In this paper,the closeness of the τ-standard part of a set is discussed.Some related propositions of the τ-neighborhood system of a set are given.And then some related conclusions of the τ-monad of a set and the τ-standard part of a set are presented.And based on it,the necessary and sufficient conditions of the enlarged model and the saturated model are showed.Finally,some sufficient conditions that the τ-standard part of a set is closed are proved in the enlarged model and the saturated model. 相似文献
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Ghislain R. Franssens 《Applicable analysis》2013,92(3):333-356
This is the second in a series of two papers in which we construct a convolution product for the set ?′ (R) of associated homogeneous distributions (AHDs) with support in R. In Part I we showed that if f a and g b are AHDs with degrees of homogeneity a ? 1 and b ? 1, the convolution f a * g b exists as an AHD, if the resulting degree of homogeneity a + b?1 ? N. In this article, we develop a functional extension process, based on the Hahn–Banach theorem, to give a meaning to the convolution product of two AHDs of degrees a ? 1 and b ? 1, in the critical case that a + b ? 1 ∈ N. With respect to this construction, the structure (?′(R), *) is shown to be closed. 相似文献
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J. Baylis 《International Journal of Mathematical Education in Science & Technology》2013,44(6):737-752
Following the example designed to encourage an interest in mathematical proof detailed in Part 1, the present part has the aim of easing the learning of the subject. This is done by examples chosen to emphasize the unity of mathematics. Three principles, chosen for their triviality, are mentioned, and each of them is shown to be the basis of non‐trivial proofs of results from quite distinct areas of mathematics. 相似文献
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