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1.
The historical development of Hensel's lemma is briefly discussed (Section 1). Using Newton polygons, a simple proof of a general Hensel's lemma for separable polynomials over Henselian fields is given (Section 3). For polynomials over algebraically closed, valued fields, best possible results on continuity of roots (Section 4) and continuity of factors (Section 6) are demonstrated. Using this and a general Krasner's lemma (Section 7), we give a short proof of a general Hensel's lemma and show that it is, in a certain sense, best possible (Section 8). All valuations here are non-Archimedean and of arbitrary rank. The article is practically self-contained. 相似文献
2.
It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability, and the axiomatic foundations.Received: 6 May 2003, Accepted: 7 July 2003, Published online: 9 December 2003PACS:
05.20.-y, 05.70.-a, 05.90. + m, 65.40.Gr 相似文献
3.
通过对已有补偿问题的模型进行总结,抽象与升华,本文建立了Banach空间中一般形式多阶段有补偿随机规划问题的一个非线性模型,使已有所有的补偿问题均成为其特例;然后利用可测集值映射理论,正规凸的被积函数的性质及文[8」中的结论等,讨论了所给模型的适定性与其基本性质. 相似文献
4.
David Schrittesser 《Proceedings of the American Mathematical Society》2007,135(4):1213-1222
-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .
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Fell topology is very widely used today, even in metric spaces; but J. Fell introduced it in a non-Hausdorff context in the
connection with the theory of C
*-algebras. In spite of this, it has been studied only on the hyperspace of a Hausdorff space, except for the first results
due to Fell himself. The present paper aims to fill this gap, in particular extending some results of H. Poppe and of G. Beer
to the general case.
Project 10251002 supported by National Natural Science Foundation of China. 相似文献
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Epistemological messages conveyed by three high-school and college mathematics textbooks 总被引:1,自引:0,他引:1
Manya Raman 《The Journal of Mathematical Behavior》2004,23(4):389-404
Mathematics textbooks embody a particular set of assumptions about mathematics or the mathematics intended for students at a particular level. Thus, an epistemological analysis of textbooks can provide some context for understanding, for example, the difficulties many students encounter when moving from high-school to collegiate mathematics. In this study, we consider how typical pre-calculus, calculus, and analysis texts treat the topic of continuity. We find that these texts send conflicting messages regarding the status and purpose of mathematical definitions. 相似文献
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