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Klaus Barner 《Mathematische Semesterberichte》2011,7(5):13-45
In his papers on the determination of maxima and minima and on the calculation of tangents Pierre Fermat uses two different
Latin verbs, ?quare and ad?quare, which do not differ semantically but are used by him obviously in different meanings. While ?quabitur is used unambiguously in the sense of “is equal” the meaning of ad?quabitur is disputed by the experts since Tannery’s French translation (Œuvres complètes de Fermat, Vol. III, 1896). Herbert Breger (Arch. Hist. Exact Sci. 46, 193–219, (1994), p. 197 f), for instance, holds the view that Fermat used the word ad?quare in the sense of “to put equal” and adds: In a mathematical context, the only difference between “?quare” and “ad?quare” (if there is any) seems to be that the latter
gives more stress on the fact that the equality is achieved. In contrast to this Michael Mahoney holds the thesis that ad?quare describes a counterfactual equality (Mahoney, M.S.: Fermat, Pierre de. In: Dictionary of Scientific Biography, vol. IV (1971), p. 569) or a pseudo-equality (Mahoney, M.S.: The Mathematical Career of Pierre de Fermat (1601–1665), (1973), p. 164), whatever that may mean. This viewpoint has been taken up again recently by Enrico Giusti (Ann. Fac. Sci. Toulouse,
Math. (6), 18 fascicule spécial, 59–85 (2009)) in order to bring arguments to bear against Breger. In contrast to these (and other) authors, I show that Fermat makes
a subtle logical distinction between the words ?quare and ad?quare. The same distinction is made by Nicolas Bourbaki introducing his ?théorie égalitaire?. Notwithstanding: both verbs stand for a ?relation d’égalité?. On this premiss, I describe—using six selected examples—that Fermat’s “method” may be justified right down to the last
detail, even from the view of today’s mathematical knowledge. 相似文献
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近日读到著名经济学家张五常回忆其大学老师的一篇文章 ,引起我的一些思考 .文章说 ,老师让学生花了四个星期的时间自己去研究问题解决的办法 ,但学生们都找不到办法 .第五个星期 ,老师进入课室 ,“在五十分钟内 ,他如长江大河 ,滔滔不绝 ,使我听得呆了 .……”作者说 ,“假若没有经过那四个星期去想 ,我不会在五十分钟之内被老师说服的吧” .虽然故事讲的是大学教学 ,但是 ,我想我们的中学教学中 ,不也存在一个“讲”与“不讲” ,“多讲”与“少讲”的问题吗 ?在“满堂灌”的授课方式受到批评后 ,不少老师又都在培养学生能力的口号下祭起了… 相似文献
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《应用数学和力学》2016,(Z1):1-10
Green energy sources and ocean wind power are plentiful in deep sea. More and more o?shore wind power plants are constructed in the deep water over hundred meters below the surface. While o?shore ?oating wind turbine system is working, wind turbine, ?oating foundation, and mooring system a?ect each other with wind, waves, and currents acting on them. Various o?shore ?oating wind turbine systems and the encoun-tered environmental loads are brie?y reviewed and discussed. It is di?cult and crucial to comprehensively analyze the aerodynamic-hydrodynamic-service system-structure un-der the coupling e?ect of o?shore ?oating wind turbine system. The environmental ?ow ?eld, structure scale, and rational applications of theories and approaches should be well considered in advance. 相似文献
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Georg Tautz 《Archiv der Mathematik》1958,9(4):287-296
Ohne ZusammenfassungHerrn Professor Dr. H.Kneser zum 60. Geburtstag gewidmet 相似文献
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Henrique F. de Lima Ulisses L. Parente 《Bulletin of the Brazilian Mathematical Society》2012,43(1):17-26
In this paper, as suitable application of the so-called Omori-Yau generalized maximum principle, we obtain a Bernstein type
theorem concerning to complete hypersurfaces immersed with constant mean curvature in the product space ℝ × ℍ
n
. Furthermore, we treat the case that such hypersurfaces are vertical graphs. 相似文献
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Victor Camillo 《代数通讯》2013,41(11):3637-3640
As is well known, idempotents in any ring R lift modulo any nil idea I. That is, if a ? R and (a2-a) ? I there is an i ? I with (a + i)2-- (a + i) = 0. An idempotent is a zero of the polynomial x 2?x 2, and a nil element satisfies x nfor some n. Seen this way, lifting occurs in considerable generality We assume R has a unit, and handle the non-unital case at the end of this paper. 相似文献
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Frank Klinker 《Mathematische Semesterberichte》2011,23(2):97-107
In this note we discuss the mathematical tools to define trend indicators which are used to describe market trends. We explain
the relation between averages and moving averages on the one hand and the so called exponential moving average (EMA) on the
other hand. We present a lot of examples and give the definition of the most frequently used trend indicator, the MACD. 相似文献
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An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions: instead of finding the
truly optimal solution, they only provide a stochastic approximation of this optimum. In this paper we look into a particular
application, portfolio optimisation. We demonstrate that the randomness of the ‘optimal’ solution obtained from the algorithm
can be made so small that for all practical purposes it can be neglected. More importantly, we look at the relevance of the
remaining uncertainty in the out-of-sample period. The relationship between in-sample fit and out-of-sample performance is
not monotonous, but still, we observe that up to a point better solutions in-sample lead to better solutions out-of-sample.
Beyond this point there is no more cause for improving the solution any further: any in-sample improvement leads out-of-sample
only to financially meaningless improvements and unpredictable changes (noise) in performance. 相似文献