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1.
"无穷小的比较"的现有定义有多种表述形式,但其中不少表述尚不够准确,有失严谨,甚至会导致错误命题的出现.引入"基"概念可使无穷小及无穷小比较的定义更为严谨、简洁、一般化.将无穷小量按含O值点的不同情况分为2类,有利于找出"无穷小的比较"现有定义中存在的问题.通过调整大前提,解决了定义项与被定义项外延不一致的问题;通过转...  相似文献   

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基于无穷级数收敛的必要条件.通过具体例子对几类无穷大量的发散"速度"进行比较研究,得出几个无穷大量发散"速度"由慢到快的排列顺序.  相似文献   

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根据多年工科研究生"应用泛函分析"的教学实践,结合重点课程建设,就工科研究生"应用泛函分析"教学内容、教学方法与教学模式提出几点见解与思考,以期对促进工科研究生"应用泛函分析"的教学起到一定的作用.  相似文献   

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"剪断"湖滨     
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根据常微分方程课程特点及常微分方程的发展,探讨了常微分方程精品课程建设中师资队伍建设和教材改革与建设的重要性,提出了对改革有关教学内容以及编写具有本课程特色的优秀教材的具体设想.  相似文献   

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黄会来 《数学通报》2011,50(1):37-38,41
数学课标中明确提出:"数学教学活动要注重课程目标的整体实现……注重学生对基础知识、基本技能的理解和掌握,引导学生积累数学活动经验、感悟数学思想,关注学生情感态度的发展."近日,笔者参与了"曲边梯形面积的计算"一课的课堂观摩、课后评议和教学再设计的全过程,聆听了市、区数学教研室老师的点评,对本节课如何有效落实教学目标有了更为深入的认识与思考.  相似文献   

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We calculate the ordinal L p index defined in [3] for Rosenthal’s space X p , \({\ell_p}\) and \({\ell_2}\). We show that an infinite-dimensional subspace of L p \({(2 < p < \infty)}\) non-isomorphic to \({\ell_2}\) embeds in \({\ell_p}\) if and only if its ordinal index is the minimal possible. We also give a sufficient condition for a \({\mathcal{L}_p}\) subspace of \({\ell_p \oplus \ell_2}\) to be isomorphic to X p .  相似文献   

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In this paper we give a classification of the orientable regular embeddings of Q_n for n=2m with m odd.Actually we prove that the known examples given by Kwon are the only regular maps of Q_n when n=2m (m odd).  相似文献   

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We study the equation −Δu + u q = 0, q > 1, in a bounded C 2 domain Ω ⊂ ℝ N . A positive solution of the equation is moderate if it is dominated by a harmonic function and σ-moderate if it is the limit of an increasing sequence of moderate solutions. It is known that in the subcritical case, 1 < q <, q c = (N + 1)/(N − 1), every positive solution is σ-moderate [32]. More recently, Dynkin proved, by probabilistic methods, that this remains valid in the supercritical case for q ≤ 2, [15]. The question remained open for q > 2. In this paper, we prove that for all qq c , every positive solution is σ-moderate. We use purely analytic techniques, which apply to the full supercritical range. The main tools come from linear and non-linear potential theory. Combined with previous results, our result establishes a one-to-one correspondence between positive solutions and their boundary traces in the sense of [36].  相似文献   

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Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained.  相似文献   

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We determine the exact order of relative widths of classes W 1 r of periodic functions in the space L 1 as n → ∞ under restrictions on higher derivatives of approximating functions. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1409–1417, October, 2005.  相似文献   

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In this paper, we consider generalized Fibonacci type second order linear recurrence {u n }. We derive a generating matrix for both the sums of squares, ∑ i=0 n u i 2 and the products of the form u n u n+2. We also derive explicit formulas for the sums and products by using matrix methods. Then we give a matrix method to generate the sums of product of two consecutive terms u n u n+1 as well as the product, u n u n+2. Further we give generating functions and combinatorial representations of the sums of squares of terms of {u n } and the product, u n u n+2.  相似文献   

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A subgroup K of G is M p -supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = p α. We study the structure of the chief factor of G by using M p -supplemented subgroups and generalize the results of Monakhov and Shnyparkov by involving the relevant results about the p-modular subgroup O p (G) of G.  相似文献   

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Let F be a finite extension of ℚ p . Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over  [`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL n (F)-representations over  [`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses.  相似文献   

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The aim of this paper is to define the localization LM n -algebra of an LM n —algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM n -algebra of fractions (defined in [3]) and the LM n -algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM n -algebras of localization.  相似文献   

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