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非ε-极限理论与微积分的教学改革 总被引:2,自引:0,他引:2
讨论了由第一作者提出的“非ε-极限理论”,它所提出的缘由、理论体系 ,它的合理性 ,它所需要加以解决的问题及其改进方案 .同时 ,还介绍了第二作者根据这种理论编写的教材《新微积分学》及其在教学中的实践效果 . 相似文献
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极限概念是数学分析理论的基础,贯穿数学分析教学的始终,在数学分析的理论体系中占有十分重要的地位.由于极限概念的严谨性和抽象性,在教学实践当中发现学生对极限概念难以理解.本文借助Matlab软件的图形处理功能,将数列极限,一元函数极限以及多元函数极限的形成过程展示出来,从而强化学生对极限概念的理解. 相似文献
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极限概念是数学分析理论的基础,贯穿数学分析教学的始终,在数学分析的理论体系中占有十分重要的地位.由于极限概念的严谨性和抽象性,在教学实践当中发现学生对极限概念难以理解.本文借助Matlab软件的图形处理功能,将数列极限,一元函数极限以及多元函数极限的形成过程展示出来,从而强化学生对极限概念的理解. 相似文献
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一、教学目标
1.通过具体例子使学生感到需要引入一种新的定义——极限,能初步理解极限的定义.
2.运用文字、图形、符号语言表述数列的极限,领略无限逼近的思想.
3.能用极限的观点看问题——不能立刻做到,可以慢慢靠近,要有锲而不舍的“极限精神”.
二、教学重点
初步理解极限定义,能解答简单问题.
三、教学难点
通过图形语言,加深对数列的极限的描述性定义的理解,逐步过渡到用符号语言表述定义. 相似文献
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ISO2859是国际标准<计数抽样检查程序及表>的代号, GB2828是国家标准<计数抽样检查程序及抽样表>的代号。从单纯用于连续提交批的调整型抽样检查方案来说,它们是基本一致,大同小异。但若全面比较两个标准,需注意下列一些差别。 一、设计思想的差别 ISO-2859主要是设计为连续提交批的调整型抽样方案。但也为孤立批的标准型方案(或极限质量LQ方案)和挑选型抽样方案的使用提供了一些辅助数据。就是表V-平均检出质量上限系数,表Ⅵ-极限质量Pa=10%和表Ⅻ-极限质量 Pa= 5%。 GB2828则是只适用连续提交批的调整型抽样方案,因此,没有上述三组… 相似文献
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《Annals of Pure and Applied Logic》2022,173(10):103143
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete for all intermediate inquisitive and dependence logics. To this end, we define inquisitive and dependence algebras and we investigate their model-theoretic properties. We then focus on finite, core-generated, well-connected inquisitive and dependence algebras: we show they witness the validity of formulas true in inquisitive algebras, and of formulas true in well-connected dependence algebras. Finally, we obtain representation theorems for finite, core-generated, well-connected, inquisitive and dependence algebras and we prove some results connecting team and algebraic semantics. 相似文献
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信用传染违约Aalen加性风险模型 总被引:1,自引:0,他引:1
本文考虑了基于加性风险模型的信用风险违约预报模型,不但考虑了宏观因素和公司个体因素,并且通过引入行业因素来刻画公司间可能存在的不同于宏观因素的信用传染效应,由此克服了以往模型对违约相关性的低估.本文在参数加性风险模型下给出极大似然估计及渐近性,提出两种估计方法并比较二者表现,得到最优权估计更加有效.同时本文还考虑了半参数的风险模型,并基于鞅的估计方程得到其估计及渐近性,均得到不错的结果. 相似文献
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Optimal control of nonlinear evolution inclusions 总被引:1,自引:0,他引:1
N. S. Papageorgiou 《Journal of Optimization Theory and Applications》1990,67(2):321-354
In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688. 相似文献
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In this research, we develop and introduce a theoretical and mathematical forecasting framework of immigrant integration using immigrant density as a single driver. First, we introduce the integration concepts we aim at forecasting. Thereafter, we introduce a theoretical and mathematical model of the relationship between integration and immigrant density. Based on this model, we develop a methodological forecasting framework. We test the framework using immigrant integration data from Spain. We produce the forecasts, and conduct the proper evaluation of them. Finally, we conclude with a brief discussion of the wider implications of our results. 相似文献
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We wish to explore all edges of an unknown directed, strongly connected graph. At each point, we have a map of all nodes and edges we have visited, we can recognize these nodes and edges if we see them again, and we know how many unexplored edges emanate from each node we have visited, but we cannot tell where each leads until we traverse it. We wish to minimize the ratio of the total number of edges traversed divided by the optimum number of traversals, had we known the graph. For Eulerian graphs, this ratio cannot be better than two, and two is achievable by a simple algorithm. In contrast, the ratio is unbounded when the deficiency of the graph (the number of edges that have to be added to make it Eulerian) is unbounded. Our main result is an algorithm that achieves a bounded ratio when the deficiency is bounded. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 265–297, 1999 相似文献
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ngela Jimnez‐Casas 《Mathematical Methods in the Applied Sciences》2019,42(18):6791-6809
Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed‐loop thermosyphons even when we consider binary fluids, this is, when we consider a solute in the fluid, as water and antifreezes, for example. In this work, we consider a linear friction law, and we show that in this case with the addition of a solute to the fluid we can prove, under some conditions, chaotic asymptotic behavior for suitable geometry of the circuit and heat flux or ambient temperature functions. 相似文献
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Antonella Fiacca Nikolaos Matzakos Nikolaos S. Papageorgiou Raffaella Servadei 《Proceedings Mathematical Sciences》2001,111(4):489-508
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities.
First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is
defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between
them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed
by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This
case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that
the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity.
Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial
solutions (multiplicity theorem). 相似文献
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《Journal of Pure and Applied Algebra》2023,227(4):107249
If every subring of an integral domain is atomic, we say that the latter is hereditarily atomic. In this paper, we study hereditarily atomic domains. First, we characterize when certain direct limits of Dedekind domains are Dedekind domains in terms of atomic overrings. Then we use this characterization to determine the fields that are hereditarily atomic. On the other hand, we investigate hereditary atomicity in the context of rings of polynomials and rings of Laurent polynomials, characterizing the fields and rings whose rings of polynomials and rings of Laurent polynomials, respectively, are hereditarily atomic. As a result, we obtain two classes of hereditarily atomic domains that cannot be embedded into any hereditarily atomic field. By contrast, we show that rings of power series are never hereditarily atomic. Finally, we make some progress on the still open question of whether every subring of a hereditarily atomic domain satisfies ACCP. 相似文献
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本文首先对IPA算法进行了修正,并证明了修正IPA算法的收敛性,然后将修正后的IPA应用到不等式约束凸优化问题中得到新的内点算法,并与传统的障碍函数法作了比较,从理论上体现了新算法的优势,并给出了其工程解求解法以及收敛性的证明. 相似文献
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This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First, we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors' preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally, we show how we can use risk measures and orderings consistent with some preferences to determine the investors' optimal choices. 相似文献