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1.
Yuxue Liang 《中学生数学》2009,(10):F0004-F0004
We know the first important limit is lim x→0 sinx/x=1, and the second important limit is lim n→∞ (1+1/n)^n=e. Although it is more important and useful than the first one, it is still named "the second important limit" because it was discovered after the first one.  相似文献   

2.
It is known that for second order linear equations the assumption of limit circle (all solutions being square integrable) is not sufficient to imply boundedness of solutions. We investigate what additional hypotheses are needed to insure that all solutions are bounded. Also, we prove certain limit circle results using Liapunov functions.  相似文献   

3.
The earlier-developed approach to the solution of the problem of estimating the number of limit cycles and their localization for autonomous systems on the plane with the use of Dulac and Poincaré auxiliary functions is generalized to autonomous systems of differential equations with cylindrical phase surface.  相似文献   

4.
The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.  相似文献   

5.
In the repair limit replacement method when an item requires repair it is first inspected and the repair cost is estimated. Repair is only then undertaken if the estimated cost is less than the "repair limit". Dynamic programming methods are used in this paper as a general approach to the problem of determining optimum repair limits. Two problems are formulated and the cases of finite and infinite planning horizons and discounted and undiscounted costs are discussed. Methods are given for allowing for equipment availability and for the introduction of new types of equipment. An improved general formulation for finite time horizon, stochastic, dynamic programming problems is developed.  相似文献   

6.
论极限教学的解决方案   总被引:5,自引:1,他引:5  
王庚 《大学数学》2004,20(3):54-58
首先探讨了极限ε语言的思维复杂性,接着介绍了种种极限教学方案以及笔者自身的实践,在回顾微积分的历史和比较各种方案后,根据教育学原理提出了一种新的极限教学的组合方案.  相似文献   

7.
8.
This paper considers a single unit system which is first repaired if it fails. If the repair is not completed up to the fixed repair limit time then the unit under repair is replaced by a new one. The cost functions are introduced for the repair and the replacement of the failed unit. The optimum repair limit replacement time minimizing the expected cost per unit of time for an infinite time span is obtained analytically under suitable conditions. Two special cases where the repair cost functions are proportional to time and are exponential are discussed in detail with numerical examples.  相似文献   

9.
本文主要阐明概率论中三个重要分布之间的关系 ,重点证明了普阿松分布的极限分布是正态分布  相似文献   

10.
极限与商群     
刘蔚萍 《大学数学》2021,37(5):90-93
基于代数系统理论,证明了函数极限相等是一个等价关系、同余关系.并证明了极限存在的一元函数集合A的代数系统(A,±)是一个群,商代数(A/R,±)是一个商群.  相似文献   

11.
Statistical Limit Superior and Limit Inferior   总被引:4,自引:0,他引:4  
Following the concept of statistical convergence and statistical cluster points of a sequence , we give a definition of statistical limit superior and inferior which yields natural relationships among these ideas: e.g., is statistically convergent if and only if . The statistical core of is also introduced, for which an analogue of Knopp's Core Theorem is proved. Also, it is proved that a bounded sequence that is -summable to its statistical limit superior is statistically convergent.

  相似文献   


12.
Let (M,g) be a compact Riemannian manifold of dimension n?3. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to g and of volume 1. We study when it is attained. As an application, we find nodal solutions of the Yamabe equation.  相似文献   

13.
The inverse of the well-known Brauer formula is given, which is a consequence of his second main theorem. The formula can be applied to an evaluation of values of characters of local subgroups. Moreover, if b is a block of CG(), B is a block of a group G, then a method is found to check the equality bG=B.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 6, pp. 736–741, June, 1992.  相似文献   

14.
本文考虑生物网络中一类复制模型度分布的极限性质.利用组合知识和概率论中鞅方法,讨论了度分布的大数定律和中心极限定理,为生物学家研究生物内部系统机制提供理论基础.  相似文献   

15.
We derive the infinite-genus limit of the KdV–Whitham equations based on the special scaling of the spectral curve introduced by Venakides in the study of the continuum limit of theta functions. The limit describes evolution of the integrated density of states in a one-dimensional soliton gas.  相似文献   

16.
The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr?hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar–Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum P, provided P is not too large. Tadahiro Miyao: This work was supported by Japan Society for the Promotion of Science (JSPS). Permanent address: The graduate school of natural science and technology, Okayama university, Okayama 700-8530, Japan. Submitted: December 14, 2006. Accepted: March 20, 2007.  相似文献   

17.
函数列的黎曼积分极限定理的应用   总被引:3,自引:0,他引:3  
利用函数列的极限理论方法,研究函数列积分极限中积分和极限可交换次序的问题.对一致收敛的可积函数列给出积分的极限定理,对一致有界局部一致收敛函数列给出积分控制收敛定理,通过大量实例表明该理论的意义所在.  相似文献   

18.
19.
Let $f,g$ be two closed $k$ -forms over $\mathbb{R }^{n}.$ The pullback equation studies the existence of a diffeomorphism $\varphi :\mathbb{R }^{n} \rightarrow \mathbb{R }^{n}$ such that $$\begin{aligned} \varphi ^{*}(g)=f. \end{aligned}$$ We prove two types of results. The first one sharpens some of the existing regularity results. The second one discusses the possibility of choosing the map $\varphi $ as the gradient of a function $\Phi :\mathbb{R }^{n} \rightarrow \mathbb R .$ We show that this is a very rare event unless the two forms are constant.  相似文献   

20.
This paper gives further numerical results on the conjecture that every odd numbern can be written as 2p +q wherep andq are primes. Strange fluctuations in the least possible value ofq needed are noted, studied, and partially predicted using the Hardy-Littlewood conjecture. Finally values of the Hardy-Littlewood constantsC 2,C 3 ...C 49 are tabulated as they are of use in other numerical verifications but difficult to compute.  相似文献   

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