共查询到20条相似文献,搜索用时 390 毫秒
1.
2.
幂级数求和函数是无穷级数问题中的重点和难点,该文针对幂级数求和函数总结出其常见类型和解法,求和函数时需要注意的几个问题,以及幂级数求和函数在级数求和、求极限等方面的应用. 相似文献
3.
随机幂级数的亏函数 总被引:13,自引:0,他引:13
孙道椿 《数学物理学报(A辑)》1999,19(3):356
研究了十分一般的随机幂级数,并证明了有限级的随机幂级数几乎必然没有亏函数. 相似文献
4.
The idea to write this paper was the completion of the paper of N. Sankaran (cf.[6]). In fact, in his theorem, he suppose that all automorphisms of the restricted power series rings with respect to the m-adic topology of the maximal ideal of a local ring is anautomorphism by substitution. But this is true for all injective endomorphisms (see our Proposition 1.5.). We study here different classes of endomorphisms of the restricted power series rings with respect to an arbitrary non nilpotent ideal in a commutative ring. To do this, we follow very closely the techniques of M.J. O'Malley concerning the rings of power series, but adapted to the case of the rings of restricted power series (cf.[3],[4]). 相似文献
5.
Feng-Kuo Huang 《Monatshefte für Mathematik》2007,151(1):45-65
This paper continues the investigation of polynomials and formal power series over a ring with various annihilator conditions
which were originally used by Rickart and Kaplansky to abstract the algebraic properties of von Neumann algebras. Results
of Armendariz on polynomial rings over a PP ring are extended to analogous annihilator conditions in nearrings of polynomials
and nearrings of formal power series. These results are somewhat striking since, in contrast to the polynomial ring case,
the nearring of polynomials or formal power series has substitution for its “multiplication” operation. These investigations
provide an alternative viewpoint in illustrating the structure of polynomials and formal power series. Extensions of Rickart
rings to formal power series rings are also discussed.
The author was partially supported by the National Science Council, Taiwan under the grant number NSC 93-2115-M-143-001. 相似文献
6.
Xiao-Xiong Gan Dariusz Bugajewski 《Bulletin of the Brazilian Mathematical Society》2011,42(3):415-437
Several kinds of formal Laurent series have been introduced with some restrictions so far. This paper systematically sets
up a natural definition and structure of formal Laurent series without those restrictions, including introducing a multiplication
between formal Laurent series. This paper also provides some results on the algebraic structure of the space of formal Laurent
series, denoted by
\mathbbL\mathbb{L}. By means of the results of the generalized composition of formal power series, we define a composition of a Laurent series
with a formal power series and provide a necessary and sufficient condition for the existence of such compositions. The calculus
about formal Laurent series is also introduced. 相似文献
7.
Hua-Chieh Li 《Journal of Number Theory》2007,123(1):59-70
Lubin conjectures that for an invertible series to commute with a noninvertible series with only simple roots of iterates, two such commuting power series must be endomorphisms of a single formal group. In this paper, we show that if the reduction of these two commuting power series are endomorphisms of a formal group, then themselves are endomorphisms of a formal group. 相似文献
8.
Jenõ Szigeti 《代数通讯》2013,41(1):245-253
In this paper we considerably strengthen a result of Ribenboim on noetherian generalised power series rings. While Ribenboim proves his result under the restrictive assumption that the monoid occuring in the definition of the geralised power series ring in cancellative we prove a corresponding result for arbitrary ordered monoids. 相似文献
9.
A. Ran 《Israel Journal of Mathematics》1971,9(1):73-92
The classical problem of analytic iteration is that of embedding analytic functions in one-parameter Lie groups of formal
power series. The main purpose of the present paper is to consider similar problems for two-parameter groups.
These problems are closely related to problems concerning conjugate power series and conjugate one parameter groups of such
series, to which the first sections of the paper are devoted.
As an application of the conjugacy theorems and the embedding theorems we bring an algebraic characterization of the class
of the two-parameter groups. 相似文献
10.
王全来 《纯粹数学与应用数学》2014,(1):14-20
探讨幂级数在收敛圆上的行为表现是函数解析开拓的一个重要问题,"具有有限多个不同系数的幂级数"是其研究的重要一类,斯泽古定理即是该类级数研究的一个重要成果.文章基于原始文献,利用历史分析和比较的方法,探讨了斯泽古定理提出的思想背景,法都猜想是其重要的思想来源,详细分析了该定理的形成过程及进一步的发展,对深入理解斯泽古定理的发展历史具有重要作用. 相似文献
11.
《European Journal of Operational Research》2006,174(1):216-233
This paper is concerned with workload minimization in re-entrant lines with exponential service times and pre-emptive control policies. Using a numerical algorithm called the power series algorithm we obtain nearly optimal policies for systems with up to 8 queues. We also improve considerably the implementation of the power series algorithm. 相似文献
12.
In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings. 相似文献
13.
Olivier Demanze 《Journal of Mathematical Analysis and Applications》2008,338(1):662-674
The point source of this work is Seleznev's theorem which asserts the existence of a power series which satisfies universal approximation properties in C∗. The paper deals with a strengthened version of this result. We establish a double approximation theorem on formal power series using a weighted backward shift operator. Moreover we give strong conditions that guarantee the existence of common universal series of an uncountable family of weighted backward shift with respect to the simultaneous approximation. Finally we obtain results on admissible growth of universal formal power series. We especially prove that you cannot control the defect of analyticity of such a series even if there exist universal series in the well-known intersection of formal Gevrey classes. 相似文献
14.
利用由三角级数和幂级数复合构成的函数项级数的有关性质,得到了一类变系数非齐次调和方程边值问题的级数解.使变系数非齐次调和方程边值问题的求解有了新的进展. 相似文献
15.
16.
Zaid M. Odibat Sunil Kumar Nabil Shawagfeh Ahmed Alsaedi Tasawar Hayat 《Mathematical Methods in the Applied Sciences》2017,40(1):40-48
This paper deals with constructing generalized ‘fractional’ power series representation for solutions of fractional order differential equations. We present a brief review of generalized Taylor's series and generalized differential transform methods. Then, we study the convergence of fractional power series. Our emphasis is to address the sufficient condition for convergence and to estimate the truncated error. Numerical simulations are performed to estimate maximum absolute truncated error when the generalized differential transform method is used to solve non‐linear differential equations of fractional order. The study highlights the power of the generalized differential transform method as a tool in obtaining fractional power series solutions for differential equations of fractional order. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
该文研究了两类幂级数的系数重排后的增长性,得到了平面上和单位圆内有限级幂级数的系数经过重排后其级和型不变的一些充要条件. 相似文献
18.
In this paper, we study the random power series of several complex variables, and give some sufficient conditions for random power series to belong to Qp and Qp,0 spaces by means of their characterizations of Carleson measure. Moreover, we show that such conditions are best possible in some sense. 相似文献
19.
Ana C. Matos 《BIT Numerical Mathematics》1991,31(4):686-696
The aim of this paper is to study the acceleration properties of the Cauchy-type approximants defined by Brezinski for periodic-linearly convergent power series. In the case where the sufficient conditions for acceleration are not satisfied, we also propose a new acceleration method for these power series based on those approximants. 相似文献
20.
本文研究了系数的模为两两NQD序列的B-值随机幂级数的增长性.利用两两NQD列推广的Borel-Cantelli引理及其它极限定理,在给定条件下得出其增长级和非随机幂级数的增长级有类似的性质. 相似文献