• Title, Summary, Keyword: formal power series

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CONTINUED FRACTION AND DIOPHANTINE EQUATION

  • Gadri, Wiem;Mkaouar, Mohamed
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.699-709
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    • 2016
  • Our paper is devoted to the study of certain diophantine equations on the ring of polynomials over a finite field, which are intimately related to algebraic formal power series which have partial quotients of unbounded degree in their continued fraction expansion. In particular it is shown that there are Pisot formal power series with degree greater than 2, having infinitely many large partial quotients in their simple continued fraction expansions. This generalizes an earlier result of Baum and Sweet for algebraic formal power series.

PRIME RADICALS OF FORMAL POWER SERIES RINGS

  • Huh, Chan;Kim, Hong-Kee;Lee, Dong-Su;Lee, Yang
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.623-633
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    • 2001
  • In this note we study the prime radicals of formal power series rings, and the shapes of them under the condition that the prime radical is nilpotent. Furthermore we observe the condition structurally, adding related examples to the situations that occur naturally in the process.

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SOME UMBRAL CHARACTERISTICS OF THE ACTUARIAL POLYNOMIALS

  • Kim, Eun Woo;Jang, Yu Seon
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.1
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    • pp.73-82
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    • 2016
  • The utility of exponential generating functions is that they are relevant for combinatorial problems involving sets and subsets. Sequences of polynomials play a fundamental role in applied mathematics, such sequences can be described using the exponential generating functions. The actuarial polynomials ${\alpha}^{({\beta})}_n(x)$, n = 0, 1, 2, ${\cdots}$, which was suggested by Toscano, have the following exponential generating function: $${\limits\sum^{\infty}_{n=0}}{\frac{{\alpha}^{({\beta})}_n(x)}{n!}}t^n={\exp}({\beta}t+x(1-e^t))$$. A linear functional on polynomial space can be identified with a formal power series. The set of formal power series is usually given the structure of an algebra under formal addition and multiplication. This algebra structure, the additive part of which agree with the vector space structure on the space of linear functionals, which is transferred from the space of the linear functionals. The algebra so obtained is called the umbral algebra, and the umbral calculus is the study of this algebra. In this paper, we investigate some umbral representations in the actuarial polynomials.

SYMBOLS OF MINIMUM TYPE AND OF ZERO CLASS IN EXPONENTIAL CALCULUS

  • LEE, Chang Hoon
    • East Asian mathematical journal
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    • v.34 no.1
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    • pp.29-37
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    • 2018
  • We introduce formal symbols of product type, of zero class, and of minimum type and show that the formal power series representations for $e^p$ and $e^q$ are formal symbols of product type giving the same pseudodifferential operator, where p and q are formal symbols of minimum type and p - q is of zero class.

ON THE HILBERT SPACE OF FORMAL POWER SERIES

  • YOUSEFI, Bahman;SOLTANI, Rahmat
    • Honam Mathematical Journal
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    • v.26 no.3
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    • pp.299-308
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    • 2004
  • Let $\{{\beta}(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers such that ${\beta}(0)=1$. We consider the space $H^2({\beta})$ of all power series $f(z)=^{Po}_{n=0}{\hat{f}}(n)z^n$ such that $^{Po}_{n=0}{\mid}{\hat{f}}(n){\mid}^2{\beta}(n)^2<{\infty}$. We link the ideas of subspaces of $H^2({\beta})$ and zero sets. We give some sufficient conditions for a vector in $H^2({\beta})$ to be cyclic for the multiplication operator $M_z$. Also we characterize the commutant of some multiplication operators acting on $H^2({\beta})$.

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A STUDY ON QUASI-DUO RINGS

  • Kim, Chol-On;Kim, Hong-Kee;Jang, Sung-Hee
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.579-588
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    • 1999
  • In this paper we study the connections between right quasi-duo rings and 2-primal rings, including several counterexamples for answers to some questions that occur naturally in the process. Actually we concern following three questions and modified ones: (1) Are right quasi-duo rings 2-primal$\ulcorner$, (2) Are formal power series rings over weakly right duo rings also weakly right duo\ulcorner and (3) Are 2-primal rings right quasi-duo\ulcorner Moreover we consider some conditions under which the answers of them may be affirmative, obtaining several results which are related to the questions.

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