• 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.

• 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.

• 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.

• East Asian mathematical journal
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• v.32 no.1
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• pp.35-41
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• 2016

We introduce formal symbols of product type and of minimum type and show that the formal power series representation for $e^p$ is a formal symbol of product type, where p is a formal symbol of minimum type.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1811-1822
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• 2018

In this paper, we exhibit the explicit forms of continued fraction expansions of a family of algebraic power series over a finite field and we study their asymptotic distribution of approximation exponents.

• 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.

• 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 $H^2({\beta})$.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.197-207
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• 2021

The main purpose of this paper is to study the zero-divisor properties of the zero-symmetric near-ring of skew formal power series R₀[[x; α]], where R is a symmetric, α-compatible and right Noetherian ring. It is shown that if R is reduced, then the set of all zero-divisor elements of R₀[[x; α]] forms an ideal of R₀[[x; α]] if and only if Z(R) is an ideal of R. Also, if R is a non-reduced ring and annR(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R), then Z(R₀[[x; α]]) is an ideal of R₀[[x; α]]. Moreover, if R is a non-reduced right Noetherian ring and Z(R₀[[x; α]]) forms an ideal, then ann_R(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R). Also, it is proved that the only possible diameters of the zero-divisor graph of R₀[[x; α]] is 2 and 3.

• Kyungpook Mathematical Journal
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• v.23 no.2
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• pp.189-192
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• 1983

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1623-1630
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• 2013

The aim of this paper is to prove that every quadratic formal power series ${\omega}$ can be expressed as a periodic non-simple continued fraction having period length one.