• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.485-498
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• 2005

In this article we show that every quasi-homogeneous convex affine domain whose boundary is everywhere differentiable except possibly at a finite number of points is either homogeneous or covers a compact affine manifold. Actually we show that such a domain must be a non-elliptic strictly convex cone if it is not homogeneous.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1445-1457
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• 2016

For a positive integer N divisible by 4, let ${\mathcal{O}}^1_N({\mathbb{Q}})$ be the ring of weakly holomorphic modular functions for the congruence subgroup ${\Gamma}^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring ${\mathcal{O}}^1_N({\mathbb{Q}})$ over ${\mathbb{Q}}$ in terms of both Fricke functions and Siegel functions, from which we are able to classify all Fricke families of such level N.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.507-514
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• 2021

Vector-valued Eisenstein series of weight 3/2 are often not holomorphic. In this paper we prove that, for an even lattice Ḻ, if there exists an odd prime p such that Ḻ is local p-maximal and the determinant of Ḻ is divisible by p2, then the Eisenstein series of weight 3/2 attached to the discriminant form of Ḻ is holomorphic.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.945-962
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• 2022

For a positive integer ℓ, $\bar{A}_{\ell}(n)$ denotes the number of over-partitions of n into parts not divisible by ℓ. In this article, we find certain Ramanujan-type congruences for $\bar{A}_{r{\ell}}(n)$, when r ∈ {8, 9} and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for $\bar{A}_{13}(n)$ by using an algorithm developed by Radu and Sellers [15].

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.769-772
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• 2022

Given a prime number p and a natural number m not divisible by p, we propose the problem of finding the smallest number r₀ such that for r ≥ r₀, every group G of order p^rm has a non-trivial normal p-subgroup. We prove that we can explicitly calculate the number r₀ in the case where every group of order p^rm is solvable for all r, and we obtain the value of r₀ for a case where m is a product of two primes.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.933-955
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• 2023

For any prime number p, let J(p) be the set of positive integers n such that the numerator of the n^th harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.433-438
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• 2007

Let $\mathbb{A}=\mathbb{F}_q[T]$ and $k=\mathbb{F}_q(T)$. Assume q is odd, and fix a prime divisor ${\ell}$ of q - 1. Let P be a monic irreducible polynomial in A whose degree d is divisible by ${\ell}$. In this paper we define a subgroup $\tilde{C}_F$ of $\mathcal{O}^*_F$ which is generated by $\mathbb{F}^*_q$ and $\{{\eta}^{{\tau}^i}:0{\leq}i{\leq}{\ell}-1\}$ in $F=k(\sqrt[{\ell}]{P})$ and calculate the unit-index $[\mathcal{O}^*_F:\tilde{C}_F]={\ell}^{\ell-2}h(\mathcal{O}_F)$. This is a generalization of [3, Theorem 16.15].

• Journal of the Korean Society for Aviation and Aeronautics
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• v.18 no.2
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• pp.46-53
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• 2010

In the aspect of the nature of aircraft maintenance work on divisible tasks carried out by a wide range of operation and expertise, any information transmission problems will not only cause a threat to flight safety but also reduce productivity by keeping the team from fulfilling its mission of delivering aircraft with airworthiness. In this regard, this study firstly identify the current status of information of aircraft maintenance and factors disturbing information transmission. Then, this article also find out the level of information culture of the AMT(Aircraft Maintenance Technicians) and problems in using information. Finally, suggestions on the model of the positive information culture in a field of aircraft maintenance through efficient use of the information including safety will be followed.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04a
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• pp.802-804
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• 2002

전자화폐는 기존의 화폐가 가져야 하는 법적인 효력과 안전성 등의 기능을 그대로 가지면서 별도의 기기나 또는 컴퓨터 등에 소프트웨어 형태로 존재하는 전자지갑에 의해 관리된다. 전자화폐는 안전성을 제공해야 하고, 이중사용이 방지되어야 판다. 또한 동전의 다중사용 가능성이나 분라성을 만족시킴으로서 사용자 편리성과 효율성을 증대시킬 수 있다. 분할성은 사용자가 전자화폐를 발급받는 경우 발급받은 전자화폐를 사용자가 원하는 대로 나누어 사용할 수 있는 성질로써 거스름돈의 발생을 줄여 효율성을 증대시킬 수 있다. 본 논문에서는 이중 해쉬함수를 이용하여 동전을 생성하고 지불인증을 이용하여 생성된 동전을 마음대로 분할하여 사용할 수 있는 방법을 제안한다. 제안된 방법은 사용자의 익명성을 제공하지는 못하지만 해쉬함수를 이용하여 효율적이고 위조 불가능한 동전을 생성하며, 분할성을 만족함으로써 편리하게 이용가능하다는 장점이 있다.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.315-324
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• 2011

In this paper, we study the effects of a deformation mapping on the resulting deformation d/BCK-algebra obtained via such a deformation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the standard BCK-algebras of posets as opposed to the properties of the class of divisible d/BCK-algebras which appear to be of interest and which form a new class of d/BCK-algebras insofar as its not having been identified before.