• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.1-12
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• 2009

Motivated by XTR cryptosystem which is based on an irreducible polynomial $x^3-cx^2+c^px-1$ over $F_{p^2}$, we study polynomials of the form $F(c,x)=x^3-cx^2+c^qx-1$ over $F_{p^2}$ with $q=p^m$. In this paper, we establish a one to one correspondence between the set of such polynomials and a certain set of cubic polynomials over $F_q$. Our approach is rather theoretical and provides an efficient method to generate irreducible polynomials over $F_{p^2}$.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.281-291
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• 2018

We associate a positive integer n and a subgroup H of the group $({\mathbb{Z}}/n{\mathbb{Z}})^{\times}$ with a polynomial $J_n,H(x)$, which is called the Galois polynomial. It turns out that $J_n,H(x)$ is a polynomial with integer coefficients for any n and H. In this paper, we provide an equivalent condition for a subgroup H to provide the Galois polynomial which is irreducible over ${\mathbb{Q}}$ in the case of $n=p^{e_1}_1{\cdots}p^{e_r}_r$ (prime decomposition) with all $e_i{\geq}2$.

• Journal of Trauma and Injury
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• v.31 no.3
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• pp.181-188
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• 2018

Urgent reduction is required in cases of traumatic hip dislocation to reduce the risk of avascular necrosis of the femoral head. However, in cases of femoral head fractures, the dislocated hip cannot be reduced easily, and in some cases, it can even be irreducible. This irreducibility may provoke further incidental iatrogenic fractures of the femoral neck. In an irreducible hip dislocation, without further attempting for closed reduction, an immediate open reduction is recommended. This can prevent iatrogenic femoral neck fracture or avascular necrosis of the femoral head, and save the natural hip joint.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1409-1422
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• 2022

A 3-fold quotient terminal singularity is of the type $\frac{1}{r}(b,1,-1)$ with gcd(r, b) = 1. In [6], it is proved that the economic resolution of a 3-fold terminal quotient singularity is isomorphic to a distinguished component of a moduli space 𝓜_𝜃 of 𝜃-stable G-constellations for a suitable 𝜃. This paper proves that each connected component of the moduli space 𝓜_𝜃 has a torus fixed point and classifies all torus fixed points on 𝓜_𝜃. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space 𝓜_𝜃 is irreducible.

• Journal of the Korean Society of Clothing and Textiles
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• v.21 no.6
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• pp.1094-1105
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• 1997

Balla within Italian art is characterized by the irreducibility of proteiforme work. He was aware of the possibility of abolishing all the barriers between major arts and minor arts and he placed dissemination of art in life: He applied his idea of a lively, joyous art to the world around him. His irruption of art into life appeared in futurist clothing. As a father of Futurist fashion he designed the futurist dress for men and women. It was invented a new type of dress. It was conceived as the realisation of his art-life-festivity and created with an mimic funtion of modern city. In futurist men's out-fit, he eliminated static lines, forms and colors and he used asymmetrical cuts and various strong bright colors. The colors was the determinent of factor of use of clothing. Women's dress was secondary to his reevaluation of the male dress but it was current with other European trend. He made dynamic patterns in textile design, which were the key point in the futurist design. The factors of the futurist textile design were abstract character, dynamic character and asymmetrical character. But the patterns was not related to the dynamic forms. His invention of the new style was simple form with dynamic patterns as a modernizing factor in clothing design.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.581-600
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• 2017

A classical result of A. Cohn states that, if we express a prime p in base 10 as $$p=a_n10^n+a_{n-1}10^{n-1}+{\cdots}+a_110+a_0$$, then the polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+{\cdots}+a_1x+a_0$ is irreducible in ${\mathbb{Z}}[x]$. This problem was subsequently generalized to any base b by Brillhart, Filaseta, and Odlyzko. We establish this result of A. Cohn in $O_K[x]$, K an imaginary quadratic field such that its ring of integers, $O_K$, is a Euclidean domain. For a Gaussian integer ${\beta}$ with ${\mid}{\beta}{\mid}$ > $1+{\sqrt{2}}/2$, we give another representation for any Gaussian integer using a complete residue system modulo ${\beta}$, and then establish an irreducibility criterion in ${\mathbb{Z}}[i][x]$ by applying this result.