• Journal of Korean Orthopaedic Sports Medicine
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• v.6 no.2
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• pp.126-129
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• 2007

An irreducible dislocation of the knee joint is quite rare. Most irreducible knee dislocations are posterolateral dislocations and result from the soft tissue interposition. To the best of our knowledge, there is no report of an irreducible knee dislocation result from interposition of the detached cartilage from the medial femoral condyle. We present a case of 51 years old female with irreducible knee dislocation which was treated with an arthroscopic debridement of the detached cartilage, result in reduction of the joint, which is failed in closed reduction. And then we perform the delayed arthroscopic reconstructions for the ruptured anterior and posterior cruciate ligaments. Debridement of the interposed structure using the arthroscope allows for reduction of the joint and good result without the need for an open procedure.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1023-1032
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• 1997

This paper deals with certain conditions under which irreducibility of a 3-manifold is preserved under attaching a 2-handle along a simple closed curve (and then, if necessary, capping off a 2-sphere boundary component by a 3-ball).

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.45-53
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• 2000

Existence of a unique invariant probability is considered for a class of Markov processes which may not be irreducible and a functional central limit theorem for a class of nonlinear irreducible uniformly ergodic processes is derived as well.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.99-110
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• 1999

We apply sector theory to obtain some characterization on Gaois groups for subfactors. As an example of a non-irreducible inclusion of small index, a locally trivial inclusion arising from an automorphism is considered and its Galois group is completely determined by using sector theory.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.215-223
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• 2003

Parks [7] showed that there is an one to one correspondence between good pairs of subgroups in G and irreducible monomial characters of G. This provides a useful criterion for a group to be monomial. In this paper, we study relative monomial groups by defining triples in G, and find relationships between the triples and irreducible relative monomial characters.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.481-492
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• 2000

As an application of Clifford theory, we are interested in a situation in which every irreducible projective character of a finite group G is an induced character of an irreducible linear character of some subgroup H of G. For this purpose, we study relative projective monomial groups with respect to subgroups.

• Clinics in Shoulder and Elbow
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• v.22 no.1
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• pp.37-39
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• 2019

Irreducible dislocation of the elbow is an uncommon event. We present the case of a posterolateral elbow dislocation after a fall injury in a 67-year-old woman. A closed reduction performed in the emergency department was unsuccessful since the limited passive range of motion resulted in difficulty to perform longitudinal traction and flexion. Computed tomography images showed that the posterolateral aspect of the capitellum was impacted by the tip of the coronoid process, thus appearing similar to the Hill-Sachs lesion in the humeral head. Subsequent open reduction of the elbow revealed the dislocation to be irreducible since the tip of the coronoid process had wedged into a triangular Hill-Sachs-like lesion in the capitellum. The joint was reduced by providing distal traction on the forearm, and main fragments were disengaged using digital pressure. At the 3-month follow-up, the patient reported no dislocations, and had an acceptable range of motion. Thus, we propose that to avoid iatrogenic injury to the joint or other nearby structures, irreducible dislocations should not be subjected to repeated manipulation.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1511-1522
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• 2022

Let H be a subgroup of $\mathbb{Z}^*_n$ (the multiplicative group of integers modulo n) and h₁, h₂, …, h_l distinct representatives of the cosets of H in $\mathbb{Z}^*_n$. We now define a polynomial J_n,H(x) to be $$J_{n,H}(x)=\prod^l_{j=1} \left( x-\sum_{h{\in}H} {\zeta}^{h_jh}_n\right)$$, where ${\zeta}_n=e^{\frac{2{\pi}i}{n}}$ is the nth primitive root of unity. Polynomials of such form generalize the nth cyclotomic polynomial $\Phi_n(x)={\prod}_{k{\in}\mathbb{Z}^*_n}(x-{\zeta}^k_n)$ as J_n,{1}(x) = Φ_n(x). While the nth cyclotomic polynomial Φ_n(x) is irreducible over ℚ, J_n,H(x) is not necessarily irreducible. In this paper, we determine the subgroups H for which J_n,H(x) is irreducible over ℚ.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.6
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• pp.3-15
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• 2009

Recently, Wu proposed a three small classes of finite fields $F_{2^n}$ for low-complexity bit-parallel multipliers. The proposed multipliers have low-complexities compared with those based on the irreducible pentanomials. In this paper, we propose a new Repeated Polynomial(RP) for low-complexity bit-parallel multipliers over $F_{2^n}$. Also, three classes of Irreducible Repeated polynomials are considered which are denoted, respectively, by case 1, case 2 and case3. The proposed RP bit-parallel multiplier has lower complexities than ones based on pentanomials. If we consider finite fields that have neither a ESP nor a trinomial as an irreducible polynomial when $n\leq1,000$. Then, in Wu''s result, only 11 finite fields exist for three types of irreducible polynomials when $n\leq1,000$. However, in our result, there are 181, 232, and 443 finite fields of case 1, 2 and 3, respectively.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.469-472
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• 2015

The n-th cyclotomic polynomial ${\Phi}_n(x)$ is irreducible over $\mathbb{Q}$ and has integer coefficients. The degree of ${\Phi}_n(x)$ is ${\varphi}(n)$, where ${\varphi}(n)$ is the Euler Phi-function. In this paper, we define Semi-Cyclotomic Polynomial $J_n(x)$. $J_n(x)$ is also irreducible over $\mathbb{Q}$ and has integer coefficients. But the degree of $J_n(x)$ is $\frac{{\varphi}(n)}{2}$. Galois Theory will be used to prove the above properties of $J_n(x)$.