• Communications of the Korean Mathematical Society
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• v.2 no.2
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• pp.205-220
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• 1987

• Communications of the Korean Mathematical Society
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• v.5 no.2
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• pp.79-86
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• 1990

• Communications of the Korean Mathematical Society
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• v.3 no.2
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• pp.205-212
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• 1988

• Journal of the Korean Operations Research and Management Science Society
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• v.11 no.1
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• pp.7-11
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• 1986

Throughout this paper we analyze the system at output point t of two stage cyclic queueing model. Our main result characterize the stochastic process (X$^{o}$ , T$^{o}$ ), the system at output point, as a Markov renewal process. The subsequent lemma exhibits the semi-Markov kernel of (X$^{o}$ , T$^{o}$ ) with state dependent feedback, the possibility of a reducible state space arises. A simple necessary and sufficient condition for the irreducibility of (X$^{o}$ , T$^{o}$ was determinded. This irreducibility implied that (X$^{o}$ , T$^{o}$ ) was aperiodic.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.465-474
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• 2019

Let ${\mathbb{Z}}$ be the ring of integers and ${\mathbb{Z}}[X]$ (resp., $h({\mathbb{Z}})$) be the ring of polynomials (resp., Hurwitz polynomials) over ${\mathbb{Z}}$. In this paper, we study the irreducibility of Hurwitz polynomials in $h({\mathbb{Z}})$. We give a sufficient condition for Hurwitz polynomials in $h({\mathbb{Z}})$ to be irreducible, and we then show that $h({\mathbb{Z}})$ is not isomorphic to ${\mathbb{Z}}[X]$. By using a relation between usual polynomials in ${\mathbb{Z}}[X]$ and Hurwitz polynomials in $h({\mathbb{Z}})$, we give a necessary and sufficient condition for Hurwitz polynomials over ${\mathbb{Z}}$ to be irreducible under additional conditions on the coefficients of Hurwitz polynomials.

• 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).

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.157-169
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• 1999

We consider the C\ulcorner-algebra O\ulcorner generated by infinite isometries \ulcorner,\ulcorner, …on Hilbert spaces with the property \ulcorner \ulcorner$\leq$1 for every n$\in$N. We present certain type of representations of C\ulcorner-algerbra O\ulcorner on a separable Hilbert space and study the conditions for irreducibility of these representations.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.309-318
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• 2004

We consider a nonlinear AR-ARCH type process subject to Markov-switching and give sufficient conditions for geometric ergodicity of the process. Existence of moments is also obtained.

• Hip & pelvis
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• v.35 no.3
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• pp.183-192
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• 2023

Purpose: This study aims to determine which intertrochanteric (IT) hip fracture and patient characteristics predict the necessity for adjunct reduction aides prior to prep and drape aiming for a more efficient surgery. Materials and Methods: Institutional fracture registries from two academic medical centers from 2017-2022 were analyzed. Data on patient demographics, comorbidities, fracture patterns identified on radiographs including displacement of the lesser trochanter (LT), thin lateral wall (LW), reverse obliquity (RO), subtrochanteric extension (STE), and number of fracture parts were collected, and the need for additional aides following traction on fracture table were collected. Fractures were classified using the AO/OTA classification. Regression analyses identified significant risk factors for needing extra reduction aides. Results: Of the 166 patients included, the average age was 80.84±12.7 years and BMI was 24.37±5.3 kg/m². Univariate regression revealed increased irreducibility risk associated with RO (odds ratio [OR] 27.917, P≤0.001), LW (OR 24.882, P<0.001), and STE (OR 5.255, P=0.005). Multivariate analysis significantly correlated RO (OR 120.74, P<0.001) and thin LW (OR 131.14, P<0.001) with increased risk. However, STE (P=0.36) and LT displacement (P=0.77) weren't significant. Fracture types 2.2, 3.2, and 3.3 displayed elevated risk (P<0.001), while no other factors increased risk. Conclusion: Elderly patients with IT fractures with RO and/or thin LW are at higher risk of irreducibility, necessitating adjunct reduction aides. Other parameters showed no significant association, suggesting most fracture patterns can be achieved with traction manipulation alone.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.499-509
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• 2008

In [4] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. Using the result, we will find conditions for a polynomial over a commutative ring to be irreducible. This can be viewed as a generalization of the Eisenstein's irreducibility criterion.