• Journal of Integrative Natural Science
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• v.8 no.4
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• pp.313-316
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• 2015

In this article, we compute the order of a general linear group $GL_n(A)$ over a finite ring A.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.225-234
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• 2021

Let D be a division ring and n > 1 be an integer. In this paper, it is shown that if D ≠ ��3, then every subpermutable subgroup of the general skew linear group GLn(D) is normal. By applying this result, we show that every subpermutable subgroup of the unit group (ℝG)∗ of the real group algebras RG of finite groups G is normal in (ℝG)∗.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.193-210
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• 1997

In this paper we find the irreducible complex characters of the automorphism group of the general linear group of degree 7 over a field with two elements. It is shown that this group has 114 irreducible complex characters.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.65-90
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• 2024

In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.619-626
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• 2006

Let m be any positive integer, R be a ring with identity, $M_m(R)$ be the matrix ring of all m by m matrices eve. R and $G_m(R)$ be the multiplicative group of all n by n nonsingular matrices in $M_m(R)$. In this pape., the following are investigated: (1) for any pairwise coprime ideals ${I_1,\;I_2,\;...,\;I_n}$ in a ring R, $M_m(R/(I_1{\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $M_m(R/I_1){\times}M_m(R/I_2){\times}...{\times}M_m(R/I_n);$ and $G_m(R/I_1){\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $G_m(R/I_1){\times}G_m(R/I_2){\times}...{\times}G_m(R/I_n);$ (2) In particular, if R is a finite ring with identity, then the order of $G_m(R)$ can be computed.

• Proceedings of the KIEE Conference
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• 2005.10c
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• pp.150-152
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• 2005

On this study is PM excited transverse flux linear motor for compressor on an air condenser. The present day, it is general use for linear motor on compressor, so this paper conducted efficiency to compare with varing mover and stator's shape.

• Archives of Plastic Surgery
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• v.51 no.1
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• pp.94-101
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• 2024

Background For the small glabrous skin defect, Thenar and Hypothenar skin are useful donors and they have been used as a free flap. Because of similar skin characteristics, both flaps have same indications. We will conduct comparative study for the donor morbidity of the Free thenar flap and Hypothenar free flap. Methods From January 2011 to December 2021, demographic data, characteristics of each flap, and complications using retrospective chart review were obtained. Donor outcomes of the patient, who had been followed up for more than 6 months, were measured using photographic analysis and physical examination. General pain was assessed by Numeric Rating Scale (NRS) score, neuropathic pain was assessed by Douleur Neuropathique 4 Questions (DN4) score, scar appearance was assessed by modified Vancouver Scar Scale (mVSS), and patient satisfaction was assessed on a 3-point scale. Statistical analysis was performed on the outcomes. Results Out of the 39 survey respondents, 17 patients received Free thenar flaps, and 22 patients received Hypothenar free flaps. Thenar group had higher NRS, DN4, and mVSS (p < 0.05). The average scores for the Thenar and Hypothenar groups were 1.35 and 0.27 for NRS, 2.41 and 0.55 for DN4, and 3.12 and 1.59 for mVSS, respectively. Despite the Hypothenar group showing greater satisfaction on the 3-point scale (1.82) compared with the Thenar group (1.47), the difference was not significant (p = 0.085). Linear regression analysis indicated that flap width did not have a notable impact on the outcome measures, and multiple linear regression analysis revealed no significant interaction between flap width and each of the outcome measures. Conclusion Despite the limited number of participants, higher donor morbidity in general pain, neuropathic pain, and scar formation was noted in the Thenar free flap compared with the Hypothenar free flap. However, no difference in overall patient satisfaction was found between the two groups.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.4
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• pp.55-65
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• 2000

This paper presents a linear programming based algorithm for pattern classification. Pattern classification is being considered to be critical in the area of artificial intelligence and business applications. Previous methods employing linear programming have been aimed at two-group discrimination with one or more linear discriminant functions. Therefore, there are some limitations in applying available linear programming formulations directly to general multi-class classification problems. The algorithm proposed in this manuscript is based on quadratic or polynomial discriminant functions, which allow more flexibility in covering the class regions in the N-dimensional space. The proposed algorithm is compared with other competitive methods of pattern classification in experimental results and is shown to be competitive enough for a general purpose classifier.

• Macromolecular Research
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• v.10 no.2
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• pp.108-114
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• 2002

Poly(butylene succinate) (PBS) prepolymers were prepared by the condensation polymerization of 1,4-butanediol (1,4-BD) and succinic atid (SCA) in the presence of titanium (VI) isoproxide(TPI) catalyst. The PBS prepolymers reacted with 1,4-BD or SCA to obtain hydroxyl or carboxylic acid group terminated PBS. High molecular weight linear or branched PBS was synthesized by a coupling reaction between hydroxyl and carboxylic acid group terminated PBS, or by a branching reaction between carboxylic acid group terminated PBS and glycerol as a branching agent. The weight average molecular weight of the prepared linear or branched PBS was in the range of 100,000-220,000. Both melting point and thermal stability of the high molecular weight linear and branched PBSs were somewhat higher than those of general PBS. From a tensile behavior by Instron test, modulus, tensile strength and elongation at break improved with increase in the molecular weight of the prepared PBS through the coupling or the branching reaction. In particular, the high molecular weight linear PBS had about 2.5 times higher value in modulus than the branched one.