• 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 Korean Society for Quality Management
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• v.28 no.3
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• pp.124-132
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• 2000

A selected subject and a standardized scoring system were newly enforced at college entrance examination from 1999. A selected subject system means each student can select one subject in addition to common subject in the field of mathematical research II and a standardized scoring system means we standardize the score of each field as mean 50 and standard deviation 10 in order to adjust the degree of difficulty between fields. In the field of mathematical research II, there may exist not only difference of the degree of difficulty but also that of general studying ability between groups of selected subjects. So when we standardize score, we have to consider them. So far a linear equating which is a parametric method and an equi-percentile equating which is a nonparametric method have been published, but both of them supposed that the general studying ability between groups was equal. So in this paper an adjusted linear and percentile equating method which seems to be adequate to our entrance examination is suggested and is investigated by computer simulation.

• 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.

• East Asian mathematical journal
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• v.30 no.3
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• pp.293-302
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• 2014

In this paper we provide a rigorous proof for the fact that there are exactly 8 connected Alexander quandles of order $2^5$ by combining properties of fixed point free automorphisms of finite abelian 2-groups and the classification of conjugacy classes of GL(5, 2). Furthermore we verify that six of the eight associated Alexander modules are simple, whereas the other two are semisimple.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.107-112
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• 1997

For a ring R with 1, the higher K-theory of Quillen is defined by the higher homotopy groups of the plus construction of the general linear group of R. On the other hand, the Volodin K-theory is defined by the higher homotopy groups of the Volodin space. In this paper we show that these two K-theories are equivalent. We show that the Volodin space is a homotopy fiber of the acyclic map from BGL(R) to its plus construction.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.643-702
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• 2021

Fix ℤ/2 is the prime field of two elements and write 𝒜₂ for the mod 2 Steenrod algebra. Denote by GL_d := GL(d, ℤ/2) the general linear group of rank d over ℤ/2 and by ${\mathfrak{P}}_d$ the polynomial algebra ℤ/2[x₁, x₂, …, x_d] as a connected unstable 𝒜₂-module on d generators of degree one. We study the Peterson "hit problem" of finding the minimal set of 𝒜₂-generators for ${\mathfrak{P}}_d$. Equivalently, we need to determine a basis for the ℤ/2-vector space $$Q{\mathfrak{P}}_d:={\mathbb{Z}}/2{\otimes}_{\mathcal{A}_2}\;{\mathfrak{P}}_d{\sim_=}{\mathfrak{P}}_d/{\mathcal{A}}^+_2{\mathfrak{P}}_d$$ in each degree n ≥ 1. Note that this space is a representation of GL_d over ℤ/2. The problem for d = 5 is not yet completely solved, and unknown in general. In this work, we give an explicit solution to the hit problem of five variables in the generic degree n = r(2^t - 1) + 2^ts with r = d = 5, s = 8 and t an arbitrary non-negative integer. An application of this study to the cases t = 0 and t = 1 shows that the Singer algebraic transfer of rank 5 is an isomorphism in the bidegrees (5, 5 + (13.2⁰ - 5)) and (5, 5 + (13.2¹ - 5)). Moreover, the result when t ≥ 2 was also discussed. Here, the Singer transfer of rank d is a ℤ/2-algebra homomorphism from GL_d-coinvariants of certain subspaces of $Q{\mathfrak{P}}_d$ to the cohomology groups of the Steenrod algebra, $Ext^{d,d+*}_{\mathcal{A}_2}$ (ℤ/2, ℤ/2). It is one of the useful tools for studying these mysterious Ext groups.

• Korean Journal of Computational Design and Engineering
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• v.9 no.4
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• pp.306-314
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• 2004

This paper explains the qualitative shape representation scheme and general shape analysis procedure based on shape feature categories. It takes two different groups of architectural drawings as examples and comparer them so as to confirm that the procedure is capable of comparing one group with another. In order to verify the validity of qualitative shape representation scheme, we used statistical methods as well as symbolic representation and analysis techniques. This paper concludes that two different groups of architectural drawings of similar kind are analyzed to be distinguished and specifically characterized. 11 drawings of Kahn and 13 drawings of Aalto are taken into considerations. Linear regressions are used in characterizing the shape featural relationships.

• Asian-Australasian Journal of Animal Sciences
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• v.7 no.3
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• pp.441-448
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• 1994

Postweaning performance data were obtained on 187 group fed purebred Angus calves from 12 selected sires (six high and six low feed conversion sires) in 1985 and 1986. The objective of this portion of the study was to develop prediction equations for feed conversion from a stepwise regression analysis. Variables measured were on-test weight (ONTSTWT), on-test age (ONTSTAG), five weights by 28-d periods, seven linear body measurements: heart girth (HG), hip height (HH), head width (HDW), head length (HDL), muzzle circumference (MC), length between hooks and pins (HOPIN) and length between shoulder and hooks (SHHO), and backfat thickness (BF). Stepwise regressions for maintenance adjusted feed conversion (ADJFC) and unadjusted feed conversion (UNADFC) over the first 140 d of the test, and total feed conversion (FC) until progeny reached 8.89 mm of back fat were obtained separately by conversion groups and sexes and for combined feed conversion groups and sexes. In general, weights were more important than linear body measurements in prediction of feed utilization. To some extent this was expected as weight is related directly to gain which is a component of feed conversion. Weight at 112 d was the most important variable in prediction of feed conversion when data from both feed conversion groups and sexes were combined. Weights at 84 and 140 d were important variables in prediction of UNADFC and FC, respectively, of bulls. ONTSTWT and weight at 140 d had the highest standardized partial regression coefficients for UNADFC and ADJFC, respectively, of heifers. Results indicated that linear measurements, such as MC, HDL and HOPIN, are useful in prediction of feed conversion when feed in takes are unavailable.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.365-386
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• 2005

Let L be the free Lie superalgebra generated by a $Z_2$-graded vector space V over C. Suppose that g is a Lie superalgebra gl(m, n) or q(n). We study the g-module structure on the kth homogeneous component Lk of L when V is the natural representation of g. We give the multiplicities of irreducible representations of g in Lk by using the character of Lk. The multiplicities are given in terms of the character values of irreducible (projective) representations of the symmetric groups.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.521-529
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• 1994

This paper studies the realization of irreducible unitary representations of $GL_2(R)$ and $GL_2(C)$ by Bargmann's classification[1]. Since the representations of general matrix groups can be obtained by the extensions of characters of a special linear group, we shall follow to a large extent the pattern of the results in [5], [6], and [8]. This article is divided into two sections. In the first section we describe the realization of principal series and discrete series and complementary series of $GL_2(R)$. The last section is devoted to the derivation of principal series and complementary series of $GL_2(C).