• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.279-302
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• 2024

In this paper, we summarise and present results on involution lengths and commutator lengths of certain linear groups such as special linear groups, projective linear groups, upper triangle matrix groups and Vershik-Kerov groups. Some open problems motivated by these results are also proposed.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.719-726
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• 1998

In this paper, we consider conjugacy of subgroups of some split metacyclic groups of odd prime power order to determine the numbers of conjugacy classes of subgroups of those groups. The study was motivated by the linear isomorphism problem of metacyclic primitive linear groups.

• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.57-73
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• 2012

The paper presents the analysis of two groups of piles subjected to lateral loads incorporating the non-linear behaviour of soil. The finite element method is adopted for carrying out the parametric study of the pile groups. The pile is idealized as a one dimensional beam element, the pile cap as two dimensional plate elements and the soil as non-linear elastic springs using the p-y curves developed by Georgiadis et al. (1992). Two groups of piles, embedded in a cohesive soil, involving two and three piles in series and parallel arrangement thereof are considered. The response of the pile groups is found to be significantly affected by the parameters such as the spacing between the piles, the number of piles in a group and the orientation of the lateral load. The non-linear response of the system is, further, compared with the one by Chore et al. (2012) obtained by the analysis of a system to the present one, except that the soil is assumed to be linear elastic. From the comparison, it is observed that the non-linearity of soil is found to increase the top displacement of the pile group in the range of 66.4%-145.6%, while decreasing the fixed moments in the range of 2% to 20% and the positive moments in the range of 54% to 57%.

• 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)∗.

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.395-410
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• 2005

For the analysis of large tables formed by many categorical variables, we suggest a method to group the variables into several disjoint groups in which the variables are completely associated within the groups. We use a simple function of Kullback-Leibler divergence as a similarity measure to find the groups. Since the groups are complete hierarchical sets, we can identify the association structure of the large tables by the marginal log-linear models. Examples are introduced to illustrate the suggested method.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.229-243
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• 2008

This paper is intended to clarify and verify two representation algorithms computing representations of elements of free groups generated by two linear fractional transformations. Moreover in practice some parts of the two algorithms are modified for computational efficiency. In particular the justification of the algorithms has been rigorously done by showing how both algorithms work correctly and efficiently according to inputs with some properties of the two linear fractional transformations.

• Restorative Dentistry and Endodontics
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• v.19 no.2
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• pp.461-472
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• 1994

The purpose of this study was to evaluate the sealing ability according to types of spreader and compatibility of accessory cone used in lateral condensation method. 120 plastic blocks with canal preformed were instrumented with K-,H-files and Gates-Gllidden bur. Shaped plastic blocks were divided into six experimental groups according to spreader and accessory cone used in lateral condensation. Then they were obturated by lateral condensation method without -sealer. Six experimental groups were as follows: Group 1 : Filling with #30 spreader & #25 gutta-percha cone Group 2 : Filling with #30 spreader & Fine accessory cone Group 3 : Filling with #3 spreader & #25 gutta-percha cone Group 4 : Filling with #3 spreader & Fine accessory cone Group 5 : Filling with #20,#30 spreader & #25 gutta-percha cone Group 6 : Filling with #2, #3 spreader & Fine accessory cone All the blocks were stored in 100% humidor at room temperature for 2 days. Each block was placed in centrifuged for 20 minutes at 3,000 rpm. Apical leakage was mesured from the apical foramen to the most coronal level of- dye leakage in millimeter under a stereoscope. The data were analysed by ANOVA. The obtained results were as follows; 1. In groups using two spreaders(Group 5,6), the linear leakage was less than one spreader using groups(Group 1-4). 2. Tn groups using two spreaders(Group 5,6), there was no significant difference in linear leakage between standardized -spreader group and non standardized group (p>0.01). 3. When one spreader was used(Group 1-4), standardized-spreader groups showed less linear leakage than nonstandardized spreader groups(P<0.01). 4. In case of using same spreader(Groupl,2 & Group 3,4), there was no significant difference in linear leakage according to accessory cone type. 5. It needs to use one more spreaders to increase apical sealability.

• Restorative Dentistry and Endodontics
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• v.20 no.2
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• pp.671-684
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• 1995

The purpose of this study was to compare the apical sealing ability, overfilling and obturation of lateral canals using two gutta-percha techniques: Thermafil obturators and cold lateral condensation. Eighty numbered epoxide blocks with one major and five lateral canals were divided into four experimental groups and obturated according to experimental groups. Four experimental groups were as follows: Group 1 : Filling with Thermafil plastic obturators and sealer(ThermaSeal) Group 2 : Filling with Thermafil plastic obturators only, without sealer(ThermaSeal) Group 3 : Fillng using lateral condensation with sealer(AH-26) Group 4 : Fillng using lateral condensation without sealer(AH-26) All the blocks were stored in 100% relative humidor at room temperature for 7 days. Each block was placed in centrifuge tube filled with India ink, and then centrifuged for 20 minutes at 3,000 rpm. Apical leakage was measured from the apical foramen to the most coronal level of dye penetration in millimeter under a stereoscope. The length of gutta-percha and sealer in each of the lateral canals was measured, too. The presence or absence of overfilling of gutta-percha and sealer was recorded. The data was analyzed by one-way ANOVA. The obtained results were as follows: l. Apical dye leakage was almost: not occurred in Group Willed with Thermafil and sealer) and Group 3(filled using lateral condensation with sealer), and there was no significant difference in linear leakage between two groups(p>0.01). 2. In both Thermafil and lateral condensation groups, linear leakage of Group I, 3(filled with sealer) was less than that of Group 2, 4(filled without sealer), and there was no significant difference in linear leakage between Group 1, 2, 3(p> 0.01). 3. Overfilling during obturation of Group 1, 2(filled with Thermafil) was more than Group 3, 4(filled using lateral condensation), and there was no significant difference between groups(p> 0.05). 4. Groups filled with Thermafil had significantly more gutta-percha than groups filled using lateral condensation in all lateral canals(p <0.01), the total length of gutta-percha and sealer found in all lateral canals were similar in Group 1 and Group 3.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.231-240
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• 2005

We examine the Fibonacci length of certain centro-polyhedral groups and show that in some cases the lengths depend on tribonacci sequences. Further we obtain specific examples of infinite families of three-generator groups with constant, linear and (3-step) Wall number dependent Fibonacci lengths.

• Journal of Nutrition and Health
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• v.52 no.4
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• pp.342-353
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• 2019

Purpose: The Dietary Reference Intakes for Koreans (KDRIs) suggest that the goal for the intake of sodium should be less than 2,000 mg, which is thought to be infeasible to achieve when eating the typical Korean diet. This study aimed to obtain the new intake goals for sodium with improved feasibility to achieve, and also to design optimized food intake patterns for Korean adults by performing linear programming. Methods: The data from a one day 24-hour dietary recall of the 2010 ~ 2014 Korea National Health and Nutrition Survey were used to quantify food items that Korean adults usually consumed. These food items were categorized into seven groups and 24 subgroups. The mean intakes and intake distributions of the food groups and the food subgroups were calculated for eight age (19 ~ 29, 30 ~ 49, 50 ~ 64, and over 65 years old) and gender (male and female) groups. A linear programming model was constructed to minimize the difference between the optimized intakes and the mean intakes of the food subgroups while meeting KDRIs for energy and 13 nutrients, and not exceeding the typical quantities of each of the food subgroups consumed by the respective age and gender groups. As an initial solution of the linear programming, the optimized intake of seasonings, including salt, was calculated as 0 g for all the age and gender groups when the sodium constraint was inserted not to exceed 2,000 mg. Therefore, the sodium constraint was progressively increased by 100 mg until the optimized intake of seasoning was obtained as the values closest to the $25^{th}$ percentile of the intake distribution of seasonings for the respective age and gender groups. Results: The optimized food intake patterns were mathematically obtained by performing linear programming when the sodium constraint values were 3,600 mg, 4,500 mg, 4,200 mg, 3,400 mg, 2,800 mg, 3,100 mg, 3,100 mg, and 2,500 mg for the eight age and gender groups. Conclusion: The optimized food intake patterns for Korean adults were designed by performing linear programming after increasing the sodium constraint values from 2,000 mg to 2500 ~ 4,500 mg according to the age and gender groups. The resulting patterns suggest that current diets should be modified to increase the intake of vegetables for all the groups, milk/dairy products for the female groups, and fruits for the female groups except for the females aged 50 ~ 64 years.