• Korean Journal of Mathematics
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• v.20 no.2
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• pp.247-254
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• 2012

The Klee-Quaife problem is finding the minimum order ${\mu}(d,c,v)$ of the $(d,c,v)$ graph, which is a $c$-vertex connected $v$-regular graph with diameter $d$. Many authors contributed finding ${\mu}(d,c,v)$ and they also enumerated and classied the graphs in several cases. This problem is naturally extended to the case of digraphs. So we are interested in the extended Klee-Quaife problem. In this paper, we deal with an equivalent problem, finding the maximum diameter of digraphs with given order, focused on 2-regular case. We show that the maximum diameter of strongly connected 2-regular digraphs with order $n$ is $n-3$, and classify the digraphs which have diameter $n-3$. All 15 nonisomorphic extremal digraphs are listed.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.671-677
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• 2021

For a distance-regular graph with valency k, second largest eigenvalue r and diameter D, it is known that r ≥ $min\{\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2},\;a_3\}$ if D = 3 and r ≥ $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ if D ≥ 4, where λ = a₁. This result can be generalized to the class of edge-regular graphs. For an edge-regular graph with parameters (v, k, λ) and diameter D ≥ 4, we compare $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ with the local valency λ to find a relationship between the second largest eigenvalue and the local valency. For an edge-regular graph with diameter 3, we look at the number $\frac{{\lambda}-\bar{\mu}+\sqrt{({\lambda}-\bar{\mu})^2+4(k-\bar{\mu})}}{2}$, where $\bar{\mu}=\frac{k(k-1-{\lambda})}{v-k-1}$, and compare this number with the local valency λ to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.35 no.5
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• pp.335-339
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• 2009

The purpose of this study was to evaluate clinical and radiographic changes of regular diameter implants placed in the posterior region. A total of 47 standard diameter implants were consecutively placed in the posterior region of 20 partially edentulous patients. The diameters of the implants were 4.1mm (N=35, 74%) and 4.3mm (N=12, 26%), respectively. Peri-implant bone loss and clinical parameters such as mobility, suppuration, swelling, bleeding on probing (BOP) were evaluated at the baseline and?the final follow-up visit. The age of the patients ranged between 24~82 years (mean age: 54.7 years). The cumulative survival rate of the regular diameter implants loaded for a period of 3-24 months (Mean: $11.7{\pm}7.9$ month) was 100%. The average bone loss over the follow-up was $0.36{\pm}0.67\;mm$. Success rate was 95.7%. Only two implants failed (bone loss exceeding 1mm after 1 year of placement). Some prosthetic complications occurred, such as screw loosening (N=1) and dissolution of cementation material (N=2). The present study describes successful outcome following the use of standard-diameter-implants placed in the posterior region, and further comprehensive maintenance practices and follow-up schedules are required.

• The Journal of the Korean dental association
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• v.53 no.9
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• pp.644-655
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• 2015

Purpose: This study was conducted to evaluate the effect of the fixture abutment connection type and diameter on the screw joint stability in external butt joint for 2nd surgery and internal cone connected type implant system for 1st and 2nd surgery using ultimate fracture strength. Materials and Methods: USII system, SSII system and GSII system of Osstem Implant were used. Each system used the fixture with two different diameters and cement-retained abutments, and tungsten carbide / carbon coated abutment screws were used. Disc shaped stainless steel metal tube was attached using resin-based temporary cement. The experimental group was divided into seven subgroups, including the platform switching shaped specimen that uses a regular abutment in the fixture with a wide diameter in USII system. A static load was increased to the metal tube at 5mm deviated point from the implant central axis until it reached the compression bending strength at a rate of 1mm/min. Then the deformations and patterns of fracture in threaded connection were compared. Results and Conclusion: 1. In the comparison between the Regular diameter, compression bending strength of SSII system was higher than USII system and GSII system. There was no significant difference between USII system and GSII system. 2. In the comparison between wide diameter, compression bending strength was increased in the order of GSII system, USII system, and SSII system. 3. In comparison between the implant diameter, compression bending strength of the wide diameter was greater than the regular diameter in any system(P<0.05). 4. There was no significant difference between the platform switching (III group) and the regular diameter (I group) in USII system. 5. In USII system, fracture of abutment screw and deformation of both fixture and abutment were observed in I, II and III subgroups. 6. Failure pattern of SSII system, which was the fracture of abutment screw and deformation of the abutment and fixture, was observed in both IV and V subgroups. Fracture of some fixtures was observed in subgroup V. 7. Failure pattern of GSII system, which was the fracture of the abutment screw and deformation of the fixture and the abutment, was observed in both VI and VII subgroups. Apart from other subgroups, subgroup VII demonstrated no bending neither the fracture at the top of the fixture. The compressive deformation of internal slope in the fixture was the only thing observed in subgroup VII.

• Journal of Dental Rehabilitation and Applied Science
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• v.25 no.4
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• pp.349-360
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• 2009

Purpose: As the esthetic demands of dental implant patients are increased, the demands of zirconia as implant abutment material are also increased. It has non-metalic color, good biocompatibility, high strength and high toughness. Even thought the advatage of zirconia abutment, there are a few studies about mechanical properties of zirconia abutment. This study evaluated the mecanical strength with compressive bending strength and endurance limit of implant-zirconia abutment assembly. Materials and Methods: Static and cyclic loading of implant-Zirconia abutment assembly were simulated under worst case condition according to ISO. Test groups were implants of external butt joint with straight regular diameter and angled regular diameter zirconia abutment, implant of external butt joint with narrow straight diameter zirconia abutment and implant of internal conical joint with straight narrow diameter zirconia abutment. All test group were evaluated the mecanical strength with compressive bending strength and endurance limit. After fatique testing, fracture surface were examined by SEM. Results: The compressive bending strengths exceed 927N. Regular diameter zirconia abutment were stronger than narrow diameter zirconia abutment(P<.05). The endurance limits ranged from 503N to 868N. Conclusion: Within the limitation of this study, zirconia implant abutment exceeded the estabilished values for maximum incisal biting forces reported in the literature.

• Journal of the Korean Society of Food Culture
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• v.21 no.6
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• pp.679-684
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• 2006

In this experiment, I used three samples of oils. The oils that I used were hydrated soybean oil, pure soybean oil and regular soybean oil. The group of rice was fried in the each sample of oil that had not been used for a few seconds. Rice was used after frying at 230-235$^{\circ}C$ every four hours terms and total frying hours was 12 hours. The hydrated soybean oils was least affected in rancidity. The other two oils were more affected in rancidity than the hydrated soybean oil. However, the trans fatty acid in hydrated soybean oil was 36.5%. The diameter of the poped rice that was fried in pure soybean oil and regular soybean oil that had been used 12 for hours was reduced while the diameter of the popped rice fried in the hydrated soybean oil was not reduced. Also, the groups of rice fried in the pure and the regular soybean oil that had been used for 12 hours reduced the hardness in rice while the group that fried in the hydrated soybean oil at the 12th hour kept the hardness well. In sensory evaluation, rancidity order was found apparently in the pure soybean oil that had been used for 12 hour and in the regular soybean oil that have been used for eight hours and 12 hours. Only the hydrated soybean oil did not have distinctive rancidity order at all. The degree of the crispiness was reduced in the pure soybean oil and in the regular soybean oil at 12th hour frying. However, the hydrated soybean oil preserved the crispiness well until the end of 12 hours of frying. In overall preference test, the pure and regular soybean oil that had been used for 12 hour were not preferable. In conclusion, I found that the group fried in the hydrated soybean oil was better in every evaluation than the groups fried in the pure soybean oil and in regular soybean oil. The hydrated Soybean oil may be better to be used in food manufacturing if the trans fatty acid in the hydrated soybean oil can be reduced.

• The Journal of Advanced Prosthodontics
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• v.6 no.2
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• pp.126-132
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• 2014

PURPOSE. This study was conducted to evaluate the influence of the implant-abutment connection design and diameter on the screw joint stability. MATERIALS AND METHODS. Regular and wide-diameter implant systems with three different joint connection designs: an external butt joint, a one-stage internal cone, and a two-stage internal cone were divided into seven groups (n=5, in each group). The initial removal torque values of the abutment screw were measured with a digital torque gauge. The postload removal torque values were measured after 100,000 cycles of a 150 N and a 10 Hz cyclic load had been applied. Subsequently, the rates of the initial and postload removal torque losses were calculated to evaluate the effect of the joint connection design and diameter on the screw joint stability. Each group was compared using Kruskal-Wallis test and Mann-Whitney U test as post-hoc test (${\alpha}$=0.05). RESULTS. The postload removal torque value was high in the following order with regard to magnitude: two-stage internal cone, one-stage internal cone, and external butt joint systems. In the regular-diameter group, the external butt joint and one-stage internal cone systems showed lower postload removal torque loss rates than the two-stage internal cone system. In the wide-diameter group, the external butt joint system showed a lower loss rate than the one-stage internal cone and two-stage internal cone systems. In the two-stage internal cone system, the wide-diameter group showed a significantly lower loss rate than the regular-diameter group (P<.05). CONCLUSION. The results of this study showed that the external butt joint was more advantageous than the internal cone in terms of the postload removal torque loss. For the difference in the implant diameter, a wide diameter was more advantageous in terms of the torque loss rate.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.5_6
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• pp.176-186
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• 2007

An interconnection network can be represented as a graph where a vertex corresponds to a node and an edge corresponds to a link. The diameter of an interconnection network is the maximum length of the shortest paths between all pairs of vertices. The fault diameter of an interconnection network G is the maximum length of the shortest paths between all two fault-free vertices when there are $_k(G)-1$ or less faulty vertices, where $_k(G)$ is the connectivity of G. The fault diameter of an R-regular graph G with diameter of 3 or more and connectivity ${\tau}$ is at least diam(G)+1 where diam(G) is the diameter of G. We show that the fault diameter of a 2-dimensional $m{\times}n$ torus with $m,n{\geq}3$ is max(m,n) if m=3 or n=3; otherwise, the fault diameter is equal to its diameter plus 1. We also show that in $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ torus with each $k_i{\geq}3$, there are 2d mutually disjoint paths joining any two vertices such that the lengths of all these paths are at most diameter+1. The paths joining two vertices u and v are called to be mutually disjoint if the common vertices on these paths are u and v. Using these mutually disjoint paths, we show that the fault diameter of $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ totus with each $k_i{\geq}3$ is equal to its diameter plus 1.

• Journal for History of Mathematics
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• v.14 no.1
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• pp.17-26
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• 2001

Ri, Sang-Hyeok(1810-\ulcorner) explained in detail and repeatedly solution of problems which find the area and diameter of inscribed and circumscribed circles of regular polygons from a side and find a side of regular polygons from the area of the book Su-Ri-Jeong-On in the chapter ‘Gak-Deung-Byeon-Hyeong-Seup-Yu’ of his book San-Sul-Gwan-Kyeun. The explanation of each question describes the procedure to make the equation in detail, but only presents the solution with few step to solve.

• Proceedings of the Korean Geotechical Society Conference
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• 2001.03a
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• pp.291-298
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• 2001

It is very difficult to accomplish load tests of piles with large diameter constructed on the offshore area, because of requirement for large scaled loading equipment and bad testing conditions. Therefore, so far in many cases pile driving dynamic formulas have applied to quality control, and recently dynamic load test method is widely used for confirming bearing capacities of such piles. However, in cases of piles with very large diameter about 2,500mm, it is nearly impossible for regular type load test methods of piles such as static and dynamic to apply owing to very large design load. This is case studies of load tests such as modified static and dynamic load tests of piles and point load tests of rock samples for estimating rational allowable bearing capacity of very large diameter piles constructed on the marine area.