• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.649-660
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• 2011

S. M. Saperstone and M. Nishihama [6] had showed both continuity and stability of the orbital and limit set maps, K(x) and L(x), where K and L are considered as maps from X to $2^X$. The main purpose of this paper is to extend continuity and stability for dynamical systems to general dynamical systems.

• Archives of Craniofacial Surgery
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• v.20 no.3
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• pp.164-169
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• 2019

Background: The conventional surgical method for reconstructing orbital floor fractures involves restoration of orbital continuity by covering an onlay with a thin material under the periorbital region. However, in large orbital floor fractures, the implant after inserting is often dislocated, leading to malposition. This study aimed to propose a novel implanting method and compare it with existing methods. Methods: Among patients who underwent surgery for large orbital floor fractures, 24 who underwent the conventional onlay implanting method were compared with 21 who underwent the novel ${\gamma}$ implanting method that two implant sheets were stacked and bent to resemble the shape of the Greek alphabet ${\gamma}$. When inserting a ${\gamma}$-shaped implant, the posterior ledge of the orbital floor was placed between the two sheets and the bottom sheet was impacted onto the posterior wall of the maxilla to play a fixative role while the top sheet was placed above the residual orbital floor to support orbital contents. Wilcoxon signed-rank test and Mann-Whitney U test were used for data analyses. Results: Compared to the conventional onlay method, the gamma method resulted in better restoration of orbital contents, better improvement of enophthalmos, and fewer revision surgeries. Conclusion: Achieving good surgical outcomes for extended orbital floor fractures is known to be difficult. However, better surgical outcomes could be obtained by using the novel implantation method of impacting a ${\gamma}$-shaped porous polyethylene posteriorly.

• East Asian mathematical journal
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• v.16 no.2
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• pp.215-223
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• 2000

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.163-176
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• 2022

In this paper, we introduce some new classes of generalized mappings and prove some common fixed point theorems for a pair of asymptotically regular mappings. Our results extend and improve various well-known results due to Kannan, Reich, Wong, Hardy and Rogers, Ćirić, Jungck, Górnicki and many others. In addition to it, a sequential fixed point for a mapping which is the point-wise limit of a sequence of functions satisfying Ćirić-Proinov-Górnicki type mapping has been proved. Supporting examples have been given in strengthening hypotheses of our established theorems.

• Archives of Plastic Surgery
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• v.43 no.4
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• pp.311-315
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• 2016

In Korea, lateral canthoplasty, along with medial epicanthoplasty, has become popular over the past years to widen the horizontal length of the palpebral fissure. However, the effect of the surgery differs greatly depending on the shape and structure of the eyes. If over-widened, complications such as eversion, scarring, and conjunctival exposure may occur. Thus, the author of this study suggests a more effective and safe method for lateral canthal lengthening that causes minimal complications. A total of 236 patients underwent lateral canthoplasty between July 2007 and December 2015. For each patient, a triangular flap 4-5 mm away from the lateral canthus was elevated and rotated 45 degrees laterally while the continuity of the lower eyelid gray line was maintained. A new lateral canthus was created by fixating the rotation flap to the lateral orbital rim with minimal skin trimming and tension-free sutures, preventing relapse and maintaining a triangular shape. In more than 95% of cases, effective and satisfactory extension was achieved. On average, a 3 mm extension of the lateral canthus was achieved. There were minor complications such as wound dehiscence, webbing, and scarring, which were easily corrected. The author not only extended the lateral canthus 3-4 mm laterally but also maintained the continuity of the gray line on the lower lid as a more natural-looking triangular shape, while minimizing complications such as webbing and conjunctival exposure.

• Archives of Craniofacial Surgery
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• v.11 no.2
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• pp.85-90
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• 2010

Purpose: The goals of a blow-out fracture reconstruction are to restore the osseous continuity, provide support for the orbital contents and prevent functional and anatomic defects. Over the past several years, a range of autogenous and synthetic implants have been used extensively in orbital reconstructions. None of these implants have any absolute indications or contraindications in certain clinical settings. However, in extensive blow-out fractures, it is difficult to restore support of the orbital contents, which can cause more complications, such as enophthalmos. This study examined the clinical outcomes of extensive or comminuted blow-out fractures that were reconstructed by the simultaneous use of a titanium mesh plate and $Medpor^{(R)}$. Methods: Eighty six patients with extensive orbital fractures, who were admitted between March 1999 and February 2007, were reviewed retrospectively. The patients' chart and CT were inspected for review. Twenty three patients were operated on with both a titanium mesh plate (Matrix MIDFACE pre-formed orbital plate, Synthes, USA) and $Medpor^{(R)}$ (Porex, GA, USA). The patients underwent pre-operative CT scans to evaluate the fracture site and measure the area of the fracture. A transconjunctival approach was used, and titanium mesh plates were inserted subperiosteally with screw fixation. $Medpor^{(R)}$ was inserted above the titanium mesh plate. The patients were evaluated post-operatively for enophthalmos, diplopia, sensory disturbances and eyeball movement for a period of at least 6 months. Results: No implant-related complications were encountered during the follow-up period. Enophthalmos occurred in 1 patient, 1 patient had permanent sensory disturbance, and 3 patients complained of ocular pain and fatigue, which recovered without treatment. Although there were no significance differences between groups, the use of 2 implants had fewer complications. Therefore, it can be an alternative method for treating blow out fractures. Conclusion: The use of both a titanium mesh plate and $Medpor^{(R)}$ simultaneously may be a safe and acceptable technique in the reconstruction of extensive blow-out fractures.

• Archives of Craniofacial Surgery
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• v.23 no.4
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• pp.171-177
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• 2022

Background: The treatment of zygoma complex fractures is of crucial importance in the field of plastic surgery. However, surgical methods to correct zygoma complex fractures, including the number of fixation sites, differ among operators. Although several studies have compared two-point and three-point fixation, no comparative research has yet been conducted on one-point versus two-point fixation using computed tomography scans of surgical results. Therefore, the present study aimed to address this gap in the literature by comparing surgical results between one-point and two-point fixation procedures. Methods: In this study, we randomly selected patients to undergo surgery using one of two surgical methods. We analyzed patients with unilateral zygoma complex fractures unaccompanied by other fractures according to whether they underwent one-point fixation of the zygomaticomaxillary buttress or two-point fixation of the zygomaticomaxillary buttress and the zygomaticofrontal suture. We then made measurements at three points-the zygomaticofrontal suture, inferior orbital wall, and malar height-using 3-month postoperative computed tomography images and performed statistical analyses to compare the results of the two methods. Results: All three measurements (zygomaticofrontal suture, inferior orbital wall, and malar height) showed significant differences (p< 0.05) between one-point and two-point fixation. Highly significant differences were found for the zygomaticofrontal suture and malar height parameters. The difference in the inferior wall measurements was less meaningful, even though it also reached statistical significance. Conclusion: Using three parameters in a statistical analysis of imaging findings, this study demonstrated significant differences in treatment outcomes according to the number of fixations. The results indicate that bone alignment and continuity can be achieved to a greater extent by two-point fixation instead of one-point fixation.

• Journal of Korea Water Resources Association
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• v.33 no.2
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• pp.181-193
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• 2000

This paper presents the flow and the suspended sediment movement over ripples for oscillatory flows. A new numerical model system is developed, and applied to a laboratory experimental condition of regular waves and a fictitious condition of irregular waves. The flow field is obtained from a programme proposed by Kim et. al.(1994), which is a modified version of SOLA based on SMAC scheme. The sub-model solves the continuity and Reynolds momentum equations in the x-z plane. The wave orbital velocities, shear stresses, and pressure are all reasonably reproduced by the model. The model results on the vertical velocity component show good agreement with the measurements. The suspended sediment transport sub-model is newly set up to solve the advection-diffusion equation of suspended sediment using a split method, and involving a special shear entrainment from the whole ripple surface. The calculated suspended sediment concentrations for regular waves show reasonable agreement with measurements at Deltaflume. The model results for random waves show that the suspended sediment concentration is higher than those for regular waves and that the sediment diffuses higher than for regular waves with the significant wave height and the peak wave period of the irregular waves.