• The Journal of Korean Society for Radiation Therapy
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• v.11 no.1
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• pp.43-48
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• 1999

Purpose : For practical application of the MR image for stereotactic radiosurgery, the target point achieved by acquisition of MR image in a relatively homogeneous phantom has to agree with the actual isocenter of irradiation in real radiosurgery and the amount of distortion of the MR image should be known. Materials and Methods : A dosimetric film with a random target point was inserted into a radish vertically and horizontally on axis Z and they were fixed with a headring. After image acquisition by stereotactic radiosurgery planning system, we achieved stereotactic coordinate of the target point and examined irradiation using the coordinate acquired as isocenter. After the irradiation, the film in the radish was developed and processed and the degree of coincidence between the target point marked on the film and the center of the radiation distribution. In order to measure the degree of distortion of the MR image in a different way, an acryl phantom was made and punctures were made at intervals of 1 cm and a drop of oil was dropped into it. Then, it was inserted into the radish vertically and horizontally on axis Z to acquire the MR image. Each coordinate was achieved and the estimation of distortion of MR image was made both in vertical and horizontal directions Results : The film from the radio was developed and for the one inserted vertically on axis Z, there was a good coincidence in the discrepancy between the target point marked on the film and the center of the radiation distribution. For the one inserted horizontally, the discrepancy between them was under 0.5 mm. As a result of estimating distortion of MR image using acryl, the discrepancy was under 0.45 mm in the case of the phantom inserted vertically on axis Z, and that of the one inserted horizontally was 1.4 mm. Conclusion : We were able to confirm good coincidence in homogeneous phantom in actual treatment position of radiosurgery using the MR image and the discrepancy measured in the analysis of distortion of the MR image did not exceed the permissible level. Therefore, it was evident the system of the hospital is suitable for radiosurgery using MR image.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.203-203
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• 2016

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.425-434
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• 2015

In this paper, a two-point fractional boundary value problem at resonance is considered. By using the coincidence degree theory some existence results of solutions are established.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.481-489
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• 2019

In this manuscript, we provide some new results with short proofs for the existence of Picard-Jungck operators in the framework of generalized metric spaces using $C_G$-simulation functions. An example is also provided to illustrate the usability of the results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.1
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• pp.16-25
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• 2021

This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.

• Journal of the Korean Society of Radiology
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• v.12 no.5
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• pp.557-563
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• 2018

Coincidence summing correction effects are known to be greater as the efficiency of the detector increases and as the distance between the source and the detector increases. A point source($^{60}Co$) was used to vary the distance in the direction of the detector's center axis and in the radial direction to obtain the P/T ratio for Coincidence summing correction calibration. In this study, values for coincidence summing corrected calibration of the values in the central and radial directions were applied to the mixed volume source(450 ml CRM source) to compare the overall peak efficiency change according to P/T with Geant4. In addition, the efficiency obtained from the mapping method is applied to the seaweed, a marine sample, and the compatibility of the P/T ratio with the detector and sample very dose together. The efficiency corrected to 1,836 keV was applied to the energy zone affected by the efficiency of 500 keV and the relative error of the measured and corrected values was well matcched by the 3.2 % peak efficiency correction. As with 450 mL CRM source, the larger the volume, the lower the P/T ratio was by ${\pm}5%$. This is due to the increased scattering of gamma-rays emitted as the source becomes farther away from the detector, and this change in P/T has been confirmed to affect the Coincidence summing corrected peak efficiency.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.199-214
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• 2015

We establish a common coupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled oincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.

• East Asian mathematical journal
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• v.31 no.1
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• pp.65-75
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• 2015

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.629-645
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• 2010

A metrical common fixed point theorem proved for a pair of self mappings due to Sastry and Murthy ([16]) is extended to symmetric spaces which in turn unifies certain fixed point theorems due to Pant ([13]) and Cho et al. ([4]) besides deriving some related results. Some illustrative examples to highlight the realized improvements are also furnished.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.117-128
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• 2012

Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].