• The Journal of the Korea Contents Association
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• v.13 no.8
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• pp.301-307
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• 2013

In the present study, space doses generated during X-ray radiography of hand, head, and abdomen, etc. were examined and whether the intensity of space doses of scattering rays is attenuated by the "inverse square law of distance" was figured out. First, the space doses of X-ray with small amounts of generated scattering rays such as hand radiography were mostly attenuated by the "inverse square law of distance" and were not detected at all at a distance of 2m. Second, the space doses of X-ray with large amounts of generated scattering rays such as head or abdomen radiography attenuated in higher rates than the rates under the "inverse square law of distance" at distances ranging from 30cm to 1m from the center of the irradiation field and were attenuated by the "inverse square law of distance" at distances ranging from 1m to 2m. Therefore, in X-ray rooms, the subject should be at least 2m away from the center of the irradiation field in the case of hand radiography and X-ray exposure prevention actions using protective devices are required in the entire spaces of the X-ray rooms in the case of head or abdomen radiography.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.4
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• pp.111-119
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• 2012

Time Stretched Pulse (TSP) is used for transmitting and analyzing the impulse signal over the designated spatial place. However, if transfer functions of transmitter and receiver are unknown, performance investigation of free field in temporal domain is barely possible due to the overlap between the direct and indirect signal from the space. Generally, the free field or hemi-free field is evaluated by the Annex A of ISO 3745 in which utilizing the inverse square law with one-third octave band signals. In this paper, the author performs analysis of free field via applying TSP with inverse square law and the results are compared with the one-third octave band signals. According to the analysis of deviation between the corresponding signal and inverse square law model, the proposed TSP method provides the comparable performance index to the one-third octave band signal with reduced measuring time. Provided that the pre-whitening can be implementable by employing the speaker and microphone transfer function, further analyses from TSP compression are able to be performed such as multipath separation from time domain data. The anechoic chamber used in this experiment is verified conformance with ISO 3745 for free field and hemi-free field condition for limited frequency of the signal.

• Journal of the Korean Society of Radiology
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• v.7 no.5
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• pp.333-338
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• 2013

Generally, it's known fact that intensity of radioactivity satisfies inverse-square law. However, the law was dissatisfied with practical experiment because of limited shape of scintillation detector. Especially, in the case of near distance between the surface of detector and the radioactive source, the difference grows larger. In the present study, reason of this difference was confirmed by experiment with $2^{{\prime}{\prime}}{\times}2^{{\prime}{\prime}}{\phi}$ NaI(Tl) scintillation detector and $^{60}Co$(1.174 MeV, 1.333 MeV)and $^{137}Cs$(0.662 MeV) gamma ray sources. From the experiment, the correction coefficient was obtained with gamma ray detection efficiency and geometrical volume. In the result of the present study, the efficiency difference of the detector was corrected with the coefficient. In the present result, we obtained that the inverse-square law experiment have to consider the efficiency and geometrical value of the detector.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.23-38
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• 2022

The study provided a perspective on which readers can see Newton's proof heuristically in order to overcome the difficulty of proof showing 'QT²/QR converges to the latus rectum of ellipse' in the proof of the inverse square law of Newton's Principia. The heuristic perspective is as follows: The starting point of the proof is the belief that if we transform the denominators and numerators of QT²/QR into expression with respect to segments related to diameter and conjugate diameter, we may obtain some constant, the desired value, by their relationship PV × VG/QV² = PC²/CD² in Apollonius' Conic sections. The heuristic perspective proposed in this study is meaningful because it can help readers understand Newton's proof more easily by presenting the direction of transformation of QT²/QR.

• The Journal of Korean Society for Radiation Therapy
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• v.8 no.1
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• pp.29-35
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• 1996

We are often faced with the clinical situations that is inevitably extended SSD for electron beam therapy due to anatomical restriction or applicator structure. But there are some difficulties in accurately predicting output and properties. In electron beam treatment , unlike photon beam the decrease in output for extended SSD does not follow inverse-square law accurately because of a loss of side scatter equilibrium, which is particularly significant for small cone size and low energies. The purpose of our study is to analyze the output in changing with the energy, cone size, air gap beyond the standard SSD and to compare inverse-square law factor derived from calculated effective SSD, mominal SSD with measured output factor. In addition, we have analyzed the change of PDD for several cones with different SSDs which range from 100cm to 120cm with 5cm step and with different energies(6MeV, 9MeV, 12MeV, 16MeV, 20MeV). In accordance with our study, an extended SSD produces a significant change in beam output, negligible change in depth dose which range from 100cm to 120cm SSDs. In order to deliver the more accurate dose to the neoplastic tissue, first of all we recommend inverse-square law using the table of effective SSDs with cone sizes and energies respectively or simply to create a table of extended SSD air gap correction factor. The second we need to have an insight into some change of dose distribution including PPD, penumbra caused by extended SSD for electron beam therapy.

• Journal of radiological science and technology
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• v.9 no.1
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• pp.89-92
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• 1986

Generally the inverse square law (ISL) is applied by use of intensity scale method, that is distance scale method, when we practice sensitometry of X-ray film. It was reported that the failure of the ISL had occurred in the many experiments. Thus authors obtained some conclusions of the exponent value of distance by use of dosimeter and fluorescence meter in the range of tube voltage 60 - 120 kvp, that is the range of diagnostic energy. Those conclusions were as follows its exponents were produced as 2.1383 - 2.1763 in dosimeter, as 2.1190-2.2152 in fluorescence meter. This revealed that the perfect ISL was failded and that numerical differences were shown in each measurem apparatus. Therefore it is need to study the exponent at each tube voltage for the precise supply of fixed quantity on the characteristic curve's horizontal axis.

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.2
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• pp.67-72
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• 1996

This paper presents a parameter adaptive control law that stabilizes and asymptotically regulates any single-input, linear time-invariant, controllable and observable, discrete-time system when only the upper bounds on the order of the system is given. The algorithm presented in this paper comprises basically a nonlinear state feedback law which is represented by functions of the state vector in the controllable subspace of the model, an adaptive identifier of plant parameters which uses inputs and outputs of a certain length, and an adaptive law for feedback gain adjustment. A new psedu-inverse algorithm is used for the adaptive feedback gain adjustment rather than a least-square algorithm. The proposed feedback law results in not only uniform boundedness of the state vector to zero. The superiority of the proposed algorithm over other algorithms is shown through some examples.

• Journal of the Korean School Mathematics Society
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• v.24 no.2
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• pp.173-190
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• 2021

This study analyzed the proof of the inverse square law, which is said to be the core of Newton's , in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximation, and the limit of the ratio of the line segments. Based on this analysis, we proposed to use Newton's geometric limit as a tool to show the usefulness of mathematics, and to use it as a means to break the conventional notion that the area of the curve can only be obtained using the definite integral. In addition, to help the desirable use of geometric limits in school mathematics, we suggested the following efforts are required. It is necessary to emphasize the expansion of equivalence in the micro-world, use some questions that lead to use as heuristics, and help to recognize that the approach of ratio is useful for grasping the equivalence of line segments in the micro-world.

• Journal of radiological science and technology
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• v.34 no.3
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• pp.183-188
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• 2011

We studied the optimal location where the radiation dose of radiological technologists is minimally measured. The measured scatter dose has been compared with the distance inverse square law. We measured the primary X-ray with different tube conditions (60, 70, 81 and 90 kVp) and distances (60, 120 and 180 cm). The scatter ray has been measured with various locations (42.5, 52.4 and 62.4 cm for front and back side, 0 to 60 cm with 10 cm interval for left and right side). The results of this study showed that the dose of primary X-ray was attenuated to 20.52 (27.20%), 28.58 (25.20%), 38.82 (26.32%) and 48.20 mR (26.27%) for each tube voltages at 120 cm. In addition, The dose were 7.06 (8.91%), 9.90 (8.73%), 13.64 (9.25%) and 16.60 mR (9.05%) at 180 cm. As for the scatter in front and back side, the attenuated dose were 0.15 mR (23.09%) and 0.15 mR (22.08%) at 120 cm, and 0.07 mR (10.43%) and 0.06 mR (8.83%) at 180 cm. Scatter was decreased in third quadrant. Therefore, it is recommended that radiological technologists should keep long distance from the object.

• Journal of Power System Engineering
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• v.15 no.4
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• pp.25-30
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• 2011

This study is made to provide with a method for correcting the geometric distortion of the digital radiography image by analytical approach based upon the inverse square law and Beer's law. This study is aimed to find out and improve a mathematic model of nonlinear type. Variations in the alignment of the X-ray source, the object, and imaging plate affect digital radiography images. A model which is expressed in parameter values; e.g, angle, position, absorption coefficient, length, width and pixel account of radiography source, is developed so as to match the sample image. For the best correction of the digital image that is the most similar to the model image, a correction technique based upon tangent is developed; then applied to the digital radiography images of steel tubes. As a result, the image correction is confirmed to be made successfully.