• Nuclear Engineering and Technology
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• v.51 no.6
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• pp.1616-1625
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• 2019

Measuring occurrence times of random events, aimed to determine the statistical properties of the governing stochastic process, is a basic topic in science and engineering, and has been the subject of numerous mathematical modeling approaches. Often, true statistical properties deviate from measured properties due to the so called dead time phenomenon, where for a certain time period following detection, the detection system is not operational. Understanding the dead time effect is especially important in radiation measurements, often characterized by high count rates and a non-reducible detector dead time (originating in the physics of particle detection). The effect of dead time can be interpreted as a suitable rarefied sequence of the original time sequence. This paper provides a limit theorem for a high rate (diffusion-scale) counter with extendable (Type II) dead time, where the underlying counting process is a renewal process with finite second moment for the inter-event distribution. The results are very general, in the sense that they refer to a general inter arrival time and a random dead time with general distribution. Following the theoretical results, we will demonstrate the applicability of the results in three applications: serially connected components, multiplicity counting and measurements of aerosol spatial distribution.

• Bulletin of the Korean Chemical Society
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• v.7 no.5
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• pp.367-371
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• 1986

Dynamic and equilibrium properties of n-alkane chains immersed in solvent molecules have been investigated by a molecular dynamics method. The n-alkane chain is assumed to be a chain of elements (CH$_2$) interconnected by bonds having a fixed bond length and bond angle, but each bond of the chain is allowed to execute hindered internal rotation. We studied the effect of the number of the chain elements (N$_c$ = 10, 15 and 20) on the equilibrium properties of the system, e.g., the pair correlation functions between a chain element and solvent molecules, g$_{cs}$(r), and between the chain elements, g$_{cc}$(r), and the configurational properties such as the mean-square end-to-end distance < R$^2$ >, the mean-square radius of gyration < S$^2$ >, and the eigenvalues of the moment-of-inertia tensor < S$_i^2$ > / < S$^2$ > (i = 1, 2 and 3). We also studied the dynamic properties of the system, e.g., the autocorrelation function C(A;t) where A = R$^2$(t), = S$^2$(t), or = ${\vec{V}}(t)({\vec{V}}$ = velocity of the center of mass), and the diffusion coefficient D. The g$_{cs}$(r)'s are almost equal irrespective of the change of Nc while g$_{cc}$(r) becomes larger as N$_c$ increases; The MD computed configurational properties < R$^2$2 > and < S$^2$ > were found to be a little different from the values calculated from the statistical equations of < R$^2$ > and < S$^2$ >, it may be due to the fact that our model for the MD simulations includes a long-range volume effect. From the < S$_i^2$ > / < S$^2$ >, it is found that the chain molecule has a nearly spherical shape irrespective of the variation of N$_c$. For the dynamic properties we found that the C(R$^2$;t) and C(S$^2$;t) of lower N$_c$ decay faster than those of higher N$_c$, while the C($\vec V$;t) of the center of mass in the chain is weakly dependent on the N$_c$. The center of mass diffusion coefficient D$_c$ decreases as N$_c$ increases while the end point diffusion coefficient D$_e$ is nearly equal irrespective of the change of N$_c$.

• The Korean Journal of Nuclear Medicine
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• v.37 no.6
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• pp.355-363
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• 2003

Purpose: Regional contractility can be calculated using the regional volume change of left ventricle measured by gated myocardial SPECT image and curve of central artery pressure obtained from radial artery pressure data. In this study, a program to obtain the regional contractility was developed, and reproducibility of regional contractility measurement was assessed. Materials and Methods: Seven patients(male:female=5:2, $58{\pm}11.9$ years) with coronary artery diseases underwent gated Tc-99m MIBI myocardial SPECT twice without delay between two scans. Regional volume change of left ventricle was estimated using CSA (Cardiac SPECT Analyzer) software developed in this study. Regional contractility was iteratively estimated from the time-elastance curve obtained using the time-pressure curve and regional time-volume curve. Reproducibility of regional contractility measurement assessed by comparing the contractility values measured twice from the same SPECT data and by comparing those measured from the pair of SPECT data obtained from a same patient. Results: Measured regional contractility was $3.36{\pm}3.38{mm}Hg/mL$ using 15-segment model, $3.16{\pm}2.25{mm}Hg/mL$ using 7-segment model, and $3.11{\pm}2.57{mm}Hg/mL$ using 5-segment model. The harmonic average of regional contractility value was almost identical to the global contractility. Correlation coefficient of regional contractility values measured twice from the same data was greater than 0.97 for all models, and two standard deviations of contractility difference on Bland Altman plot were 1.5%, 1.0%, and 0.9% for 15-, 7-, and 5-segment models, respectively. Correlation coefficient of regional contractility values measured from the pair of SPECT data obtained from a same patient was greater than 0.95 for all models, and two standard deviations on Bland Altman plot were 2.2%, 1.0%, and 1.2%. Conclusion: Regional contractility of left ventricle measured using developed software in this study was reproducible. Regional contractility of left ventricle will be a new useful index for myocardial function after analysis of the clinical data.