• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.935-946
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• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.43-47
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• 2006

Consider a multitype queue where queued customers arc served in their order of arrival at a rate which depends on the customer type. Here we calculate the sharp asymptotics of the probability the total number of customers in the queue reaches a high level before emptying. The natural state space to describe this queue is a tree whose branches increase in length as the number of customers in the queue grows. Consequently it is difficult to prove a large deviation principle. Moreover, since service rates depend on the customer type the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Instead, we use a change of measure technique which increases the arrival rate of customers and decreases the departure rate thus making large deviations common.

• Nuclear Engineering and Technology
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• v.55 no.8
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• pp.2734-2741
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• 2023

Brachytherapy is a special case of radiotherapy. It should be arranged according to some principles in medical radiation applications and radiation physics. The primary principle is to use as low as reasonably achievable dose in all ionizing radiation applications for diagnostic and therapeutic treatments. Dosimetric distributions are dependent on radioactive source properties and radiation-matter interactions in an absorber medium such as phantom or tissue. In this consideration, the geometrical structure and material of the seed capsule, which surrounds a radioactive material, are directly responsible for isodose profiles and dosimetric functions. In this study, the radiometric properties of capsule material were investigated on dose distribution in a water phantom by changing its nuclear properties using the EGSnrc Monte Carlo (MC) simulation code. Effective atomic numbers of hypothetic mixtures were calculated by using different elements with several fractions for capsule material. Model 6711 brachytherapy seed was modeled by EGSnrc/Dosrcnrc Code and dosimetric functions were calculated. As a result, dosimetric parameters of hypothetic sources have been acquired in large-scale atomic number. Dosimetric deviations between the data of hypothetic seeds and the original one were analyzed. Unit dose (Gy/Particle) distributions belonging to different types of material in seed capsule have remarkably differed from the original capsule's data. Capsule type is major variable to manage the expected dose profile and isodose distribution around a seed. This study shows us systematically varied scale of material type (cross section or effective atomic number dependent) offers selective material usage in production of seed capsules for the expected isodose profile of a specific source.

• Korean Journal of Optics and Photonics
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• v.18 no.6
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• pp.375-382
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• 2007

The Shack-Hartmann wavefront sensor is composed of a lenslet array generating the spot images from which local slope is calculated and overall wavefront is measured. Generally the principle of wavefront reconstruction is that the spot centroid of each lenslet array is calculated from pixel intensity values in its subaperture, and then overall wavefront is reconstructed by the local slope of the wavefront obtained by deviations from reference positions. Hence the spot image of each lenslet array has to remain in its subaperture for exact measurement of the wavefront. However the spot of each lenslet array deviates from its subaperture area when a wavefront with large local slopes enters the Shack-Hartmann sensor. In this research, we propose a spot image searching method that finds the area of each measured spot image flexibly and determines the centroid of each spot in its area Also the algorithms that match these centroids to their reference points unequivocally, even if some of them are situated off the allocated subaperture, are proposed. Finally we verify the proposed algorithm with the test of a defocus measurement through experimental setup for the Shack-Hartmann wavefront sensor. It has been shown that the proposed algorithm can expand the dynamic range without additional devices.