• 대한수학회지
• /
• 제56권4호
• /
• pp.935-946
• /
• 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
• /
• 한국데이터정보과학회 2006년도 PROCEEDINGS OF JOINT CONFERENCEOF KDISS AND KDAS
• /
• pp.43-47
• /
• 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
• /
• 제55권8호
• /
• pp.2734-2741
• /
• 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.

• 한국광학회지
• /
• 제18권6호
• /
• pp.375-382
• /
• 2007

샥-하트만 센서는 렌즐릿 배열을 이용하여 파면의 국부적인 기지를 계산하고 이로부터 파면의 왜곡된 정도를 측정하는 파면측정 센서이다. 일반적으로 하나의 점영상에 대한 중심점을 추출하여 기준 점영상의 중심점에 대한 상대적 이동량을 통해 파면의 국부 기울기를 계산, 전체 파면을 복원하는 원리이다. 따라서 하나의 점영상에 대한 정확한 중심점의 추출을 위하여 해당하는 하부개구 내에 점영상이 존재하여야 한다. 하지만 큰 기울기의 파면이 샥-하트만 센서에 입사하게 되면 측정범위를 벗어나게 되어 일반적인 방법으로는 파면의 국부적인 기울기를 계산할 수 없게 되는 문제점이 있다. 이를 해결하기 위해 특정 측정시스템에만 국한된 알고리즘이 아닌 모든 파면에 대해 측정 가능하면서도 추가적인 장비 없이 일반적인 샥-하트만 파면 센서가 지니고 있는 측정범위의 한계를 극복할 수 있는 알고리즘이 필요하다. 본 연구에서는 영상처리 기법을 이용하여 각 점영상에 대한 유동적인 탐색영역을 설정하고 이러한 탐색영역 내에서 중심점을 추출하는 방법을 제안하였다. 또 점영상 대응법을 적용하여 측정 점영상과 기준 점영상을 일대일 대응시킴으로써 전체 측정파면을 복원할 수 있는 알고리즘을 제안함으로써 측정범위에 제한 없이 파면왜곡을 측정할 수 있는 측정방법을 제시하였다. 이렇게 제안된 알고리즘을 샥-하트만 파면 센서 시스템을 이용한 초점벗어남 측정실험을 통하여 검증하였다.