• Radiation Oncology Journal
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• 제17권2호
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• pp.120-129
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• 1999

목적 : 방사선치료를 시행한 자궁경부암 환자에서 혈중 SCC항원을 치료 전과 치료 후 추적기간 동안의 수치변화와 치료결과의 상관관계를 조사하기 위하여 자료를 분석하였다. 대상 및 방법 : 순천향대학병원 방사선종양학과에서 방사선치료를 시행한 환자 중에서 1991~1997년 사이에 혈중SCC 검사를 치료 전 시행하였거나 추적관찰 중 시행한 181명의 환자를 대상으로 후향적 분석을 실시하였다. 여러가지 통계방법을 통하여 치료 전 농도와 무병생존기간, 예후인자 등을 비교하고 추적기간 중 수치 변화의 임상적 의미를 조사하였다. 결과 : 혈중 SCC항원의 양성비율은 15ng/ml 기준으로 병기그룹에 따라 71~91%, 2.5ng/ml 기준으로 57~91%로 유의하게 증가하였으며 각 그룹의 5년 무병생존율은 IB-IIA 79.2%, IIB 68.7%, III 33.4%, IV 0% 였다. 그리고 5년 무병생존율은 치료 전 항원농도가 5ng/ml 이상인 경우 34%로 1.5ng/ml 이하, 1.5~5ng/ml의 55~62% 보다 매우 낮았다. 항원 수치 추적검사 결과 임상증상보다 1~13개월(평균 4.8개월) 재발을 빨리 발견할 수가 있었고 항원의 수치와 무병생존기간은 유의한 상관관계를 가졌고(r=-0.266) 다변량 분석상 치료전 SCC항원의 수치는 독립된 예후인자였다. 결론 : 치료 전 혈중 SCC항원 농도는 편평상피 자궁경부암의 예후에 영향을 미치는 인자이며 치료 후 추적기간 중에 하는 검사는 재발을 빨리 발견하는데 유용하다.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.39-53
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• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• 대한수학회지
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• 제55권5호
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• pp.1207-1220
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• 2018

The generalized hyperharmonic numbers $h^{(m)}_n(k)$ are defined by means of the multiple harmonic numbers. We show that the hyperharmonic numbers $h^{(m)}_n(k)$ satisfy certain recurrence relation which allow us to write them in terms of classical harmonic numbers. Moreover, we prove that the Euler-type sums with hyperharmonic numbers: $$S(k,m;p):=\sum\limits_{n=1}^{{\infty}}\frac{h^{(m)}_n(k)}{n^p}(p{\geq}m+1,\;k=1,2,3)$$ can be expressed as a rational linear combination of products of Riemann zeta values and harmonic numbers. This is an extension of the results of Dil [10] and $Mez{\ddot{o}}$ [19]. Some interesting new consequences and illustrative examples are considered.

• 대한수학회보
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• 제55권3호
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• pp.763-776
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• 2018

In this paper we consider the element-wise (Hadamard) product (or sum) of elliptic divisibility sequences and study the periodic structure of these sequences. We obtain that the element-wise product (or sum) of elliptic divisibility sequences are periodic modulo a prime p like linear recurrence sequences. Then we study periodicity properties of product sequences. We generalize our results to the case of modulo $p^l$ for some prime p > 3 and positive integer l. Finally we consider the p-adic behavior of product sequences and give a generalization of [9, Theorem 4].

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1993년도 춘계학술대회논문집; 한국과학연구소, 21 May 1993
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• pp.52-56
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• 1993

An efficient method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. The method is based upon the mode synthesis formulation procedure, but does not construct the equations of motion of the combined whole structure compared with the conventional methods. For modal bases of each linear substructure, either fixed or free interface modes can be employed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurate and efficient in calculating transient responses compared with the direct numerical integration method.

• 대한수학회지
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• 제57권4호
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• pp.1019-1030
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• 2020

Efficient computation of r-th root in 𝔽_q has many applications in computational number theory and many other related areas. We present a new r-th root formula which generalizes Müller's result on square root, and which provides a possible improvement of the Cipolla-Lehmer type algorithms for general case. More precisely, for given r-th power c ∈ 𝔽_q, we show that there exists α ∈ 𝔽_q^r such that $$Tr{\left(\begin{array}{cccc}{{\alpha}^{{\frac{({\sum}_{i=0}^{r-1}\;q^i)-r}{r^2}}}\atop{\text{ }}}\end{array}\right)}^r=c,$$ where $Tr({\alpha})={\alpha}+{\alpha}^q+{\alpha}^{q^2}+{\cdots}+{\alpha}^{q^{r-1}}$ and α is a root of certain irreducible polynomial of degree r over 𝔽_q.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.205-228
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• 2005

Let I(f) be the integral defined by : $I(f) = \int\limits_{a}^{b} f(x)w(x)dx$ with f a given function, w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value of I(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.

• 한국통신학회논문지
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• 제41권5호
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• pp.499-503
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• 2016

Cipolla-Lehmer 알고리즘을 향상시킨 새로운 알고리즘을 통해 효율적으로 세제곱근을 찾을 수 있는 방법을 연구하였다. 본 논문에서는 일반적인 Cipolla-Lehmer 알고리즘보다 곱셈량을 줄인 향상된 두 가지 알고리즘을 소개한다. 유한체상에서 세제곱근을 찾는 곱셈량이 비슷한 두 가지 알고리즘을 제안하고, 곱셈량이 비슷하더라도 저장변수의 개수가 적을수록 효율적임을 보인다.