• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.473-506
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• 2016

This paper continues the study of recursion formulas of multivariable hypergeometric functions. Earlier, in [4], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava's triple hypergeometric functions and k-variable Lauricella functions. Further, in [5], we have obtained recursion formulas for the general triple hypergeometric function. We present here the recursion formulas for Exton's triple hypergeometric functions.

• 대한수학회논문집
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• 제33권1호
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• pp.207-236
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• 2018

We obtain recursion formulas for q-hypergeometric and q-Appell series. We also find recursion formulas for the general double q-hypergeometric series. It is shown that these recursion relations can be expressed in terms of q-derivatives of the respective q-hypergeometric series.

• Bulletin of the Korean Chemical Society
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• 제7권1호
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• pp.6-12
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• 1986

Overlap integrals for the case in which the ground and excited states are represented by Morse potential functions were derived. In order to calculate the spectral intensities in Morse wavefunctions, a method of expanding the wavefunctions of one state in terms of the other was developed to allow the ground and the excited state frequencies to be different. From the expansion of Morse wavefunctions, recursion formulas were developed for variational matrix elements of Morse wavefunctions. The matrix elements can be calculated using these recursion formulas and the diagonalized results which eigenvalues (allowed energies) were all successfully satisfied to Morse energy formulas.

• 충청수학회지
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• 제21권2호
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• pp.183-188
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• 2008

We will derive recursion formulas satisfied by the traces of singular moduli for the higher level modular function.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.389-394
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• 2006

Fully flexible cell preserves Hamiltonian in structure, so the symplectic time integrator is applied to the equations of motion. Primarily, generalized leapfrog time integration (GLF) is applicable, but the equations of motion by GLF have some of implicit formulas. The implicit formulas give rise to a complicate calculation for coding and need an iteration process. In this paper, the time integration formulas are obtained for the fully flexible cell molecular dynamics simulation by using the splitting time integration. It separates flexible cell Hamiltonian into terms corresponding to each of Hamiltonian term, so the simple and completely explicit recursion formula was obtained. The explicit formulas are easy to implementation for coding and may be reduced the integration time because they are not need iteration process. We are going to compare the resulting splitting time integration with the implicit generalized leapfrog time integration.

• East Asian mathematical journal
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• 제34권1호
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• pp.59-67
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• 2018

We present new recurrence formulas for the raw and central moments of a compound binomial random variable. Our approach involves relating two compound binomial random variables that have parameters with a difference of 1 for the number of trials, but which have the same parameters for the success probability for each trial. As a consequence of our recursions, the raw and central moments of a binomial random variable are obtained in a recursive manner without the use of Stirling numbers.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.147-154
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• 2009

Tamanoi proposed higher Schwarzian operators which include the classical Schwarzian derivative as the first nontrivial operator. In view of the relations between the classical Schwarzian derivative and the analogous differential operator defined in terms of Peschl's differential operators, we define the generating function of our generalized higher operators in terms of Peschl's differential operators and obtain recursion formulas for them. Our generalized higher operators include the analogous differential operator to the classical Schwarzian derivative. A special case of our generalized higher Schwarzian operators turns out to be the Tamanoi's operators as expected.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.98.6-98
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• 2001

In the double-talk situation where both the near-end and far-end signal present, the performance of echo cancellation using the conventional LMS algorithm is easily degraded because it freezes the adaptation in this situation. Recently CLMS and ECLMS algorithms were proposed to solve this problem. These algorithms could be used to adapt the filter´s parameters continuously even in the double-talk situation. In this paper, we propose new recursion formulas to calculate the ECLMS algorithm. And we compare and analyze the performances of double-talk echo canceller according to changing the value of channel tracking factors ${\alpha}$, ${\beta}$ and forgetting factor λ. The computer simulation was performed and the results showed that, ...

• 대한수학회지
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• 제36권4호
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• pp.707-723
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• 1999

Since the modular curve $X(4)=\Gamma(4)/{\mathfrak{}}^*$ has genus 0, we have a field isomorphism K(X(4)){\approx}\mathcal{C}(j_{4})$ where $j_{4}(z)={\theta}_{3}(\frac{z}{2})/{\theta}_{4}(\frac{z}{2})$ is a quotient of Jacobi theta series ([9]). We derive recursion formulas for the Fourier coefficients of $j_4$ and $N(j_{4})$ (=the normalized generator), respectively. And we apply these modular functions to Thompson series and the construction of class fields.

• 한국안광학회지
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• 제12권3호
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• pp.39-48
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• 2007

엄밀한 조절자극과 폭주자극 값 그리고 프리즘 디옵터는 어떻게 정의되어야 하는지를 고찰하여 정리 하였다. 양안시기능 검사와 분석의 실무에서 조절자극과 폭주자극 값은 어떻게 처리되는지를 고찰하여 정리 했다. 그 결과 실무에서의 처리과정은 근거리를 렌즈면으로부터 40 cm로 하는 경우 평균 P.D가 64 mm일 때 안구의 회선점에서 시험렌즈까지 거리 $l_c$이 26.67 mm인 경우에 가장 적합하였다. 본 논문에서 이 값들을 사용하여 필요한 값들을 계산하였다. 그리고 실무에서 사용되는 (5)식의 조절자극 값이 지니는 오차를 눈의 물측 주점에서 시험렌즈까지 거리 $l_H$를 15.07 mm로 하여 계산했다. 굴절력이 $P_m$인 프리즘 가입에 의한 폭주자극 값의 변화량 P'을 순환 계산법으로 계산하였다. P'는 $P_m$, 회선점에서 프리즘까지의 거리 $p_c$, 프리즘을 가입하기 전의 폭주 값 $C_o$와 프리즘 재질의 굴절률 n에 따라 변한다. 그리고 순환 계산법과 필요한 수식들을 자세히 제시했다. P'를 증대시키는 요인에는 두 가지가 있다. 그 첫 번째는 주된 것으로서 폭주 값이 보통의 덧셈법에 따라 더해지지 않는 성질이다. 다른 하나는 영향력이 작은 것으로서 프리즘의 실제 굴절력이 빛의 입사각에 따라 다르게 되는 이유이다. 그리고 $p_c$와 $C_o$가 커짐에 따라 P'은 괄목할 만큼 작아진다. $P_m=20{\Delta}$, P.D=64 mm 그리고 n=1.7인 경우에 대해 $p_c$와 $C_o$값들에 따르는 $P^{\prime}/P_m$을 계산하여 그래프로 나타냈다. $P^{\prime}/P_m$의 굴절률 n에 대한 의존성은 무시 할만 큼 아주 작다(Fig. 6 참조). 가입 프리즘의 굴절력과 폭주자극 값의 변화량이 같게 되는 프리즘의 위치 값 $p_c$를 구했다(Table 1). 실무에서 약식으로 처리되는 조절자극과 폭주자극 값의 참 값을 구하였다. 이를 토대로 약식으로 처리된 조절자극과 폭주자극 값이 참 값의 위치에 표시 되게 하는 두 가지의 그래프 양식을 제시하였다. 하나는 기존의 것과 같은 형태(Fig. 9)이고 다른 하나는 프리즘 가입에 의한 폭주자극 값의 변화량만을 나타내는 형식이다(Fig. 11).