• Kyungpook Mathematical Journal
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• v.56 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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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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• v.7 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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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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• v.34 no.1
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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.

• The Pure and Applied Mathematics
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• v.16 no.1
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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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• 2001.10a
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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, ...

• Journal of the Korean Mathematical Society
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• v.36 no.4
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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.

• Journal of Korean Ophthalmic Optics Society
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• v.12 no.3
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• pp.39-48
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• 2007

The stimulus of accommodation A, the stimulus of convergence C and the prism diopter ${\Delta}$ are reviewed and redefined more obviously. How the A and C are managed in the practice are reviewed and summarized. As a result, the common practical process of the binocular vision findings is most suitable in the case of the $l_c=26.67mm$, where the near distance is measured from the test lens to the near target and its value is 40 cm and the average of the P.D equal to 64 mm. The $l_c$ is the distance between the test lens and the center of rotation. Those values were used at calculating the various values in this paper. The error of the stimulus of accommodation values which are evaluated by the practically used formula (5) are calculated. Where the distance between lens and the principle point of eye is 15.07 mm ($=l_H$). The incremental stimulus of convergence values P' caused by the addition prism $P_m$ are evaluated by the recursion computation method. The P' are varied with the $P_m$, the distance $p_c$ between the prism and the center of rotation, the initial convergence value (or inverse target distance) $C_o$ and the refractive index n of the prism material. The recursion computation method and the other formulas are described in detail. In this paper n=1.7 is used. The two factors by which the P' is increased are exist. The one which is major is the property by which the values of convergence whose unit is ${\Delta}$ are not added in the generally way. The other is the that the actual power of the prism is varied with the angle of incidence light. And the P' is decreased remarkably by an increase in the $p_c$ and $C_o$. The $P^{\prime}/P_m$ are calculated and graphed which are varied with the $p_c$ and $C_o$, where the $P_m=20{\Delta}$, P.D=64 mm and n=1.7. The index n dependence of the $P^{\prime}/P_m$ is negligible (refer to fig. 6). The $p_c$ are evaluated at which the P' equal to the $P_m$ for various $P_m$ (refer to table 1). The actual values of the stimulus of convergence and accommodation which are manipulated simply in the practice are calculated. Two graphical forms are suggested. The one is like as the commonly used one. But the stimulus of convergence and of accommodation values in the practice are positioned at the exact positions when the graphic is made (refer to fig. 9). The other is the form that the incremental stimulus of convergence values caused by the addition prisms are represented at actual positions (refer to fig. 11).