• 대한수학회지
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• 제49권5호
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• pp.1053-1064
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• 2012

For a double array of random elements $\{X_{mn};m{\geq}1,n{\geq}1\}$ in a $p$-uniformly smooth Banach space, $\{b_{mn};m{\geq}1,n{\geq}1\}$ is an array of positive numbers, convergence of double random series ${\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}X_{mn}$, ${\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}b^{-1}_{mn}X_{mn}$ and strong law of large numbers $$b^{-1}_{mn}\sum^m_{i=1}\sum^n_{j=1}X_{ij}{\rightarrow}0$$ as $$m{\wedge}n{\rightarrow}{\infty}$$ are established.

• 대한수학회논문집
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• 제37권2호
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• pp.551-566
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• 2022

We apply Fourier-Legendre-based integration methods that had been given by Campbell in 2021, to evaluate new rational double hypergeometric sums involving ${\frac{{1}}{\pi}}$. Closed-form evaluations for dilogarithmic expressions are key to our proofs of these results. The single sums obtained from our double series are either inevaluable $_2F_1({\frac{4}{5}})$- or $_2F_1({\frac{1}{2}})$-series, or Ramanujan's ₃F₂(1)-series for the moments of the complete elliptic integral K. Furthermore, we make use of Ramanujan's finite sum identity for the aforementioned ₃F₂(1)-family to construct creative new proofs of Landau's asymptotic formula for the Landau constants.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• 호남수학학술지
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• 제36권2호
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• pp.263-273
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• 2014

Ever since Euler solved the so-called Basler problem of ${\zeta}(2)=\sum_{n=1}^{\infty}1/n^2$, numerous evaluations of ${\zeta}(2n)$ ($n{\in}\mathbb{N}$) as well as ${\zeta}(2)$ have been presented. Very recently, Ritelli [61] used a double integral to evaluate ${\zeta}(2)$. Modifying mainly Ritelli's double integral, here, we aim at evaluating certain interesting alternating series.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.271-289
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• 2018

Let 0 < q < ${\infty}$. In this study, we introduce the spaces ${\mathcal{BV}}_q$ and ${\mathcal{LS}}_q$ of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix ${\Delta}$ and summation matrix S in the space ${\mathcal{L}}_q$ of absolutely q-summable double sequences, respectively. Also, we determine their ${\alpha}$- and ${\beta}-duals$ and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q ${\leq}$ 1.

• 한국음향학회지
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• 제18권7호
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• pp.39-44
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• 1999

직사각형 평판의 고유진동수와 진동모드를 연구하였다. 이중 퓨리에 사인시리즈를 직사각형 평판의 모달 변위함수로 사용하였으며, 다양한 경계조건을 가지는 자유진동 해석에 적용하였다. 유한급수 전개로써 근사해를 나타내는 고전적인 Ritz 방법을 이용해서 직사각형 평판의 고유진동수를 해석한 Leissa의 결과와 본 연구의 결과를 비교하였다. 그리고, 평판의 형상비에 따른 영향도 연구하였다. 자유경계 평판, 외팔평판, 고정평판, 그리고 모서리가 단순지지된 직사각형 평판의 진동형태를 가시화 하였다.

• Journal of Electrical Engineering and Technology
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• 제13권1호
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• pp.298-306
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• 2018

This paper presents a harmonic analysis of the modular multilevel converter (MMC) using a double Fourier series (DFS) algorithm. First, the application of DFS for harmonic calculation in the MMC is made by considering the effect of arm inductor. The analytical results are then confirmed by comparing with the simulation results of using the fast Fourier transform (FFT) algorithm. Finally, distribution of harmonics and total harmonic distortion (THD) in the MMC will be analyzed in three cases: harmonics versus number of levels of MMC, harmonics versus total switching frequency and harmonics versus modulation index. The simulation results are performed in the PSCAD/EMTDC simulation program in order to verify the analytical results obtained by Matlab programming.

• 대한전기학회논문지
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• 제35권3호
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• pp.95-101
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• 1986

This paper describes two methods for analyzing distributed parameter systems (DPS) via Walsh series expansions. Firstly, a Walsh-Galerkin expansion approach technique (WGA) introduced by S.G. Tzafestas. is considered. The method which is based on Galerkin scheme, is well established by using Walsh series. But then, there are some difficulty in finding the proper basic functions at each systems. Secondly, a double Walsh series approach technique (DWA) is developed. The essential feature of DWA propoesed here is that it reduces the analysis problem of DPS to that of solving a set of linear algebraic equation which is extended in double Walsh series.

• 설비공학논문집
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• 제18권9호
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• pp.753-760
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• 2006

The purpose of the present work is to investigate the influence of the refrigerant adulteration by LiBr solution on the cooling capacity and COP for three different types of abso게tion chillers: a single-effect type, a series-flow double-effect type and a parallel-flow with double-effect type. A simulation program has been prepared for the cyclic analysis of absorption chillers. With some assumptions, the calculations have been performed by solving the mass balance equation, energy balance equation and the state equation simultaneously. The range of the LiBr concentration of refrigerant was 0% to 20% in the present study. For the single-effect absorption chiller, the maximum decrease in the cooling capacity was 10% at the 20% of LiBr concentration. For the double-effect chiller, the capacity was decreased by 11.1% for the parallel-flow type and the series-flow type. Also, the COP was reduced by 3.0% in single-effect, 2.8% in series-flow type (SR=0.4) and 2.3% in parallel-flow type.

• Kyungpook Mathematical Journal
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• 제19권2호
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• pp.241-243
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• 1979