• 대한수학회보
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• 제38권4호
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• pp.763-772
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• 2001

The rate of convergence for an almost surely convergent series $S_n={\Sigma^n}_{i-1}X_i$ of independent random variables is studied in this paper. More specifically, when S$_{n}$ converges almost surely to a random variable S, the tail series $T_n{\equiv}$ S - S_{n-1} = {\Sigma^\infty}_{i-n} X_i$ is a well-defined sequence of random variables with T$_{n}$ $\rightarrow$ 0 almost surely. Conditions are provided so that for a given positive sequence {$b_n, n {\geq$ 1}, the limit law sup$_{\kappa}\geqn | T_{\kappa}|/b_n \rightarrow$ 0 holds. This result generalizes a result of Nam and Rosalsky [4].

• Bulletin of the Korean Chemical Society
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• 제10권6호
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• pp.529-535
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• 1989

A general perturbation series solution of the Smoluchowski equation is applied to investigate the rate of recombination and the remaining probability of a pair of particles in liquids. The radiative boundary condition is employed and the convergence of the perturbation series is analyzed in terms of a convergene factor in time domain. The upper bound to the error introduced by the n-th order perturbation scheme is also evaluated. The long time behaviors of the rate of recombination and the remaining probability are found to be expressed in closed forms if the perturbation series is convergent. A new and efficient method of purely numerical integration of the Smoluchowski equation is proposed and its results are compared with those obtained by the perturbation method. For the two cases where the interaction between the particles is given by (i) the Coulomb potential and (ii) the shielded Coulomb potential, the agreement between the two results is found to be excellent.

• 한국콘텐츠학회논문지
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• 제6권5호
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• pp.29-34
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• 2006

본 연구에서는, Banach 공간의 값을 갖는 확률요소들의 합 $S_n=\sum_{i=1}^nV-i$ 수렴하는 경우에, Tail 합 $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$에 대한 대수의 법칙을 고찰하여 $S_n$이 하나의 확률변수 S로 수렴하는 속도를 연구한다. 좀 더 구체적으로 말하자면, 확률변수들의 Tail 합과 확률요소들의 Tail 합에 대한 극한 성질의 유사성을 연구하여, Banach 공간에서 독립인 확률요소들의 Tail 합에 대한 약 대수의 법칙과 하나의 수렴법칙이 동등함을 기술하는 기존의 정리를 다른 대체적인 방법으로 증명한다.

• 한국콘텐츠학회논문지
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• 제6권4호
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• pp.63-68
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• 2006

본 연구에서는, 서로 독립인 확률변수들의 합 $S_n$이 수렴하는 경우에, 확률변수들의 Tail 합 $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}X_i$의 극한 성질을 연구함으로써, $S_n$이 하나의 확률변수 S로 수렴하는 속도를 연구한다. 좀 더 구체적으로 말하자면, 유사-단조감소(Quasi-monotone decreasing)하는 상수(Norming constants)의 수열에 대하여, 확률변수들의 Tail 합에 대한 약대수법칙과 하나의 수렴법칙이 동등함을 정리로 기술하고 증명하여, 기존의 연구 결과를 더 넓은 부류의 상수들의 경우에 적용할 수 있도록 확장한다.

• Steel and Composite Structures
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• 제15권2호
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• pp.175-202
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• 2013

The super convergent laminated composite beam element is newly derived for the lateral stability analysis. For this, a theoretical model of the laminated composite beams is developed based on the first-order shear deformation beam theory. The present laminated beam takes into account the transverse shear and the restrained warping induced shear deformation. The second-order coupling torque resulting from the geometric nonlinearity is rigorously derived. From the principle of minimum total potential energy, the stability equations and force-displacement relationships are derived and the explicit expressions for the displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the member stiffness matrix is determined using the force-displacement relationships. In order to show accuracy and superiority of the beam element developed by this study, the critical lateral buckling moments for bisymmetric and monosymmetric I-beams are presented and compared with other results available in the literature, the isoparametric beam elements, and shell elements from ABAQUS.

• Bulletin of the Korean Chemical Society
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• 제22권7호
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• pp.699-702
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• 2001

A series of cleft-type ionophores having two convergent hydroxamic acid functions are prepared and their selective ionophoric properties toward heavy metal and transition metal ions have been investigated. Hydroxamic acids 3 exhibited a prominent selectivity toward heavy metal ions of Hg2+ and Pb2+, and transition metal ions of Cu2+ over other transition metal and alkaline earth metal ions from slightly acidic source phase (pH 6) to an acidic receiving phase (pH 1). Selective ionophoric properties toward Pb2+ and Cu2+ ions over other surveyed metal ions are also confirmed by the FAB-MS measurements.

• Bulletin of the Korean Chemical Society
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• 제18권5호
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• pp.519-522
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• 1997

A series of new ligands having convergent dicarboxylic acid functions, based-upon Rebek's cleft-type ionophore, have been prepared and their ion binding properties were investigated by the competitive extraction and transport experiments. The main purpose of the modification was to increase the lipophilicity of the Rebek's ionophore, which was attempted by utilizing propyl analog of Kemp's triacid or by changing the bridging unit. Ionophores 5 and 6 were found to have a pronounced ion-binding property toward Ca2+ ion. The selectivity in competitive extraction of ionophore 5 at pH 9 for Ca2+ over Mg2+ and Sr2+ is 2.0 and 59.3, respectively. The selectivity in competitive transport of ionophore 5 for Ca2+ over Mg2+ and Sr2+ is 29.8 and 99.3, and that of ionophore 6 is 10.0 and 23.2, respectively.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• 한국전자파학회논문지
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• 제7권5호
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• pp.440-446
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• 1996

다중 ridge 원형 도파관을 퓨리에 급수 전개와 모드 정합법을 이용하여 정확하게 해석하였다. 경계 조건을 이용하여 두 급수식을 전개하고 이를 풀어 모드를 정확하게 구하였다. 다중 ridge 원형 도파관의 ridge의 수, 길이, 폭에 따른 차단 파수(cutoff wavenumber)의 변화를 살펴보았다. 구한 해는 정확하고 수렴성이 뛰어나며 dominant mode에 대해서는 간단한 근사식을 제시하였다.

• 대한수학회보
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• 제52권5호
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• pp.1729-1735
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• 2015

It is known that the partial sum of the Taylor series of an holomorphic function of one complex variable converges in norm on $H^p(\mathbb{D})$ for 1 < p < ${\infty}$. In this paper, we consider various type of partial sums of a holomorphic function of several variables which also converge in norm on $H^p(\mathbb{B}_n)$ for 1 < p < ${\infty}$. For the partial sums in several variable cases, some variables could be chosen slowly (fastly) relative to other variables. We prove that in any cases the partial sum converges to the original function, regardlessly how slowly (fastly) some variables are taken.