• Bulletin of the Korean Chemical Society
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• v.11 no.6
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• pp.557-560
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• 1990

The transition from one stable steady state branch to another stable steady state branch in a simple metabolic system with positive feedback is discussed with the aid of the bimodal Gaussian probability distribution method. Fluctuations lead to transitions from one stable steady state branch to the other, so that the bimodal Gaussian evolves to a new distribution. We also obtain the fractional occupancies in the two stable steady states in terms of a parameter characterizing conditions of the system.

• Computers and Concrete
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• v.11 no.5
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• pp.411-440
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• 2013

Large fluctuations in surface strain at the level of steel are expected in reinforced concrete flexural members at a given stage of loading due to the emergent structure (emergence of new crack patterns). This has been identified in developing deterministic constitutive models for finite element applications in Ibrahimbegovic et al. (2010). The aim of this paper is to identify a suitable probability distribution for describing the large deviations at far from equilibrium points due to emergent structures, based on phenomenological, thermodynamic and statistical considerations. Motivated by the investigations reported by Prigogine (1978) and Rubi (2008), distributions with heavy tails (namely, alpha-stable distributions) are proposed for modeling the variations in strain in reinforced concrete flexural members to account for the large fluctuations. The applicability of alpha-stable distributions at or in the neighborhood of far from equilibrium points is examined based on the results obtained from carefully planned experimental investigations, on seven reinforced concrete flexural members. It is found that alpha-stable distribution performs better than normal distribution for modeling the observed surface strains in reinforced concrete flexural members at these points.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.923-943
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• 1999

In this paper we consider functionals of the empirical age distribution of supercritical Bellman-Harris processes. Let f : R+ longrightarrow R be a measurable function that integrates to zero with respect to the stable age distribution in a supercritical Bellman-Harris process with no extinction. We present sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.13-33
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• 2006

In this article, we study the relations of horizontally conformal maps and harmonic morphisms with the stability of minimal fibers. Let ${\varphi}:(M^n,g){\rightarrow}(N^m,h)$ be a horizontally conformal submersion. There is a tensor T measuring minimality or totally geodesics of fibers of ${\varphi}$. We prove that if T is parallel and the horizontal distribution is integrable, then any minimal fiber of ${\varphi}$ is volume-stable. As a corollary, we obtain that any fiber of a submersive harmonic morphism whose fibers are totally geodesics and the horizontal distribution is integrable is volume-stable. As a consequence, we obtain if ${\varphi}:(M^n,g){\rightarrow}(N^2,h)$ is a submersive harmonic morphism of minimal fibers from a compact Riemannian manifold M into a surface N, T is parallel and the horizontal distribution is integrable, then ${\varphi}$ is energy-stable.

• Nuclear Engineering and Technology
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• v.51 no.5
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• pp.1261-1271
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• 2019

Droplet size and distribution are important parameters determining venturi scrubber performance. In this paper, we proposed physical models for a maximum stable droplet size prediction and upper limit log-normal (ULLN) distribution parameters. For the proposed maximum stable droplet size prediction model, a Eulerian-Lagrangian framework and a Reitz-Diwakar breakup model are solved simultaneously using CFD calculations to reflect the effect of multistage breakup and droplet acceleration. Then, two ULLN distribution parameters are suggested through best fitting the previously published experimental data. Results show that the proposed approach provides better predictions of maximum stable droplet diameter and Sauter mean diameter compared to existing simple empirical correlations including Boll, Nukiyama and Tanasawa. For more practical purpose, we developed the simple, one dimensional (1-D) calculation of Sauter mean diameter.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.295-303
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• 1997

Let ${X_k : k = 1, 2, \cdots}$ be a sequence of independent, identically distributed integer-valued random variables with common distribution function F.

• Macromolecular Research
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• v.17 no.7
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• pp.483-490
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• 2009

Stable poly(styrene-co-divinylbenzene) [P(St-co-DVB)] micro spheres with narrow size distribution were synthesized in the presence of 2,2'-azobis(2,4-dimethyl valeronitrile) (V-65) and co-initiator in an acetone/water mixture in the precipitation polymerization at $53^{\circ}C$ for 24 h. Potassium peroxodisulfate (KPS), ammonium peroxodisulfate (APS) and sodium peroxodisulfate (NaPS) were used as co-initiators. The optimum ratio of acetone to water for the formation of a narrow distribution of P(St-co-DVB) particles was 49:11 (g/g). The optimum co-initiator compositions for narrow distribution were 9:1 (g/g) for V-65 to KPS, 11:1 for V-65 to APS and 6:1 for V-65 to NaPS. The yield for these compositions was $54{\sim}57%$ and the largest particle size was obtained with the lowest zeta-potential and CV values. From the XPS measurements, the charge density was increased but the zeta potential decreased with increasing sulfur content, implying that the sulfate group provides the electrostatic stabilization on the particle surface. This suggested that the self-crosslinking between styrene and DVB, the electrostatic stabilization of initiators, and the balanced hydrophobic and hydrophilic properties of the solvents are responsible for the formation of stable P(St-co-DVB) spherical particles with narrow size distribution.

• Journal of Industrial Technology
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• v.29 no.B
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• pp.221-228
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• 2009

For a stable supply of electric power, periodical inspection of the electric facilities and repair of the distribution lines are required. In case of any unexpected accidents, looped operation among distribution lines may be necessary in order to supply electricity through the sound lines, separating the faulted lines. As a result of this study, it was found that normal looped operation became impossible when phase difference of the looped distribution lines is more than 3 degrees compared with the voltage supply of the distribution lines. Therefore, for a stable supply of electric power to Chuncheon, it is judged to be desirable that looped operation of the distribution lines coming from the same substation M. Tr Bank shall be performed in principle and in case of looped operation with the substation of different system, looped operation among the lines shall be performed after voltage regulation of the substation M. Tr Bank, maintaining similar voltages and load supply volume in order to avoid phase difference through checking the operation conditions of each substation M. Tr Banks. And when looped operation among the distribution lines is scheduled, voltage regulation schedule has been established so far by calculating maximum supply volume through the transformer of the substation and the maximum load volume through the distribution lines but in the future, looped operation of the distribution lines shall be carried out by removing voltage difference with regulating tap or load of the surrounding transformers, with giving prior notice to the substation operators.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.287-293
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• 1997

(t); t \geq 0} on R^1$ satisfying the following stochastic differential equation.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.1
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• pp.151-156
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• 2012

In this paper robust nonlinear image denoising algorithms are introduced for the distribution which is Gaussian in the center and Laplacian in the tails. The distribution is known as the least favorable ${\epsilon}$-contaminated normal distribution that maximizes the asymptotic variance. The proposed filter proves to be the maximum likelihood estimator under the heavy-tailed Gaussian noise environments. It is optimal in the respect of maximizing the efficacy under the above noise environment. Another filter for reducing impulsive noise is proposed by mixing with the myriad filter to propose an amplitude-limited myriad filter. Extensive experiment is conducted with images corrupted with ${\alpha}$-stable noise to analyze the behavior and performance of the proposed filters.