• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.21-24
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• 2003

In the recent papers by Harris and Park (1994) and by Hui and Park (2000), a family of lattice distributions derived from a sum of independent identically distributed random variables is examined. In this paper we generalize a result of Hui and Park (2000) on lattice distributions on the torus using the Poisson summation formula.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.315-318
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• 2000

In this note we use the Poisson Summation Formula to generalize a result of Harris and Park (1994) on lattice distributions induced by uniform (0,1) random variables to those generated by random variables with step functions as their probability functions.

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• Journal of Industrial Technology
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• v.11
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• pp.3-16
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• 1991

The lattice-fluid theory are adopted for modeling the phese equilibria in supercritical fluids, In order to investigate effects of the nonrandom distribution of holes in mixtures on the phase equilibria, the equation of state and the chemical potential of the binary miture are formulated with taking into account nonrandomness of holes distributions in the fluid mixture. The relations of phase equilibria formulated in this work are tested through predictions of solubility of heavy solids in supercritical fluids and predictions of high pressure phase equilibria of binary mixtures. Results obtained exhibit that the lattice fluid model with assumptions of nonrandomness of hole distributions is successful in quantatively mideling the phase equilibria of mixtures of molecules of dissimilar sizes, specifically solids-supercritical fluid mixtures.

• Transactions on Electrical and Electronic Materials
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• v.13 no.1
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• pp.16-18
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• 2012

LED lighting systems that combine lighting capability, emotional and physiological characteristics are required for lighting source and multifunctional applications. In this work, Simulation studies using optical analysis software packages, Light Tools, are presented. This is done to estimate the uniformity ratio of illuminance and photosynthetic photon flux density (PPFD) of the periodic 2D lattice arrangements, such as square, diamond, two-way bias quadrangular, hexagonal, and Kagome lattices, under the same transmissivity, absorptance and reflectivity. It has been found out that the two-dimensional Kagome lattice arrangement exhibited high uniformity ratio of illuminance and PPFD compared to other lattices. Accordingly, these results can be used to guide a design and improve the lighting environment which in turn would maximize the uniform distributions of illuminance.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.4
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• pp.402-416
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• 1999

The thermal distributions near the growth interface of 150nm CZ crystals were measured by three thermocouples installed at the center, middle (half radius) and edge (10nm from surface) of the crystals. The results show that larger growth rates produced smaller thermal gradients. This contradicts the widely used heat flux balance equation. Using this fact, it is confirmed in CZ crystals that the type of point defects created is determined by the value of the thermal gradient(G) near the interface during growth, as already reported for FZ crystals. Although depending on the growth systems the effective length of the thermal gradient for defect generation are varied, we defined the effective length as 10n,\m from th interface in this experiment. If the G is roughly smaller than 20C/cm, vacancy rich CZ crystals are produced. If G is larger than 25C/cm, the species of point defects changes dramatically from vacancies to interstitials. The experimental results after detaching FZ and CZ crystals from the melt show that growth interfaces are filled with vacancies. We propose that large G produces shrunk lattice spacing and in order to relax such lattice excess interstitials are necessary. Such interstitials recombine with vacancies which were generated at the growth interface, nest occupy interstitial sites and residuals aggregate themselves to make stacking faults and dislocation loops during cooling. The shape of the growth interface is also determined by te distributions of G across the interface. That is, the small G and the large G in the center induce concave and convex interfaces to the melts, respectively.

• Bulletin of the Korean Chemical Society
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• v.17 no.8
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• pp.700-706
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• 1996

We present the results of molecular dynamics simulations of monolayers of long-chain alkyl thiol [S(CH2)15CH3] molecules on an air-solid interface using the extended collapsed atom model for the chain-molecule and a gold surface for the solid surface. Several molecular dynamics simulations have been performed on monolayers with areas per molecule ranging from 18.30 to 32.10 Å2/molecule. It is found that there exist three possible transitions: a continuous transition characterized by a change in molecular configuration without change in lattice structure, a sudden transition characterized by the distinct lattice defects and perfect islands, and a third transition characterized by the appearance of a random, liquid-like state. The analysis of probability distributions of the segments shows that the structure of the chain-molecules at the air-solid interface is completely different from that at the air-water interface in the view of the degree of overlap of the probability distributions of the neighbor segments. The calculated diffusion coefficients of the chain-molecules on the monolayers seem to be not directly related to any one of the three transitions. However, the large diffusion of the molecules enhanced by the increment of the area per molecule may induce the second transition.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.97-104
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• 1997

The large deviations theorem of Cramer is extended to conditional probabilities in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. The probability that the first falls outside a certain convex set given that the second is fixed is shown to decrease with the sample size at an exponential rate which depends on the Kullback-Leibler distance between two distributions in an associated exponential familiy of distributions. Examples are given which include a method of computing the Bahadur exact slope for tests of certain composite hypotheses in exponential families.

• Nuclear Engineering and Technology
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• v.48 no.3
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• pp.660-672
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• 2016

In Part I of this paper, the two-temperature homogenized model for the fully ceramic microencapsulated fuel, in which tristructural isotropic particles are randomly dispersed in a fine lattice stochastic structure, was discussed. In this model, the fuel-kernel and silicon carbide matrix temperatures are distinguished. Moreover, the obtained temperature profiles are more realistic than those obtained using other models. Using the temperature-dependent thermal conductivities of uranium nitride and the silicon carbide matrix, temperature-dependent homogenized parameters were obtained. In Part II of the paper, coupled with the COREDAX code, a reactor core loaded by fully ceramic microencapsulated fuel in which tristructural isotropic particles are randomly dispersed in the fine lattice stochastic structure is analyzed via a two-temperature homogenized model at steady and transient states. The results are compared with those from harmonic- and volumetric-average thermal conductivity models; i.e., we compare $k_{eff}$ eigenvalues, power distributions, and temperature profiles in the hottest single channel at a steady state. At transient states, we compare total power, average energy deposition, and maximum temperatures in the hottest single channel obtained by the different thermal analysis models. The different thermal analysis models and the availability of fuel-kernel temperatures in the two-temperature homogenized model for Doppler temperature feedback lead to significant differences.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05b
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• pp.405-408
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• 2006

The purpose of this study was to determine the optimum length distribution of hybrid PVA(Poly vinyl alcohol) fiber. To produce blended PVA fiber length, first the length distribution of PVA fiber in the cement composites were identified in an experimental study based on simplex lattice design. Among the different length distributions investigated, fiber length was found to have statistically significant effect on plastic shrinkage cracking of cement composites. Subsequently, Complex analysis techniques were used to devise an experimental program that helped determine the optimum combinations of the selected fiber length distribution based on plastic shrinkage crack. The optimum blended PVA length ratio was 0.0146% 4mm fiber, 0.0060% 6-mm fiber, 0.0285% 8-mm fiber, and 0.0209% 12-mm fiber.