• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1541-1565
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• 2020

Let f be a meromorphic function of finite order ρ with few poles in the sense S_λ(r, f) := O(r^λ+ε) + S(r, f), where λ < ρ and ε ∈ (0, ρ - λ), and let g(f) := Σ^k_j=1b_j(z)f^(k_j)(z + c_j) be a linear delay-differential polynomial of f with small meromorphic coefficients b_j in the sense S_λ(r, f). The zero distribution of fⁿ(g(f))^s - b₀ is considered in this paper, where b₀ is a small function in the sense S_λ(r, f).

• Journal of Plant Biology
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• v.33 no.4
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• pp.237-242
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• 1990

Geographical distribution of diploid plant with AA genome (2n=16) and allotetraploid with AABB genome (2n=34) of Scilla scilloides Complex from Korea has been studied. The composition and frequencies of B chromosomes ere also investigated. Plants with AABB genome were predominant over AA genome plants. A mixed population of AA and AABB genome plants was found for the first time. Aneuploid plants have not been found. Chromosomes of AA genome were composed of three pairs of metacentric, two pairs of submetacentric, two pairs of subtlocentric and one pair of telocentric chromosomes, whereas BB genome was four pairs of metacentric and five pairs of subtelocentric chromosomes. B chromosomes were classified into two categories, isochromosome (F) and chromosome fragment (f). The frequencies of B chromosomes were 43% in AA genome plants and 44% in AABB genome plants. The number of B chromosome ranged from 1 to 3 and 1 to 7 in AA and AABB genome plants, respectively. B chromosome combinations were F and F+f in AA genome plants and F, F+f and f in AABB genome plants.

• The KIPS Transactions:PartB
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• v.9B no.3
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• pp.271-276
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• 2002

The test statistic in ANOVA tests has a single or doubly noncentral F distribution and the noncentral F distribution is applied to the calculation of the power functions of tests of general linear hypotheses. Although various approximations of noncentral F distribution are suggested, they are troublesome to compute. In this paper, the calculation of noncentral F distribution is applied to the neural network theory, to solve the computation problem. The neural network consists of the multi-layer perceptron structure and learning process has the algorithm of the backpropagation. Using fables and figs, comparisons are made between the results obtained by neural network theory and the Patnaik's values. Regarding of accuracy and calculation, the results by neural network are efficient than the Patnaik's values.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.2
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• pp.167-175
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• 1999

B.P.F.(Blade Passing Frequency) levels were measured with the cut-off clearance changes. The velocity inside the scroll, pressure fluctuation at cut-off region, and the scroll surface pressure distribution along the scroll from the cut-off to outlet were measured. With a certain cut-off clearance the improvement of efficiency and attenuation of B.P.F. noise level could be achieved. The measured results of pressure fluctuation and scroll surface pressure distribution showed that the secondary flow inside the scroll increased B.P.F. noise level at the cut-off region as the cut-off clearance got wide.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.379-387
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• 2001

In this paper, we study the value distribution of meromorphic functions and prove the following theorem: Let f(z) be a transcendental meromorphic function. If f and f'have the same zeros, then f'(z) takes any non-zero value b infinitely many times.

• The Journal of the Korean dental association
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• v.25 no.12 s.223
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• pp.1145-1156
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• 1987

The purpose of this experimental study was to analyze the stress distribution from fixed partial dentures to the surrounding structures. This study was carried out on the experimental bridges with K-L blade, F.D.B.I.-11 type, F.D.B.I.-21 type, shape-memory metal blade and two-Apacerams as posterior abutment. The stress patterns and fringes were observed through the circular transmission polariscope. The results of this study were obtained as follows: 1. The stress was more concentrated to the roots apex than the implants. 2. In all blade implants, the stress was more concentrated to the distal side than the mesial side. 3. F.D.B.I.-11 type was more stress concentrated than the 21 type. 4. Shape-memory metal blade was the most effective for stress distribution. 5. Apacerams were more stress concentrated than the blde types and in the model of Apaceram with rubber-ring, anterior root was tipped distally.

• Proceedings of the Korean Magnestics Society Conference
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• 2012.11a
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• pp.104-105
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• 2012

The temperature dependence of the effective magnetic anisotropy constant K(T) of ferrite nanoparticles is obtained based on the measurements of SQUID magnetometry. For this end, a very simple but intuitive and direct method for determining the temperature dependence of anisotropy constant K(T) in nanoparticles is introduced in this study. The anisotropy constant at a given temperature is determined by associating the particle size distribution f(r) with the anisotropy energy barrier distribution $f_A(T)$. In order to estimate the particle size distribution f(r), the first quadrant part of the hysteresis loop is fitted to the classical Langevin function weight-averaged with the log?normal distribution, slightly modified from the original Chantrell's distribution function. In order to get an anisotropy energy barrier distribution $f_A(T)$, the temperature dependence of magnetization decay $M_{TD}$ of the sample is measured. For this measurement, the sample is cooled from room temperature to 5 K in a magnetic field of 100 G. Then the applied field is turned off and the remanent magnetization is measured on stepwise increasing the temperature. And the energy barrier distribution $f_A(T)$ is obtained by differentiating the magnetization decay curve at any temperature. It decreases with increasing temperature and finally vanishes when all the particles in the sample are unblocked. As a next step, a relation between r and $T_B$ is determined from the particle size distribution f(r) and the anisotropy energy barrier distribution $f_A(T)$. Under the simple assumption that the superparamagnetic fraction of cumulative area in particle size distribution at a temperature is equal to the fraction of anisotropy energy barrier overcome at that temperature in the anisotropy energy barrier distribution, we can get a relation between r and $T_B$, from which the temperature dependence of the magnetic anisotropy constant was determined, as is represented in the inset of Fig. 1. Substituting the values of r and $T_B$ into the $N{\acute{e}}el$-Arrhenius equation with the attempt time fixed to $10^{-9}s$ and measuring time being 100 s which is suitable for conventional magnetic measurement, the anisotropy constant K(T) is estimated as a function of temperature (Fig. 1). As an example, the resultant effective magnetic anisotropy constant K(T) of manganese ferrite decreases with increasing temperature from $8.5{\times}10^4J/m^3$ at 5 K to $0.35{\times}10^4J/m^3$ at 125 K. The reported value for K in the literatures is $0.25{\times}10^4J/m^3$. The anisotropy constant at low temperature region is far more than one order of magnitude larger than that at 125 K, indicative of the effects of inter?particle interaction, which is more pronounced for smaller particles.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.169-177
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• 2004

For a stationary field $\{X_{\b{j}},\b{j}{\;}\in{\;}{\mathbb{Z}}^d_{+}\}$ of associated random variables with distribution function $F(x)\;=\;P(X_{\b{1}}\;{\leq}\;x)$ we study strong consistency and asymptotic normality of the empirical distribution function, which is proposed as an estimator for F(x). We also consider strong consistency and asymptotic normality of the empirical survival function by applying these results.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.19-24
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• 1994

Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample $\chi$$_1$,…, $\chi$$\_$n/ is the empirical df: F$\_$n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)