• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.109-116
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• 2004

In this paper, we study the uniqueness of entire functions and prove the following result: Let f(z) and g(z) be two nonconstant entire functions, $n\;{\geq}\;7$ a positive integer, and let a be a nonzero finite complex number. If $f^{n}(z)(f(z)\;-\;1)f'(z)\;and\;g^{n}(z)(g(z)\;-\;1)g'(z)$ share a CM, then $f(z)\;{\equiv}\;g(z)$. The result improves the theorem due to ref. [3].

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.521-534
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• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.109-127
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• 2017

In this paper, we solve the following quadratic ${\rho}-functional$ inequalities ${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$ (0.1) ${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\frac{1}{{\mid}4{\mid}}}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$ (0.2) ${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\mid}8{\mid}$. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ${\rho}-functional$ equations associated with the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

• Journal of computational fluids engineering
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• v.17 no.2
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• pp.65-70
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• 2012

The droplet ejection behavior from drop-on-demand printhead are investigated numerically in terms of the non-dimensional parameters. The numerical simulation is performed using a volume-of-fluid model. It is important to eject droplet within the printability range, where the droplet is ejected in stable manner without satellite droplets. Generally, the printability range has been determined by Z number, which is the inverse of Oh number. However, it is found that the ejection of droplets with same Z number can exhibit different behavior depending on the value of Ca and We number. Therefore, it is insufficient to determine the printability range only with Z number. Instead, other non-dimensional parameters, such as Ca and We number, should be considered comprehensively.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.227-233
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• 1999

Let $k$ be a real abelian field and $k_{\infty}={\bigcup}_{n{\geq}0}k_n$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. For each $n{\geq}0$, we denote the class number of $k_n$ by $h_n$. The following is a well known theorem: Theorem. Suppose $p$ remains inert in $k$ and the prime ideal of $k$ above $p$ totally ramifies in $k_{\infty}$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$. The aim of this paper is to generalize above theorem: Theorem 1. Suppose $H^1(G_n,E_n){\simeq}(\mathbb{Z}/p^n\mathbb{Z})^l$, where $l$ is the number of prime ideals of $k$ above $p$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$. Theorem 2. Let $k$ be a real quadratic field. Suppose that $H^1(G_1,E_1){\simeq}(\mathbb{Z}/p\mathbb{Z})^l$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$.

• Journal of Preventive Medicine and Public Health
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• v.11 no.1
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• pp.14-23
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• 1978

This survey was conducted on a total 672 pulmonary tuberculosis patients who were registered at certain health center in Busan, during the period from July 15th to August 31st, 1977, based on Modified Cornell Medical Index(CMI) consisting of 70 questions. Number of 'Yes' response of an individual patients was collected by each large section of Modified CMI. The each number of 'Yes' response was standardized by mean of Z scoring. Z score was obtained by following formula. Z=50+10(Xi-m)/s M : means of 'Yes' response by each section for all subjects s : standard deviation of the mean Xi : number of 'Yes' response by each section in an individual patients The results of obtained were as follows: 1. The number of investigated cases were 672 (459 males and 213 females). The most prevalent group was 20-24 years old group as 18.4% by age, moderate advanced group as 50.8% by radiological diagnosis, INH+PAS+SM group as 34.7% by antituberculotics and unemployed group as 59.9% by occupation. By bacteriological examination of sputum, the rate of negative group was 60.5% and positive group was 39.5%. 2. Z score of complaints by sex was higher in female as 52.4 than in male as 48.9 in general. By radiological diagnosis, there was decreasing tendency with age in male but increasing tendency with age in female. 3. By age group, Z score of complaints was increasing tendency with age in male but there was non-significant differences in female. 4. By bacteriological examination of sputum, the Z score of complaints was increasing tendency with the more discharged bacteria in both sex generally. 5. By antituberculotics, INH group was revealed the highest Z score of complaints as 50.4 in male and INH+PAS group was the highest as 51.21 in female. 6. By occupation, agricultural and fisherman group was the highest as 53.5 and the next group was professional, technical and related workers, unemployed and sales workers in that order.

• Journal of the Korea Fashion and Costume Design Association
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• v.22 no.3
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• pp.49-61
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• 2020

This study analyzed the social media accounts and performed a Big Data analysis of Z-generation fashion using Textom Text Mining Techniques program and Ucinet Big Data analysis program. The research results are as follows: First, as a result of keyword analysis on 67.646 Z-generation fashion social media posts over the last 5 years, 220,211 keywords were extracted. Among them, 67 major keywords were selected based on the frequency of co-occurrence being greater than more than 250 times. As the top keywords appearing over 1000 times, were the most influential as the number of nodes connected to 'Z generation' (29595 times) are overwhelmingly, and was followed by 'millennials'(18536 times), 'fashion'(17836 times), and 'generation'(13055 times), 'brand'(8325 times) and 'trend'(7310 times) Second, as a result of the analysis of Network Degree Centrality between the key keywords for the Z-generation, the number of nodes connected to the "Z-generation" (29595 times) is overwhelmingly large. Next, many 'millennial'(18536 times), 'fashion'(17836 times), 'generation'(13055 times), 'brand'(8325 times), 'trend'(7310 times), etc. appear. These texts are considered to be important factors in exploring the reaction of social media to the Z-generation. Third, through the analysis of CONCOR, text with the structural equivalence between major keywords for Gen Z fashion was rearranged and clustered. In addition, four clusters were derived by grouping through network semantic network visualization. Group 1 is 54 texts, 'Diverse Characteristics of Z-Generation Fashion Consumers', Group 2 is 7 Texts, 'Z-Generation's teenagers Fashion Powers', Group 3 is 8 Texts, 'Z-Generation's Celebrity Fashions' Interest and Fashion', Group 4 named 'Gucci', the most popular luxury fashion of the Z-generation as one text.

• Journal of Korea Multimedia Society
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• v.8 no.2
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• pp.249-257
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• 2005

This paper aims at reducing aliasing in pixel-based rendering for 3D implicit surfaces by shifted multi Z-buffers. The voxelized implicit surfaces with high resolution take so much time in generating high Quality image without aliasing. So in rendering a voxelized implicit surfaces, a new antialiasing method which can generate a high quality image at a lower resolution is required. Therefore, this paper suggests that a method which get various sampling values by shifting several z-buffers in each voxel and average them, The advantages are effective memory, simple calculation and easy convergence with various filters. But, the increase of number of z-buffer also increase the consuming time rapidly. Therefore, the research for representing the relation the degree of image quality with the consumption of time as a number is required.

• The Transactions of the Korea Information Processing Society
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• v.2 no.1
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• pp.55-65
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• 1995

Existing multiple-row downdating algorithms have adopted a CFD(Cholesky Factor Downdating) that recursively downdates one row at a time. The CFD based algorithm requires 5/2p $n^{2}$ flops(floating point operations) downdating a p$\times$n observation matrix $Z^{T}$ . On the other hands, a HCFD(Hybrid CFD) based algorithm we propose in this paper, requires p $n^{2}$＋6/5 $n^{3}$ flops v hen p$\geq$n. Such a HCFD based algorithm factorizes $Z^{T}$ at first, such that $Z^{T}$ = $Q_{z}$ RT/Z, and then applies the CFD onto the upper triangular matrix Rt/z, so that the total number of floating point operations for downdating $Z^{T}$ would be significantly reduced compared with that of the CFD based algorithm. Benchmark tests on the Sun SPARC/2 and the Tolerant System also show that performance of the HCFD based algorithm is superior to that of the CFD based algorithm, especially when the number of rows of the observation matrix is large.rge.