• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.331-360
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• 2013

Let ${\sigma}_s(N)$ denote the sum of the sth powers of the positive divisors of a positive integer N and let $\tilde{\sigma}_s(N)={\sum}_{d|N}(-1)^{d-1}d^s$ with $d$, N, and s positive integers. Hahn [12] proved that $$16\sum_{k. In this paper, we give a generalization of Hahn's result. Furthermore, we find the formula ${\sum}_{k=1}^{N-1}\tilde{\sigma}_1(2^{n-m}k)\tilde{\sigma}_3(2^nN-2^nk)$ for $m(0{\leq}m{\leq}n)$.

• Korean Journal of Materials Research
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• v.2 no.5
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• pp.330-336
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• 1992

Four distinctive hot pressed and heat treated S${i_3}{N_4}$ceramics, S${i_3}{N_4}$-8%${Y_2}{O_3}$, S${i_3}{N_4}$-6% ${Y_2}{O_3}$-2% $A{l_2}{O_3}$, S${i_3}{N_4}$-4% ${Y_2}{O_3}$-3% $A{l_2}{O_3}$, 그리고 S${i_3}{N_4}$-1% MgO-1% Si$O_2$(in wt%), were prepared and characterized by X-ray diffraction, scanning electron microscopy, image analysis and mechanical tests. The fracture toughness of S${i_3}{N_4}$-8% ${Y_2}{O_3}$specimens containing large elongated grains showed the highest value of about 9.8MPa$m^{1/2}$. Two out of four S${i_3}{N_4}$, ceramics(S${i_3}{N_4}$-6% ${Y_2}{O_3}$-2% $A{l_2}{O_3}$and S${i_3}{N_4}$-4% ${Y_2}{O_3}$-3% $A{l_2}{O_3}$) heat treated at 200 $0^{\circ}C$retained the fracture strength of over 900MPa and fracture toughness of over 8.0MPa$m^{1/2}$. Large ${\beta}$-S${i_3}{N_4}$grains having a diameter larger than 1${\mu}$m appeared to contribute to increase in fracture toughness.

• The Journal of the Korea Contents Association
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• v.6 no.5
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• pp.29-34
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• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.27 no.2
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• pp.105-116
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• 1997

The purpose of this study is to evaluate the cephalometric reproducibility in digitized cephalometric radiography by comparing the measurement errors between the remeasured and retaken conventional and digitized lateral cephalometric radiography. The mean of the differences and error percentage of each cephalometric measurement were obtained using 96 lateral cephalometric radiography from 48 patients between the age of 11 and 13. The results were as follows; 1. The repeated measurement group of conventional radiography showed least amount of mean differences while those of the retaken measurement group of digitized image showed largest amount of mean differences in every measurement. 2. The measurements which showed statistically significant difference between the conventional radiography and digitized image were S-Go, Ar-Go, S-Ar-Go and S-sN-sNT in repeated measurement group. 3. The measurements which showed statistically significant difference between the repeated and retaken measurement groups were N-S-Ar, MP-Ll and S-sN-sPog in conventional radiography and S-N, Go-Me and N-A in digitized Image. 4. Large amount of error percentage was shown at A-N-B and N-A in retaken measurement group of conventional radiography and N-S-Ba and A-N-B in retaken measurement group of digitized image. 5. The amount of error percentage at Ar-Go and N-S- Ar in retaken measurement group of conventional radiography and S-N, N-A, S-N-B and N-S-Ba in retaken measurement group of digitized image was more than double than those from remeasured groups.

• Journal of the Korea Fashion and Costume Design Association
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• v.9 no.1
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• pp.123-140
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• 2007

Fashion magazine advertising is the most excellent source of information in predicting the fashion trend. It plays a pivotal role in setting a direction for the fashion trend in the upcoming season. The purpose of this study was to review by photos of the $pr{\hat{e}}t-{\acute{a}}-porter$ collection shown in LONDON, NEW YORK, MILAN, and PARIS during 2002-2006 A/W and 2003-2005 S/S seasons, being focused on such fashion items published as coat, dress, one-piece, two-pieces(jacket+skirt/pants, blouse+skirt/pants). In the results of this study, designers presented coat(n=144) chiefly, blouse+pants(n=29) were presented few during 2002-2003 A/W seasons. During 2003-2004 A/W seasons one-piece(n=156) was looking bullish, blouse+pants(n=34) were declining. Dress(n=149) was presented mostly, blouse+pants(n=17) was presented few during 2004-2005 A/W seasons. During 2005-2006 A/W seasons coat(n=180) was revived, blouse+pants(n=26) were presented lowly. Therefore designers presented coat(n=605, 28.4%) extremely much during 2002-2006 A/W seasons. Designers presented one-piece(n=109) much, jacket+pants(n=22) were presented few in 2003 S/S. In 2004 S/S seasons one-piece(n=167) was presented vastly different than jacket+pants(n=42). Also one-piece(n=152) was presented mostly, blouse+pants(n=48) was presented few in 2005 S/S seasons. During 2003-2005 S/S seasons one-piece(n=428, 28.2%) was presented most. And designers in these four world fashion centers didn't prefer blouse+pants in A/W seasons and jacket+pants in S/S seasons. Based on the above findings, it could be confirmed that the fashion items trend was almost similar among the four collections of $pr{\hat{e}}t-{\acute{a}}-porter$. The results of this study suggest that the fashion collections are the most reliable information sources for fashion product planning. Lastly, it is hoped that this study will provide for some useful basic data for domestic fashion businesses in producing fashion items.

• Korean Journal of Optics and Photonics
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• v.27 no.6
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• pp.223-228
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• 2016

The birefringence of distributed, uniaxially anisotropic molecules like liquid crystals is calculated as the degree of ordering is varied. The relation between the normalized birefringence ${\Delta}n_{rel}$ and the orientational order parameter S is investigated. The distribution function, which enables one to monitor the degree of ordering of liquid crystals including randomly distributed ones, is introduced. Using this distribution function, a series of distributed liquid crystals with order parameters ranging from 0 to 1 are generated, and ${\Delta}n_{rel}$ and S of the correspondingly distributed liquid crystals are calculated. Based on the calculated data, it is revealed that ${\Delta}n_{rel}$ and S satisfy the quasi-linear relation of $S=(1+a){\Delta}n_{rel}-a{\Delta}n^2_{rel}$, where a can be approximated as $n_o{\frac{{\Delta}n}{4}}$. The anisotropy of molecular polarizability is also calculated, using the birefringence, and separately following Vuks' method and Neugebauer's method, and it is shown that the relations between S and the molecular-polarizability anisotropy are also quasi-linear.

• Toxicological Research
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• v.14 no.2
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• pp.177-181
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• 1998

Dithiocarbamate and mixed disulfide containing allyl functions were designed and synthesized as putative chemopreventive agents, i.e. N,N-diallyldithiocarbamate (DATC) and S-(N,N-diallyldithiocarbamoyl)-N-acetylcysteine (AC-DATC). DATC and AC-DATC were administered and the activities of cytosolic glutathione S-transferase (GST), glutathione reductase (GR) and microsomal N-nitrosodiethylamine (NDEA) deethylase were assayed in order to test the effects of these organosulfur com-pounds on the detoxification and metabolic activation system of NDEA. The amounts of hepatic glutathione (GSH and GSSG) was also determined. The administration of DATC to rats led to an increase in the activity of GR and to an inhibition of CYP2E1-mediated NDEA deethylation. AC-DATC induced the activity of GR and GST, increased the hepatic GSH content and inhibited the rate of NDEA deethylation. The level of GSSG was decreased as a consequence of the increased activity of GR. These effects may contribute to possible antimutagenic and anticarcinogenic action of the dithiocarbamates investigated.

• Korean Journal of Optics and Photonics
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• v.28 no.1
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• pp.33-38
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• 2017

The universality of the quasi-linear relation between the order parameter S and the normalized birefringence ${\Delta}n_{rel}$, $S=(1+a){\Delta}n_{rel}-a{\Delta}n^2_{rel}$ is confirmed. It is verified that the refractive index of liquid crystals distributed with regular polyhedral symmetry is isotropic and it is given as $\frac{1}{n^2_{av}}=\frac{1}{3}\(\frac{1}{n^2_e}+\frac{2}{n^2_o}\){\cdot}S$ and ${\Delta}n_{rel}$ of angular weighted liquid crystals that are initially distributed with regular polyhedral symmetry, are numerically calculated. Also ${\Delta}n_{rel}$ and S of liquid crystals that are conically distributed, keeping the rotational symmetry about z-axis are calculated as the apex angle of the cone is varied. Based on these calculated results, it is confirmed that the quasi-linear relation between S and ${\Delta}n_{rel}$ is universal, independent of the details of the distribution function.

• Bulletin of the Korean Chemical Society
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• v.22 no.4
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• pp.421-423
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• 2001

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.321-336
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• 1997

Let S be the Ricci curvature of an n-dimensional compact minimal totally real submanifold M of a quaternion projective space $HP^n (c)$ of quaternion sectional curvature c. We proved that if $S \leq \frac{16}{3(n -2)}c$, then either $S \equiv \frac{4}{n - 1}c$ (i.e. M is totally geodesic or $S \equiv \frac{16}{3(n - 2)}c$. All compact minimal totally real submanifolds of $HP^n (c)$ satisfy in $S \equiv \frac{16}{3(n - 2)}c$ are determined.