• Korean Journal of Mathematics
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• v.25 no.4
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• pp.483-494
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• 2017

In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power nonlinearity given in the following form: $$T_{\lambda}(f;x)={\int_a^b}{\sum^n_{m=1}}f^m(t)K_{{\lambda},m}(x,t)dt,\;{\lambda}{\in}{\Lambda},\;x{\in}(a,b)$$, where ${\Lambda}$ is an index set consisting of the non-negative real numbers, and $n{\geq}1$ is a finite natural number, at ${\mu}$-generalized Lebesgue points of integrable function $f{\in}L_1(a,b)$. Here, $f^m$ denotes m-th power of the function f and (a, b) stands for arbitrary bounded interval in ${\mathbb{R}}$ or ${\mathbb{R}}$ itself. We also handled the indicated problem under the assumption $f{\in}L_1({\mathbb{R}})$.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.9-13
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• 1983

M$_{n}$(F) denotes the set of all n*n matrices over F={0, 1}. For a, b.mem.F, define a+b=max{a, b} and ab=min{a, b}. Under these operations a+b and ab, M$_{n}$(F) forms a multiplicative semigroup (see [1], [4]) and we call it the semigroup of the n*n boolean matrices over F={0, 1}. Since the semigroup M$_{n}$(F) is the matrix representation of the semigroup B$_{n}$ of the binary relations on the set X with n elements, we may identify M$_{n}$(F) with B$_{n}$ for finding all D-classes.l D-classes.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.615-632
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• 2019

We study generic lightlike submanifolds M of an indefinite trans-Sasakian manifold ${\bar{M}}$ or an indefinite generalized Sasakian space form ${\bar{M}}(f_1,f_2,f_3)$ endowed with an $({\ell},m)$-type metric connection subject such that the structure vector field ${\zeta}$ of ${\bar{M}}$ is tangent to M.

• Journal of Korean Society of Water and Wastewater
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• v.35 no.3
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• pp.197-204
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• 2021

In MBR, extracellular polymeric substance (EPS) is known as an important factor of fouling; soluble EPS (sEPS) affects internal contamination of membrane, and bound EPS (bEPS) affects the formation of the cake layer. The production of EPS changes according to the composition of influent, which affects fouling characteristics. Therefore, in this study, the effects of the F/M ratio on the sEPS concentration, bEPS content, and fouling were evaluated. The effects of F/M ratio on the amount and composition of EPS were confirmed by setting conditions that were very low or higher than the general F/M ratio of MBR, and the fouling occurrence characteristics were evaluated by filtration resistance distribution. As a result, it was found that the sEPS increased significantly with the increase of the F/M ratio. When the substrate was depleted, bEPS content decreased because bEPS was hydrolyzed into BAP and seemed to be used as a substrate. In contrast, when the substrate is sufficient, UAP (utilization-associated products) was rapidly generated in proportion with the consumption of the substrate. UAP has a relatively higher Protein/Carbohydrate ratio (P/C ratio) than BAP, and this means, it has a higher adhesive force to the membrane surface. As a result, UAP seems like causing fouling rather than BAP (biomass-associated products). Therefore, R_f (Resistance of internal contamination) increased rapidly with the increase of UAP, and R_c (Resistance of cake layer) increased with the accumulation of bEPS in proportion, and as a result, the fouling interval was shortened. According to this study, a high F/M ratio leads to an increment in UAP generation and accumulation of bEPS, and by these UAP and bEPS, membrane fouling is promoted.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.641-644
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• 2005

Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L(${\alpha}^{{\frac{1}{n}}$) where ${\alpha}{\in}L{\ast}$. We show that if $N_{L/F}({\alpha})\;{\in}L^n{\cap}F$, and [N : L] = m, then $G(N/ F) {\simeq}D_m$ or generalized quaternion group whether $N_{L/F}({\alpha})\;{\in}\;F^n\;or\;{\notin}F^n$, respectively.

• Korean Journal of Digital Imaging in Medicine
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• v.9 no.1
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• pp.37-43
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• 2007

1. Purpose : This study is to present effective exposure conditions to acquire the best image of simple abdomen in Film Screen (F.S) system and Computed Radiography (C.R) system. 2. Method : In the F.S system, while an exposure condition was fixed as 70kVp, images of a patients simple abdomen were taken under the different mAs exposure conditions. Among these images, the best one was chosen by radiologists and radiological technologists. In the C.R system, the best image of the same patient was acquired with the same method from the F.S system. Both characteristic curves from F.S system and C.R system were analyzed. 3. Results : In the F.S system, the best exposure condition of simple abdomen was 70kVp and 20mAs. In the CR system, with the fixed condition at 70kVp, the image densities of human organs, such as liver, kidney, spleen, psoas muscle, lumbar spine body and iliac crest, were almost same despite different environments (3.2mAs, 8mAs, 12mAs, 16mAs and 20mAs). However, when the exposure conditions were over or under (below) 12mAs, the images between the abdominal wall and the directly exposed part became blurred because the gap of density was decreased. In the C.R system, while the volume of mAs was decreased, an artifact of quantum mottle was increased. 4. Conclusion : This study shows that the exposure condition in the C.R system can be reduced 40% than in the F.S system. This paper concluded that when the exposure conditions are set in CR environment, after the analysis of equipment character, such as image processing system(EDR : Exposure Data Recognition processing), PACS and so on, the high quality of image with maximum information can be acquired with a minimum exposure dose.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.323-334
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• 2008

We define injective and projective representations of quivers with two vertices with n arrows. In the representation of quivers we denote n edges between two vertices as ${\Rightarrow}$ and n maps as $f_1{\sim}f_n$, and $E{\oplus}E{\oplus}{\cdots}{\oplus}E$ (n times) as ${\oplus}_nE$. We show that if E is an injective left R-module, then $${\oplus}_nE{\Longrightarrow[50]^{p_1{\sim}p_n}}E$$ is an injective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $p_i(a_1,a_2,{\cdots},a_n)=a_i,\;i{\in}\{1,2,{\cdots},n\}$. Dually we show that if $M_1{\Longrightarrow[50]^{f_1{\sim}f_n}}M_2$ is an injective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are injective left R-modules. We also show that if P is a projective left R-module, then $$P\Longrightarrow[50]^{i_1{\sim}i_n}{\oplus}_nP$$ is a projective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $i_k$ is the kth injection. And if $M_1\Longrightarrow[50]^{f_1{\sim}f_n}M_2$ is an projective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are projective left R-modules.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.1-12
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• 2019

For a finite poset $P=(X,{\preceq})$ the fractional weak discrepancy of P, denoted $wd_F(P)$, is the minimum value t for which there is a function $f:X{\rightarrow}{\mathbb{R}}$ satisfying (1) $f(x)+1{\leq}f(y)$ whenever $x{\prec}y$ and (2) ${\mid}f(x)-f(y){\mid}{\leq}t$ whenever $x{\parallel}y$. In this paper, we determine the range of the fractional weak discrepancy of (M, 2)-free posets for $M{\geq}5$, which is a problem asked in [9]. More precisely, we showed that (1) the range of the fractional weak discrepancy of (M, 2)-free interval orders is $W=\{{\frac{r}{r+1}}:r{\in}{\mathbb{N}}{\cup}\{0\}\}{\cup}\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$ and (2) the range of the fractional weak discrepancy of (M, 2)-free non-interval orders is $\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$. The result is a generalization of a well-known result for semiorders and the main result for split semiorders of [9] since the family of semiorders is the family of (4, 2)-free posets.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.465-472
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• 2010

In this paper, we consider two extreme sets of zero-term rank sum of fuzzy matrix pairs: $$\cal{z}_1(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=min\{z(X),z(Y)\}\};$$ $$\cal{z}_2(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=0\}$$. We characterize the linear operators that preserve these two extreme sets of zero-term rank sum of fuzzy matrix pairs.

• Journal of the korean Society of Automotive Engineers
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• v.9 no.4
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• pp.61-68
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• 1987

The Bellows Joint which was used as a absorber or safety equipment to prevent the deformation or fracture of a structure, have been analyzed by the F.E.M using axi-symmetric conical frustum element. Using the F.E.M the general behavior of Bellows Joint corrugation can be investigated easily, and the stability of the analysis be guaranteed. In annular type corrugation, the F.E.M results were agreed with those of other theoretical analyses, but in the U type corrugation, the F.E.M results were more acceptable than those of others.