• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• Microbiology and Biotechnology Letters
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• v.36 no.1
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• pp.28-33
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• 2008

The expression vector (pWHM3-TR1R2) for sprT gene encoding Streptomyces griseus trypsin (SGT) followed by two regulatory genes, sgtR1 and sgtR2, was introduced into Streptomyces lividans TK24 and Streptomyces griseus IFO 13350. Various media with different compositions were used to maximize the productivity of SGT in the recombinant trains. he SGT productivity was best when the transformant of S. lividans TK24 was cultivated in R2YE medium (0.74 unit/mL) at 5 days of cultivation. C5/L (0.66 unit/mL) medium also gave a good productivity, but Livid (0.08 unit/mL) and NDSK (0.06 unit/mL) yielded poor productivities. S. griseus IFO 13350/pWHM3-TR1R2 produced SGT by 1.518 unit/mL (C5/L), 1.284unit/mL (R2YE),0.932 unit/mL (NDSK), and 0.295 unit/mL (Livid) at 7 days of cultivation, which was much higher than those from S. lividans TK24/TR1R2. The SGT protein was purified from the culture broth of S. griseus IFO 13350/pWHM3-TR1R2 in C5/L to homogeneity via ammonium sulfate fractionation, and CM-sepharose and SP-sepharose column chromatographies. The specific activity of purified SGT was 69,252 unit/mg, and the final purification fold and recovery yield were 6.5 and 1.4%, respectively.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.311-318
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• 1996

For positive integral vectors $R = (r_1, \cdots, r_m)$ and $S = (s_1, \cdots, s_n)$, we consider the class $U(R,S)$ of all $m \times n$ matrices of 0's and 1's with the row sum vector R and the column sum vector S.

• East Asian mathematical journal
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• v.28 no.2
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• pp.159-172
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• 2012

In all Mathematics I Textbooks(Kim, S. H., 2010; Kim, H. K., 2010; Yang, S. K., 2010; Woo, M. H., 2010; Woo, J. H., 2010; You, H. C., 2010; Youn, J. H., 2010; Lee, K. S., 2010; Lee, D. W., 2010; Lee, M. K., 2010; Lee, J. Y., 2010; Jung, S. K., 2010; Choi, Y. J., 2010; Huang, S. K., 2010; Huang, S. W., 2010) in high schools in Korea these days, it is written and taught that for a positive real number $a$, $a^{\frac{m}{n}}$ is defined as $a^{\frac{m}{n}}={^n}\sqrt{a^m}$, where $m{\in}\mathbb{Z}$ and $n{\in}\mathbb{N}$ have common prime factors. For that situation, the author shows his opinion that the definition is not well-defined and $a^{\frac{m}{n}}$ must be defined as $a^{\frac{m}{n}}=({^n}\sqrt{a})^m$, whenever $^n\sqrt{a}$ is defined, based on the field axiom of the real number system including rational number system and natural number system. And he shows that the following laws of exponents for reals: $$\{a^{r+s}=a^r{\cdot}a^s\\(a^r)^s=a^{rs}\\(ab)^r=a^rb^r$$ for $a$, $b$>0 and $s{\in}\mathbb{R}$ hold by the completeness axiom of the real number system and the laws of exponents for natural numbers, integers, rational numbers and real numbers are logically equivalent.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.4
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• pp.941-951
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• 1994

The resilient behavior of subbase materials, locally used in Korea. were evaluated in this study by performing laboratory MR tests. The variations of the MR value according to LVDT's location in experiments and moisture conditions, respectively, were evaluated. And, in order to determine the relevant MR characteristics of the prototype materials, laboratory model tests containing smaller particles than those of the prototype were conducted. Based on above results, the relationship of the MR and the bulk stress (${\theta}$) was suggested. The case using internal LVDT. gave much larger $M_R$ value than that using external LVDT, since the external LVDT somewhat overestimates the resilient strain. The measured $M_R$ in damp conditions ($S_r$=40%) was larger than that in wet conditions ($S_r$=70%) by about 10%. The relationship between the $M_R$ and the void ratio was linear according to particle size effect. The relationship of the $M_R$ and the bulk stress (${\theta}$) on subbase materials in damp conditions to be used in Korea could be recommended as $M_R=3960{\cdot}{\theta}^{0.60}$ psi.

• Bulletin of the Korean Chemical Society
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• v.27 no.7
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• pp.1038-1042
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• 2006

A new type of DTPA-bis-amides (L1-L4) and their Gd(III)-complexes of the type $[Gd(L)(H_2O)]{\cdot}nH_2O$ (5: L1; 6: L2; 7: L3; 8: L4) have been prepared and characterized by analytical and spectroscopic techniques. The X-ray crystal structure of 8 has been determined for structural confirmation. The coordination geometry adopts a tricapped trigonal prism geometry with L4 acting as a chelate octadentate and a water molecule in the coordination sphere. Crystals are monoclinic, $P2_1$, a = 14.468(3), b = 19.235(4), c = 13.527(2) $\AA$ $\beta$ = $107.245(3)^{\circ}$, V = 3595.2(11) $\AA^3$, Z = 4, $D_{calc}$ = 1.570. Significant increases in relaxivities are observed with 6 and 7 as compared with that of $Omniscan^{(R)}$, a commercial MR agent: R1 = 12.46 $mM^{-1}\;s^{-1}$, R2 = 8.76 $mM^{-1}\;s^{-1}$ for 6; R1 = 12.77 nm-1 s-1, R2 = 7.60 mM-1 s-1 for 7; R1 = 4.9 $mM^{-1}\;s^{-1}$, R2 = 4.8 $mm^{-1}\;s^{-1}$ for $Omniscan^{(R)}$. In the case of 5, however, both R1 and R2 are found to be lower to show 2.09 $mM^{-1}\;s^{-1}$, and 1.82 $mM^{-1}\;s^{-1}$, respectively.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.37-42
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• 2011

Let M be an R-module and S a semigroup. Our goal is to discuss zero-divisors of the semigroup module M[S]. Particularly we show that if M is an R-module and S a commutative, cancellative and torsion-free monoid, then the R[S]-module M[S] has few zero-divisors of size n if and only if the R-module M has few zero-divisors of size n and Property (A).

• Proceedings of the Korean Magnestics Society Conference
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• 2008.12a
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• pp.4.2-4.2
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• 2008

• IE interfaces
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• v.21 no.3
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• pp.254-261
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• 2008

Connected-(r,s)-out of-(m,n) : F system is an important topic in redundancy design of the complex system reliability and it's maintenance policy. Previous studies applied Monte Carlo simulation and genetic, simulated annealing algorithms to tackle the difficulty of maintenance policy problem. These algorithms suggested most suitable maintenance cycle to optimize maintenance pattern of connected-(r,s)-out of-(m,n) : F system. However, genetic algorithm is required long execution time relatively and simulated annealing has improved computational time but rather poor solutions. In this paper, we propose the ant colony optimization approach for connected-(r,s)-out of-(m,n) : F system that determines maintenance cycle and minimum unit cost. Computational results prove that ant colony optimization algorithm is superior to genetic algorithm, simulated annealing and tabu search in both execution time and quality of solution.

• 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.