• Korean Journal of Mathematics
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• v.18 no.4
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• pp.335-342
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• 2010

Let D be an integral domain with quotient field K,$\mathcal{I}(D)$ be the set of nonzero ideals of D, and $w$ be the star-operation on D defined by $I_w=\{x{\in}K{\mid}xJ{\subseteq}I$ for some $J{\in}\mathcal{I}(D)$ such that J is finitely generated and $J^{-1}=D\}$. The D is called a Pr$\ddot{u}$fer $v$-multiplication domain if $(II^{-1})_w=D$ for all nonzero finitely generated ideals I of D. In this paper, we show that D is a Pr$\ddot{u}$fer $v$-multiplication domain if and only if $(A{\cap}(B+C))_w=((A{\cap}B)+(A{\cap}C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $(A(B{\cap}C))_w=(AB{\cap}AC)_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $((A+B)(A{\cap}B))_w=(AB)_w$ for all $A,B{\in}\mathcal{I}(D)$, if and only if $((A+B):C)_w=((A:C)+(B:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with C finitely generated, if and only if $((a:b)+(b:a))_w=D$ for all nonzero $a,b{\in}D$, if and only if $(A:(B{\cap}C))_w=((A:B)+(A:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with B, C finitely generated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.9-14
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• 2007

A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1379-1410
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• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.

• Microbiology and Biotechnology Letters
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• v.38 no.4
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• pp.455-460
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• 2010

A polymerase chain reaction (PCR)-restriction fragment length polymorphism (RFLP) analysis was applied to detect and identify ten Weissella spp. frequently found in kimchi. The previously reported genus-specific primers designed from 16S rDNA sequences of Weissella spp. were adopted but PCR was performed at the increased annealing temperature by $4^{\circ}C$. The sizes of amplified PCR products and restricted fragments produced by AluI, MseI, and BceAI endonucleases were well correspond with the expected sizes. W. kandleri, W. koreensis, W. confusa, W. minor, W. viridescens, W. cibaria, and W. soli were distinguished by AluI and MseI and W. hellenica and W. paramesenteroides were identified by BceAI. W. thailandensis was distinguished when restriction pattern of other species was compared but identified by the single use of MspI.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.10
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• pp.14-27
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• 2009

Polar Code was proposed by Turkish professor Erdal Arikan in 2006 as an idea that splitted input channel is increasing the cutoff rate. The channel polarization consisted of code sequences with symmetric high rate capacity in a given B-DMC(Binary-input Discrete Memoryless Channel) W. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. The channel polarization is said to a set of given N independent outputs of B-DMC W. In other word, N increases when N is a set of binary-input channels {$W^{(i)}_N\;:\;1{\leq}\;i\;{\leq}\;N$}, in I{WN(i)} as the fraction of indices is near to 1, which is approaching to I(W), and it is near to 0, then to 1-I(W), where I(W) presents high rates in reliable wireless communication channel as inputs of W with equal frequences. After all, {WN(i)} is shown to be a state of channel coding. On the based on this Polar codes, this paper analyzes Polar coding and decoding of Arikan and propose Radix4 Polar coding newly.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1341-1354
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• 2021

Let r ≥ 2, and let k_i ≥ 2 for 1 ≤ i ≤ r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k₁, k₂, k₃, …, k_r; r) such that for any n ≥ w, every r-colouring of [1, n] admits a k_i-term arithmetic progression with colour i for some i ∈ [1, r]. For k ≥ 3 and r ≥ 2, the mixed van der Waerden number w(k, 2, 2, …, 2; r) is denoted by w₂(k; r). B. Landman and A. Robertson [9] showed that for k < r < $\frac{3}{2}$(k - 1) and r ≥ 2k + 2, the inequality w₂(k; r) ≤ r(k - 1) holds. In this note, we establish some results on w₂(k; r) for 2 ≤ r ≤ k.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.239-248
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• 2021

In this paper we study modules with the W F I⁺-extending property. We prove that if M satisfies the W F I⁺-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the W F I⁺-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M₁ ⊕ M₂ for some semisimple submodule M₁ and Noetherian (respectively, Artinian) submodule M₂. Moreover, we show that if M is a W F I-extending module with pseudo duo, C₂ and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.735-744
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• 2024

In this note, we shed new light on Krull domains from the point view of Gorenstein homological algebra. By using the so-called w-operation, we show that an integral domain R is Krull if and only if for any nonzero proper w-ideal I, the Gorenstein global dimension of the w-factor ring (R/I)_w is zero. Further, we obtain that an integral domain R is Dedekind if and only if for any nonzero proper ideal I, the Gorenstein global dimension of the factor ring R/I is zero.

• Journal of Korean Medicine Rehabilitation
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• v.21 no.4
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• pp.23-40
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• 2011

Objectives: This study was designed to examine the effects of extracts of Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) on the lipid lowering, anti-oxidation and concentration of proinflammatory cytokines and was investigated on hyperlipidemic rats. Methods: Male rats weighing $182.39{\pm}4.71g$ were fed high fat diet for 8 weeks and 36 rats(above 400 g) were divided into 4 groups. Each of 9 rats was divided a control group and experimental groups. We fed a control group of rats a basal diet and administered normal saline(100 mg/kg, 1 time/1 day) for 4 weeks. And we fed each experimental group of rats basal diet and administered an extract of Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) extracts(100 mg/kg, 200mg/kg, 300 mg/kg, 300 mg/kg, 1 time/1 day) for 4 weeks. At the end of the experiment, the rats were sacrificed to determine their chemical composition. We measured lipid of plasma and liver, concentration of proinflmmatory cytokines, anti-oxidative activity and $TNF-{\alpha}$, Apo-B, Apo-E and leptin gene expression. Results: 1. Concentration of plasma free fatty(FFA) showed no significant difference in all the treatment groups. Concentration of plasma triglyceride(TG) showed a significant decrement in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. 2. Concentration of plasma total cholesterol showed a significant decrement in the 200 and 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. Concentration of plasma low density lipoprotein(LDL)-cholesterol showed a Significant decrement in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. Concentration of plasma high density lipoprotein(HDL)-cholesterol showed a significant increment in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) group. 3. Concentration of liver total cholesterol showed a tendence to decrease in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups. Concentration of liver TG showed a significant decrement in all Ojeoksangamibang groups than that of control group. 4. Concentration of plasma and liver thiobarbituric acid reactive substance(TBARS) showed a tendence to decrease in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups. 5. The values of glutathione peroxidase(GSH-Px), superoxide dismutase(SOD) and catalase(CAT) activity showed a significant increment in all Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. 6. The values of plasma aspartate aminotransferase(AST) and alanine aminotransferase(ALT) activity showed no significant different in all treatment group. 7. Concentration of plasma $interleukin(IL)-1{beta}$ showed no significant difference in all the treatment groups. Concentration of plasma IL-6 showed a significant decrement in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) group than that of control group. Concentration of plasma tumor necrosis $factor-{\alpha}(TNF-{\alpha})$ a siginifant decrement in the 200 and 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) group than that of control group. However the concentration of plasma IL-10 in the 300 mg/kg Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups showed a significant increment than that of control group. 9. In the analysis of reverse transcription-polymerase chain reaction(RT-PCR), gene expression of $TNF-{\alpha}$, Apo-B and Apo-E in the Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups showed a lower expression than that of control group. However the gene expression of leptin showed no difference in the treatment groups. 10. The ratio of $TNF-{\alpha}$, Apo-B, and Apo-E per ${\beta}-actin$ expression in the Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups showed a significant decrement than that of control group. However The ratio of leptin expression per ${\beta}-actin$ expression showed no significant difference among all the treatment groups. Conclusions: According to above results, in lowering lipid effect, anti-oxidation and control of pro-inflammatory cytokines production, Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) gives effect.

• Journal of the military operations research society of Korea
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• v.5 no.1
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• pp.123-135
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• 1979

Weapon System effectiveness indices are a key factor to the cost-effectiveness analysis in the process of allocating national resources in an optimal fashion. First part of this paper reviews the need of weapon -effectiveness indices, historical development of methodologies on military strength evaluation with various models of indices, and the interrelation-ship between weapon effectiveness indices and war-game. Second part of this paper analyzes the concepts and usage of the already developed methodologies, i .e., index of power, weapon lethality index (W.L.I.), index of fire power potential (I.F.P), fire power potential (F. P. P), and weapon effectiveness indices/weighted unit value (W. E. I/W. U. V.). Finally, weaknesses and limits of these methodologies are compared and evaluated. Result of this research shows that the W. L. I, I. F. P, and F. P. P seem to possess many non-scientific or ambiguous facets, but the W. E. I/W. U. V method produces more detailed, inclusive, and reasonable indices. The paper concludes with the emphasis on the importance of the provision of the theoretical bases to develop effectiveness indices which can be used to evaluate Korean weapon systems, and the early establishment of a specialized research group to manage and develop methodologies on the weapon effectiveness indices.