• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.847-868
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• 2016

Let M be an invariant subspace of $H^2$ over the bidisk. Associated with M, we have the fringe operator $F^M_z$ on $M{\ominus}{\omega}M$. It is studied the Fredholmness of $F^M_z$ for (generalized) zero based invariant subspaces M. Also ker $F^M_z$ and ker $(F^M_z)^*$ are described.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.515-527
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• 2009

Let R be a commutative ring with identity. Then we prove $M_n(R)=GL_n(R)$ ${\cup}${$A{\in}M_n(R)\;{\mid}\;detA{\neq}0$ and det $A{\neq}U(R)$}${\cup}Z(M-n(R))$ where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring $M_n(F)$ over a field F is the disjoint union of the general linear group $GL_n(F)$ of degree n over the field F and the set $Z(M_n(F))$ of all zero-divisors of $M_n(F)$. Using the result and universal mapping property we prove that $M_n(F)$ is its total ring of fractions.

• Journal of Korean Institute of Industrial Engineers
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• v.13 no.2
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• pp.117-128
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• 1987

A major problem in the adoption of advanced manufacturing systems such as F.M.S. (Flexible Manufacturing Systems) is the prerequisite economic justification process because of high investment needed for the acquisition and installation of F.M.S. While some of the benefits expected are readily quantifiable, others are very difficult or even impossible, using conventional method. Thus the investment in F.M.S. should be considered as a strategic decision rather than a tactical decision which concerns with only financial implications. In this paper we review papers on major justification techniques developed during thelast decade and identify the benefits of F.M.S. and describe the considerations in the justification of F.M.S. Also, we deal with the current and future research directions in justifying F.M.S.

• East Asian mathematical journal
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• v.37 no.5
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• pp.613-617
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• 2021

Abstract. For a positive square-free integer m, let K = ℚ($\sqrt{m}$) be a real quadratic field. The relative class number H_d(f) of K of discriminant d is the ratio of class numbers 𝒪_K and 𝒪_f, where 𝒪_K is the ring of integers of K and 𝒪_f is the order of conductor f given by ℤ + f𝒪_K. In 1856, Dirichlet showed that for certain m there exists an infinite number of f such that the relative class number H_d(f) is one. But it remained open as to whether there exists such an f for each m. In this paper, we give a result for existence of real quadratic field ℚ($\sqrt{m}$) with relative class number one where the period of continued fraction expansion of $\sqrt{m}$ is 6.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.845-852
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• 2010

A nonlinear algebraic equation f(x) = 0 is considered to find a root with integer multiplicity $m{\geq}1$. A variant of Newton-secant method for a multiple root is proposed below: for n = 0, 1, $2{\cdots}$ $$x_{n+1}=x_n-\frac{f(x_n)^2}{f^{\prime}(x_n)\{f(x_n)-{\lambda}f(x_n-\frac{f(x_n)}{f^{\prime}(x_n)})\}$$, $$\lambda=\{_{1,\;if\;m=1.}^{(\frac{m}{m-1})^{m-1},\;if\;m{\geq}2$$ It is shown that the method has third-order convergence and its asymptotic error constant is expressed in terms of m. Numerical examples successfully verified the proposed scheme with high-precision Mathematica programming.

• The KIPS Transactions:PartA
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• v.18A no.6
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• pp.225-232
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• 2011

Restricted Hypercube-Like (RHL) graphs are a graph class that widely includes useful interconnection networks such as crossed cube, Mobius cube, Mcube, twisted cube, locally twisted cube, multiply twisted cube, and generalized twisted cube. In this paper, we show that for an m-dimensional RHL graph G, $m{\geq}4$, with an arbitrary faulty edge set $F{\subset}E(G)$, ${\mid}F{\mid}{\leq}m-2$, graph $G{\setminus}F$ has a hamiltonian path between any distinct two nodes s and t if dist(s, V(F))${\neq}1$ or dist(t, V(F))${\neq}1$. Graph $G{\setminus}F$ is the graph G whose faulty edges are removed. Set V(F) is the end vertex set of the edges in F and dist(v, V(F)) is the minimum distance between vertex v and the vertices in V(F).

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.597-609
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• 2008

In this paper, we will consider certain amalgamated free product structure in crossed product algebras. Let M be a von Neumann algebra acting on a Hilbert space Hand G, a group and let ${\alpha}$ : G${\rightarrow}$ AutM be an action of G on M, where AutM is the group of all automorphisms on M. Then the crossed product $\mathbb{M}=M{\times}{\alpha}$ G of M and G with respect to ${\alpha}$ is a von Neumann algebra acting on $H{\bigotimes}{\iota}^2(G)$, generated by M and $(u_g)_g{\in}G$, where $u_g$ is the unitary representation of g on ${\iota}^2(G)$. We show that $M{\times}{\alpha}(G_1\;*\;G_2)=(M\;{\times}{\alpha}\;G_1)\;*_M\;(M\;{\times}{\alpha}\;G_2)$. We compute moments and cumulants of operators in $\mathbb{M}$. By doing that, we can verify that there is a close relation between Group Freeness and Amalgamated Freeness under the crossed product. As an application, we can show that if $F_N$ is the free group with N-generators, then the crossed product algebra $L_M(F_n){\equiv}M\;{\times}{\alpha}\;F_n$ satisfies that $$L_M(F_n)=L_M(F_{{\kappa}1})\;*_M\;L_M(F_{{\kappa}2})$$, whenerver $n={\kappa}_1+{\kappa}_2\;for\;n,\;{\kappa}_1,\;{\kappa}_2{\in}\mathbb{N}$.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• The Korean Journal of Nuclear Medicine
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• v.30 no.4
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• pp.484-492
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• 1996

To detect ischemic tissue in experimental model of cerebral ischemia made by middle cerebral artery(MCA)-occlusion, we acquired triple image of $^{99m}Tc$-glucarate, [$^{18}F$]fluoro-deoxyglucose (FDG), and 2,3,5- triphenyltetrazolium (TTC) staining. We made cerebral infarction either with reperfusion (after occlusion of 2 hours) or without reperfusion in 10 Sprague-Dawley rats by inserting thread to MCA through internal carotid artery. After 22 hours, we injected 740 MBq of $^{99m}Tc$-glucarate and 55.5 MBq of [$^{18}F$]FDG through tail vein. Each 1 mm slice of rat brains was frozen and exposed to imaging plate for 20 minutes in freezer to get an [$^{18}F$]FDG image. After 20 hours enough to fade radioactivity of [$^{18}F$]FDG, the slices were again imaged by BAS1500 for $^{99m}Tc$-glucarate uptake. Finally, these brain tissues were stained with TTC. Semi-quantitative visual analysis was done by grading 0 to 3 points according to the degree of uptakes($^{99m}Tc$-glucarate) and decreased uptakes([$^{18}F$]FDG and TTC). Ten rats survived with neurologic symptoms. TTC staining confirmed the development of infarction. The size of the infarction was relatively larger in the group without reperfusion. [$^{18}F$]FDG images were similar to TTC-stained images. However, we found regions with intermediate uptake which were not stained with TTC. We found regions with intermediate [$^{18}F$]FDG uptake where TTC staining was normal. $^{99m}Tc$-glucarate uptake was round only in TTC non-stained region. In the TTC stained regions, there were no uptake of $^{99m}Tc$-glucarate. We could not find clear relation between $^{99m}Tc$-glucarate uptake with [$^{18}F$]FDG uptake. This was partly because percent uptake of $^{99m}Tc$-glucarate was so small (less than 1 percent of injected dose) and because there were quite heterogeneity of patterns of [$^{18}F$]FDG uptake and TTC. With these findings, we could conclude that $^{99m}Tc$-glucarate were taken up only in part of ischemic tissues which were proven to be nonviable. The establishment of MCA-occluded rat model with or without reperfusion and triple imaging for $^{99m}Tc,\;^{18}F$ and TTC helped the characterization of $^{99m}Tc$-glucarate uptakes. Further work is needed to clarify the meaning or diversities or [$^{18}F$]FDG and TTC and their relation with $^{99m}Tc$-glucarate.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1711-1726
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• 2014

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.