• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.401-408
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• 2014

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.705-714
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• 2023

Bennis and El Hajoui have defined a (commutative unital) ring R to be S-coherent if each finitely generated ideal of R is a S-finitely presented R-module. Any coherent ring is an S-coherent ring. Several examples of S-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the S-coherent property to trivial ring extensions and amalgamated duplications.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.323-340
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• 2021

The purpose of this case study is to explore the similarities revealed in the process of solving and generalizing word problems related to systems of linear equations in two variables according to covariational reasoning. As a result, student S, who reasoned with coordination of value level, had a static image of the quantities given in the situation. student D, who reasoned with smooth continuous covariation level, had a dynamic image of the quantities in the problem situation and constructed an invariant relationship between the quantities. The results of this study suggest that the activity that constructs the relationship between the quantities in solving word problems helps to strengthen the mathematical problem solving ability, and that teaching methods should be prepared to strengthen students' covariational reasoning in algebra learning.

• Journal of the Korea Society for Simulation
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• v.28 no.3
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• pp.65-74
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• 2019

For many years, it has been widely studied on fork-join production systems but there is not much literature focusing on the finite buffer(s) of either individuals or shared, and generally distributed processing times. Usually, it is difficult to handle finite buffer(s) through a standard queueing theoretical approach. In this study, by using the max-plus algebraic approach we studied buffer-shared fork-join production systems with general processing times. However, because it cannot provide proper computational ways for performance measures, we developed simulation models using @RISK software and the expressions derived from max-plus algebra. From the simulation experiments, we compared some properties on waiting time with respect to a buffer capacity under two blocking policies: BBS (Blocking Before Service) and BAS (Blocking After Service).

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.743-755
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• 2019

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.479-484
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S：sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp ：sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.405-417
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• 2012

We find the Hilbert function and the minimal free resolution of a star-configuration in $\mathbb{P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in $\mathbb{P}^2$ is generic or non-generic We also prove that if $\mathbb{X}$ and $\mathbb{Y}$ are linear star-configurations in $\mathbb{P}^2$ of types t and s, respectively, with $s{\geq}t{\geq}3$, then the Artinian k-algebra $R/(I_{\mathbb{X}}+I_{\mathbb{Y})$ has the weak Lefschetz property.

• Journal of the Korea Computer Graphics Society
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• v.6 no.1
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• pp.37-50
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• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.

• Journal of the Korean Society of Industry Convergence
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• v.6 no.3
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• pp.171-176
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• 2003

The poly(triazine bissulfide) synthesized from 6-dibutylamino-1,3,5-triazine-2,4-dithiol with bis(4-chloro-3-nitrophenyl) sulfone in the presence of the phase transfer catalyst, the maximum algebra viscosity (0.57 dL/g) is stable at reaction temperature of $60^{\circ}C$ overall. We could not acquire the good result about solubility, thermal property, and molecular weight to make cast film, we made base for the synthesis of functionalization polymer material.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.2
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• pp.73-80
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• 2005

In this paper, we consider characteristics of waiting times in s1n91e-server 3-node tandem queues with finite buffers, a Poisson arrival process and deterministic service times at all nodes. There are three buffers : one at the first node is infinite and the others are finite. We obtain the fact that sojourn time or departure process is independent of the capacities of the finite buffers and does not depend on the order of service times, which are the same results in the literature. Moreover, the explicit expressions of stationary waiting times in all areas of the systems can be derived as functions of the finite buffer capacities. We also disclose a relationship of waiting times in subareas of the systems between two blocking policies communication and manufacturing. Some numerical examples are also provided.