• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.63-86
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• 2013

This study aimed to explore how middle school students perceive constructed-response items and how they solve those items and the patterns of the processes. For this purpose, data were collected from middle school students through survey, written responses on those items that were developed for this particular purpose, and interviews. The survey data were analyzed by using Excel and the written responses and interview data qualitatively. The findings about the students' perceptions about the constructed-response items suggested that the middle school students perceive the items primarily as involving writing solutions logically(17%) and being capable of explaining while solving them(7%). The most difficulties they encounter when solving the items were understanding(26%), applying(12%), mathematical writing(25%), computing(23%), and reasoning(14%). The findings about the students' mathematical proficiencies showed that they made an error most in reasoning (35%), then in understanding(31%), in applying(9%), and least in computing(3%).

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.359-370
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• 1997

In this paper we get the Morava K-theory of the double loop spaces of quarternionic Stiefel manifolds for an odd prime p by computing the Atiyah - Hirzebruch spectral sequence. We also get the homology with Z/(p) coefficients and analyze p torsion in the homology with Z coefficients.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.397-413
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• 2009

In this paper, for functionals of a generalized Brownian motion process, we show that the generalized Fourier-Feynman transform of the convolution product is a product of multiple transforms and that the conditional generalized Fourier-Feynman transform of the conditional convolution product is a product of multiple conditional transforms. This allows us to compute the (conditional) transform of the (conditional) convolution product without computing the (conditional) convolution product.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.317-332
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• 2005

In this paper we consider the hp-version to solve non-constant coefficients elliptic equations on a bounded, convex polygonal domain ${\Omega}$ in $R^2$. A family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties can be used for calculating the integrals. When the numerical quadrature rules $I_m{\in}G_p$ are used for computing the integrals in the stiffness matrix of the variational form we will give its variational form and derive an error estimate of ${\parallel}u-{\widetilde{u}}^h_p{\parallel}_{1,{\Omega}$.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.735-750
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• 1995

We present a domain decomposition algorithm for solving large sparse linear systems of equations arising from queuing networks. Such techniques are attractive since the problems in subdomains can be solved independently by parallel processors. Many of the methods proposed so far use some form of the preconditioned conjugate gradient method to deal with one large interface problem between subdomains. However, in this paper, we propose a "nested" domain decomposition method where the subsystems governing the interfaces are small enough so that they are easily solvable by direct methods on machines with many parallel processors. Convergence of the algorithms is also shown.lso shown.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.283-287
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• 2002

In this paper, we will investigate the set of linear operators on real square matrices that strongly preserve multivariate majorisation without any additional conditions on the operator. This answers earlier conjecture on nonnegative matrices in [3] .

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.149-161
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• 2002

We study the torsions in the integral homology of the double loop space of the compact simple Lie groups by determining the higher Bockstein actions on the homology of those spaces through the Bockstein lemma and computing the Bockstein spectral sequence.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.497-505
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• 2017

The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.547-563
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• 2020

We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.575-584
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• 1996

We investigate how the code automorphism groups can be used to study such combinatorial objects as codes, finite projective planes and Hadamard matrices. For this purpose, we write down a computer program for computing code automorphisms in PASCAL language. Then we study the combinatorial properties using those code automorphism group algorithms and the relationship between combinatorial objects and codes.