• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.163-170
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• 2021

We present a concise proof of the conjecture of Mazur-Rubin-Stein on the distribution of modular symbols.

• Education of Primary School Mathematics
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• v.16 no.1
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• pp.21-33
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• 2013

In this study, We analyzed the mathematical thinking of sixth grade students showed mathematics lessons through the application of Lakatos' methodology and search for the role of their teachers in this lessons. We supposed to find the solution to the way of teaching-learning regarding the Lakatos' methodology for the elementary school level. According to the stages of presenting a problem situation, suggesting an initial conjecture, examining the conjecture, and improving the conjecture, we had lessons 8 times that are applied to Lakato's methodology. We gathered and analyzed data from lessons and interviews recording videotapes, documents for this study. The participants showed a lot of mathematical thinking. They understood the problem situation with the skill of fundamental thinking and suggested the initial conjecture by the skill of developmental thinking and they found a counter-example to be able to rebut the initial conjecture by critical thinking. Correcting the conjecture not to have counter-example, they drew developmental thinking and made their thinking generalize.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.791-795
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• 2010

We study the consequences of Gross's conjecture for cyclic extensions of degree $l^2$ where l is prime, and deduce that the L-values at s = 0 satisfy certain congruence relations.

• East Asian mathematical journal
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• v.28 no.5
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• pp.605-615
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• 2012

In this paper, we show that any definite lattice over $\mathbb{F}_q[x]$ is universal if and only if it is quaternary and its discriminant is of degree 2, where $ch(\mathbb{F}_q){\neq}2$. The Four Conjecture follows as an immediate consequence.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.173-176
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• 2007

The non-existence is proved of four-dimensional mod 2 semisimple representations of Gal ($\=\mathbb{Q}/\mathbb{Q}$) which are unramified outside 2.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.869-873
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• 2005

In this note we give a positive answer to the conjecture by Fong and Istratescu.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.23-27
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• 2004

In this paper we explicitly compute the orders of ambiguous ideal class groups of layers of the basic ${\mathbb{Z}}_3-extension$ of certain cubic fields and give an example for Greenberg's conjecture.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1323-1333
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• 2020

In 2009, Borg [2] suggested a conjecture concerning the size of a t-intersecting k-uniform family of faces of an arbitrary simplicial complex. In this paper, we give a strengthening of Borg's conjecture for shifted simplicial complexes using algebraic shifting.

• Journal of Integrative Natural Science
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• v.10 no.4
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• pp.240-244
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• 2017

We study the behavior of some invariants under completion. We also give a counterexample, which is the same as a counterexample to Ding's Conjecture, to Koh-Lee's Conjecture.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.168-172
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• 1993

As the worst-case analysis for interval plants, a conjecture whether the supremum of the integral of square error(ISE) is attained at the extreme point such as vertices, Kharitonov vertices, CB segment, and edges is suggested. We present a sufficient condition for which the worst performance index occurs at one ofvertices of uncertain parameter space. Numerical examples are also given.