• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.837-858
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• 2015

In this paper, we realize the algebra of ${\mathbb{Z}}_2$ relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of [2]. Using the results of Graham and Lehrer in [1], we give the modular representations of the algebra of ${\mathbb{Z}}_2$-relations, signed partition algebras and partition algebras.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.537-543
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• 2015

In [9], the authors determine an infinite class of non-unimodal Gorenstein sequence, which includes the example $$\bar{h}_1\text{ = (1, 125, 95, 77, 71, 77, 95, 125, 1)}$$. They raise a question whether there is a Gorenstein algebra with Hilbert function $$\bar{h}_2\text{= (1, 125, 95, 77, 70, 77, 95, 125, 1)}$$, which has remained an open question. In this paper, we prove that there is no Gorenstein algebra with Hilbert function $\bar{h}_2$.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.809-823
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• 2020

Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C₀[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C₀[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L²[0, T].

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.265-270
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• 1994

In 1966, Iseki [2] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. Lei and Xi [3] discussed a new class of BCI-algebra, which is called a p-semisimple BCI-algebra. For p-semisimple BCI-algebras, a subalgebra is an ideal. But a subalgebra of an arbitrary BCI/BCK-algebra is not necessarily an ideal. In this note, a BCI/BCK-algebra that every subalgebra is an ideal is called a normal BCI/BCK-algebra, and we give characterizations of normal BCI/BCK-algebras. Moreover we give a positive answer to the problem which is posed in [4].(omitted)

• School Mathematics
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• v.2 no.1
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• pp.29-51
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• 2000

In this study, we tried to suggest an example of the analysis on the use of mathematical manipulatives. Taking algebra tiles as an example of mathematical manipulatives, we analysed several effects resulted from the use of algebra tiles. The algebra tiles make it possible to do activities that are needed to introduce and explain the distributive law and factoring. The algebra tiles have a several advantages; First of all, This model is simple. Even though they cannot make algebra easy, this model can play an important role in the transition to a new algebra course. This model provides access to symbol manipulation for students who had previously been frozen out of the course because of their weak number sense. This model provides a geometric interpretation of symbol manipulation, thereby enriching students' understanding, This model supports cooperative learning, and help improve discourse in the algebra class by giving students objects to think with and talk about. On the other hand, The disadvantages of this model are as follows; the model reinforces the misconception that -x is negative, and x is positive; the area model of multiplication is not geometrically sound when minus is involved; only the simplest expressions involving minus can be represented; It is ineffective when be used the learning of already known concept. Mathematics teachers must have a correct understanding about these advantages and disadvantages of manipulatives. Therefore, they have to plan classroom work that be maximized the positive effect of manipulatives and minimized the negative effect of manipulatives.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.117-133
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• 2006

Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S of analytic Feynman integrable functions on classical Wiener space. Yoo and Skoug extended these results to abstract Wiener space for a generalized Fresnel class $F_{A1,A2}$ containing the Fresnel class F(B) which corresponds to the Banach algebra S on classical Wiener space. In this paper, we present a change of scale formula for Wiener integrals of various functions on $B^2$ which need not be bounded or continuous.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.451-459
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• 2023

We give a characterization of zero divisors of the ring C[a, b]. Using the Weierstrass approximation theorem, we completely characterize topological divisors of zero of the Banach algebra C[a, b]. We also characterize the zero divisors and topological divisors of zero in ℓ^∞. Further, we show that zero is the only zero divisor in the disk algebra 𝒜 (𝔻) and that the class of singular elements in 𝒜 (𝔻) properly contains the class of topological divisors of zero. Lastly, we construct a class of topological divisors of zero of 𝒜 (𝔻) which are not zero divisors.

• Journal of the Institute of Convergence Signal Processing
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• v.24 no.3
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• pp.147-152
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• 2023

This paper is a study of a linear algebra course taught in a high school on-demand course. Compared to the regular course, flipped learning was added to the course, and applications to signal processing related problems were covered in consideration of students' career aspirations. Overall, the class was a mixture of traditional lectures and flipped learning. Flipped learning was implemented twice. The flipped class consisted of pre-class, in-class and post-class. To verify the effectiveness of the course, a survey was conducted and most of the evaluation items were above 4. The topics of the flipped learning were Markov chains and least squares problem, which are very important in the field of signal processing.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1131-1148
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• 2009

Algebra is one of the important subjects that not only mathematics but many science major students should know at least at the elementary level. Unfortunately abstract algebra, specially, is seen as an extremely difficult course to learn. One reason of difficulties is because of its very abstract nature, and the other is due to the lecture method that simply telling students about mathematical contents. In this paper we study about the teaching and learning abstract algebra in universities in corporation of a programming language such as ISETL. ISETL is a language whose syntax closely imitates that of mathematics. In asking students to read and write code in ISETL before they learn in class, we observe that students can much understand and construct formal statements that express a precise idea. We discuss about the classroom activities that may help students to construct and internalize mathematical ideas, and also discuss about some barriers we might overcome.