• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.427-450
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• 2012

Using representations is essential for students to organize their thinking, to solve problems and to communicate each other. Students express information or situations suggested by problems easily and organize and infer them systematically using representations. Also, teachers are able to comprehend students' levels of understanding and thinking process better through them, and influence their representations. This study was conducted to understand mathematical representations of students uprightly and to seek implications for proper teaching of representations, by analyzing representations of students in mathematical problem solving process and the transformation process of representation via interactions.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.481-493
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• 2007

This paper deals with, by employing the relation between Cauchy representation and the Fourier transform and properties of the former in $L_1$-space, the investigation of the Cauchy representation of integrable Boehmians as a natural extension of tempered distributions, we have investigated Cauchy representation of tempered Boehmians. An inversion formula is also proved.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.689-697
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• 2022

In this paper, we study dual integrable representations of locally compact commutative hypergroups and give a sufficient and necessary condition for a dual integrable representation to have an admissible vector.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.941-947
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• 2009

Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.993-1015
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• 2012

In this paper, we study the quantum sl($n$) representation category using the web space. Specially, we extend sl($n$) web space for $n{\geq}4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl($n$). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial ($n=0$) and Jones polynomial ($n=2$) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

• East Asian mathematical journal
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• v.19 no.2
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• pp.317-335
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• 2003

In this paper, we characterize SL(2, $\mathbb{C}$)-representations of an n-periodic link $\tilde{L}$ in terms of SL(2, $\mathbb{C}$)-representations of its quotient link L and express the SL(2, $\mathbb{C}$)-representation variety R($\tilde{L}$) of $\tilde{L}$ as the union of n affine algebraic subsets which have the same dimension. Also, we show that the dimension of R($\tilde{L}$) is bounded by the dimensions of affine algebraic subsets of the SL(2, $\mathbb{C}$)-representation variety R(L) of its quotient link L.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.33-42
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• 2000

We generalize LePage-type representation of infinitely divisible processes and survey type G processes. Finally, we get integral representation and some inequality of processes of type G.

• Kyungpook Mathematical Journal
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• v.3 no.2
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• pp.49-54
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• 1960

• Bulletin of the Korean Mathematical Society
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• v.10 no.2
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• pp.63-68
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• 1973