• Korean Journal of Mathematics
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• v.6 no.1
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• pp.1-7
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• 1998

We introduce the notions of McShane-Stieltjes representable operators nearly McShane-Stieltjes representable operators and then investigate some properties of theses operators.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.407-423
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• 2022

In this paper, we determine the structure of rings that have secondary representation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce completely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be completely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.179-186
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• 1999

In this paper, we define the Henstock-Stieltjes representable and nearly Henstock-Stieltjes representable operators for vector-valued function, which are the generalizations of Pettis representable operator and then study some properties of these operators.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.433-436
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• 2006

In this note we show that a representable difference algebra is equivalent to a commutative BCK-algebra.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.775-780
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• 1998

In this paper it is shown that Dunford-Pettis operators obey the "Pettis-divisor property": if T is a Dunford-Pettis operator from $L_1$($\mu$) to a Banach space X, then there is a non-Pettis representable operator S : $L_1$($\mu$)longrightarrow$L_1$($\mu$) such that To S is Pettis representable.

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.53-59
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• 2001

In this paper, we define the $H_1$-Stieltjes representable, nearly $H_1$-Stieltjes represnetable for vector-valued function, which is the generalization of Bochner representable and than study some properties of these operators.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.71-84
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• 2007

In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2013-2020
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• 2013

We study some properties of representable generalized local homology modules. By duality, we get some properties of good generalized local cohomology modules.

• Journal of Korean Elementary Science Education
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• v.28 no.3
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• pp.263-276
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• 2009

The purpose of this study was to analyze the elementary students' selection of representable value and confident method that appear in measuring activities by using a microgenetic method. The participants were seven elementary students in the fourth grade. They performed the same measuring activities six times for the study period. Data were collected by interview and observation with their activity recording papers and video tape transcription. Their activities were recorded and documented for the analysis. Results were as follows. First, in the time measuring activity, elementary students developed desirably as their measuring experience increased, for example they selected a representable value in use of a repeated measurement and used a various method in the domain of a time measurement and they showed an increase of a quantitative observation in the volume domain except in the length domain. Second, in a confident method of a representable value, though they must rely upon a repeated measurement, they only measure repeatedly in the time domain. Also in the time domain, it doesn't get accomplished a exact confidence of a representable value at a shortage of skill about a measurement. Accordingly this study will be implications for teachers to teach a handling abilities of measuring instruments to elementary students and to be promote understanding a nature of measurement.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.917-928
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• 2022

Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let M be a finitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension r^I(M, N) and artinianness dimension a^I(M, N) of M, N with respect to I by r^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not representable} and a^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not artinian} and we show that a^I(M, N) = r^I(M, N) = inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)} ≥ inf{a^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)}. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N/∩_t>0I^tN is artinian we prove that inf{i : H^I_i(M, N) is not minimax}=inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)＼Max(R)}.